HK40001158B - Video encoding and decoding apparatus using a quantization matrix - Google Patents

Description

Video encoding and decoding device using quantization matrix

This patent application is a divisional application of the following invention patent applications:

Application number: 201380014811.0

Application date: January 21, 2013

Invention Title: Method for encoding and decoding quantization matrix and device using the same

Technical Field

The present invention relates to image encoding and decoding technology, and more particularly, to a method and apparatus for encoding and decoding a quantization index.

Background Art

Broadcast services with high definition (HD) resolution have recently been expanding worldwide and locally. As a result, many users have become accustomed to images with high resolution and high picture quality, and many organizations are encouraging the development of next-generation image devices.

As there is growing interest in ultra high definition (UHD) having a resolution four times higher than that of HDTV as well as HDTV, there is a demand for compression technology for images with higher resolution and higher picture quality.

Regarding image compression, information about pixels of a current picture can be encoded by prediction. For example, an inter-frame prediction technique in which pixel values included in the current picture are predicted based on temporally previous and/or temporally subsequent pictures, and an intra-frame prediction technique in which pixel values included in the current picture are predicted using information about pixels in the current picture can be used.

Furthermore, using an entropy coding technique in which short symbols are assigned to symbols with a high frequency of occurrence and long symbols are assigned to symbols with a low frequency of occurrence, encoding efficiency can be improved and the amount of transmitted information can be reduced.

In this case, a method of more efficiently performing quantization of transform coefficients of a residual block generated by prediction is problematic.

Summary of the Invention

An object of the present invention is to provide a method and apparatus for limiting quantization matrix encoding/decoding based on the size of an available transform block.

Another object of the present invention is to provide an encoding/decoding method and apparatus, in which a default quantization matrix and a non-default quantization matrix can be mixed and used according to the size of each transform block or the type of quantization matrix in a sequence, picture or slice.

Another object of the present invention is to provide an encoding/decoding method and apparatus in which a default quantization matrix is used based on a reference quantization matrix ID.

Another object of the present invention is to provide an encoding/decoding method and apparatus which increase encoding efficiency by performing prediction of a quantization matrix only when a reference quantization matrix exists.

Another object of the present invention is to provide a method and apparatus for efficiently performing prediction and encoding/decoding on DC matrix coefficients.

Another object of the present invention is to provide an encoding/decoding method and apparatus for performing prediction of a quantization matrix from a quantization matrix having the same size as a quantization matrix when encoding/decoding is performed.

Another object of the present invention is to provide a method and apparatus for performing prediction and encoding/decoding based on a first coefficient within a quantization matrix.

An embodiment of the present invention provides a video encoding device, which may include: a quantization module, configured to determine a quantization matrix to be used in quantization and perform quantization; and an entropy encoding module, configured to encode information about the quantization matrix according to a prediction scheme of the quantization matrix, wherein the prediction scheme of the quantization matrix is any one of a prediction scheme between coefficients in the quantization matrix and a quantization matrix copy scheme, wherein the quantization matrix has a size of 4×4, 8×8, 16×16 or 32×32.

Another embodiment of the present invention provides a video decoding device, which may include: an entropy decoding module configured to decode a quantization matrix according to a prediction scheme of the quantization matrix; and an inverse quantization module configured to perform inverse quantization using the quantization matrix, wherein the prediction scheme of the quantization matrix is any one of a prediction scheme between coefficients in the quantization matrix and a quantization matrix copy scheme, wherein the quantization matrix has a size of 4×4, 8×8, 16×16 or 32×32.

An embodiment of the present invention provides a method for encoding a quantization matrix, comprising: determining a quantization matrix to be used in quantization and quantizing it, determining a prediction method for the quantization matrix used in quantization, and encoding information about the quantization matrix according to the determined prediction method, wherein the prediction method can be any one of a method of predicting an inter-coefficient prediction method in a quantization matrix and a copy of the quantization matrix.

Another embodiment of the present invention provides a method for decoding a quantization matrix, comprising: determining a prediction method of a quantization matrix to be used in inverse quantization, and decoding the quantization matrix to be used in inverse quantization according to the determined prediction method, wherein the prediction method of the quantization matrix can be any one of an inter-coefficient prediction method within the quantization matrix and a copy of the quantization matrix.

According to the present invention, by limiting the encoding of the quantization matrix based on the size of an available transform block, encoding efficiency can be improved and computational complexity can be reduced.

According to the present invention, by mixing and using default quantization matrices and non-default quantization matrices according to the size or type of quantization matrix of each transform block within a sequence, picture, or segment, encoding efficiency can be improved and the freedom of the encoder in selecting a quantization matrix can be increased.

According to the present invention, by encoding/decoding information about whether a default quantization matrix will be used based on a reference quantization matrix ID, or performing prediction of the quantization matrix only when a reference quantization matrix exists, coding efficiency can be improved, calculation complexity can be reduced, and the encoder's freedom in selecting a quantization matrix can be increased.

According to the present invention, by predicting and encoding/decoding DC matrix coefficients or performing prediction of the quantization matrix from a quantization matrix having the same size as the quantization matrix when encoding/decoding is performed, the coding efficiency can be improved, the complexity of calculation can be reduced, and the freedom of the encoder in selecting the quantization matrix can be increased.

Furthermore, according to the present invention, by encoding/decoding the first coefficient within a quantization matrix using frequently occurring coefficient values, encoding efficiency can be improved and computational complexity can be reduced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a configuration according to an embodiment of an image encoding apparatus to which the present invention is applied.

FIG. 2 is a block diagram showing a configuration according to an embodiment of an image decoding apparatus to which the present invention is applied.

FIG. 3 is a conceptual diagram schematically illustrating an embodiment in which one unit is partitioned into a plurality of lower-level units.

FIG4 is a flowchart schematically illustrating an image encoding method according to the present invention.

FIG. 5 is a flowchart schematically illustrating an example of the operation of a decoder for decoding information about a quantization matrix and performing decoding by using the decoded information.

FIG6 is a flowchart schematically illustrating an example of a method of performing inverse quantization according to the present invention.

FIG. 7 is a diagram schematically illustrating an example of a method of obtaining information on a quantization matrix when the quantization matrix exists in a parameter set, and performing inverse quantization by using the information.

FIG8 is a diagram schematically illustrating another example of a method of obtaining information on a quantization matrix when the quantization matrix exists in a parameter set, and performing inverse quantization by using the information.

DETAILED DESCRIPTION

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, in describing the embodiments of the present invention, detailed descriptions of known functions and configurations will be omitted if they are deemed to make the gist of the present invention unnecessarily obscure.

In this specification, when an element is referred to as being “connected,” “combined,” or “coupled” to another element, the element may be directly connected or coupled to the other element, but it should also be understood that a third element may be “connected,” “combined,” or “coupled” between the two elements. In addition, in this specification, descriptions of “including (or comprising)” specific elements do not mean excluding elements other than the specific elements, but rather mean that additional elements may be included within the scope of implementation of the present invention or the technical spirit of the present invention.

Terms such as "first" and "second" may be used to describe various elements, but the elements are not limited to these terms. These terms are used to distinguish one element from another. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element without departing from the scope of the present invention.

In addition, the elements described in the embodiments of the present invention are shown separately to indicate different and characteristic functions, and this does not mean that each element constitutes a separate hardware or software module. That is, these elements are arranged for ease of description, and at least two of these elements can be combined to form one element, or one element can be divided into multiple elements, and the multiple elements can perform functions. Embodiments in which the elements are combined or each element is divided are included in the scope of the present invention without departing from the spirit of the present invention.

In addition, in the present invention, some elements may not be essential elements for performing essential functions, but may be optional elements for merely improving functions. The present invention may be implemented using only essential elements for achieving the essence of the present invention rather than elements for merely improving performance, and a structure including only these essential elements without including optional elements for merely improving functions is included in the scope of the present invention.

First, for the convenience of description and to help understanding of the present invention, terms used in this specification are briefly described.

A unit refers to a unit of image encoding and decoding. In other words, in image encoding/decoding, when a picture is subdivided and encoded or decoded, a coding unit or decoding unit represents a partitioned unit. This unit is also called a block, macroblock, coding unit, prediction unit, transform unit, coding block, prediction block, transform block, etc. A unit can be partitioned into smaller units.

A transform unit is a basic unit for performing encoding/decoding of a residual block (such as transform, inverse transform, quantization, inverse quantization, and transform coefficient encoding/decoding). One transform unit can be partitioned into multiple smaller transform units. In addition, a transform unit can be used to have the same meaning as a transform block. A form including syntax elements related to transform blocks for luminance and chrominance signals can be called a transform unit.

A quantization matrix is a matrix used in quantization or inverse quantization to improve the subjective or objective image quality of an image. A quantization matrix is also called a scaling matrix. Inverse quantization is the same as inverse quantization.

The quantization matrix used in quantization/inverse quantization can be transmitted in the form of a bitstream, and a default matrix already included in the encoder and/or decoder can be used as the quantization matrix. Depending on the size of each quantization matrix or the size of the transform block to which the quantization matrix is applied via a sequence parameter set (SPS) or a picture parameter set (PPS), information about the quantization matrix can be transmitted all at once (in a lump). For example, a 4x4 quantization matrix for a 4x4 transform block can be transmitted, an 8x8 matrix for an 8x8 transform block can be transmitted, a 16x16 matrix for a 16x16 transform block can be transmitted, and a 32x32 matrix for a 32x32 transform block can be transmitted.

The quantization matrix applied to the current block may be (1) obtained by copying a quantization matrix having the same size and (2) generated by predicting based on previous matrix coefficients in the quantization matrix. The matrix having the same size may be a quantization matrix that has been previously encoded, decoded, or used, a reference quantization matrix, or a default quantization matrix. Alternatively, the matrix having the same size may be selectively determined by a combination including at least two of a quantization matrix that has been previously encoded, decoded, or used, a reference quantization matrix, and a default quantization matrix.

The parameter set corresponds to information on a header of a structure in a bitstream, and has a meaning collectively indicating a sequence parameter set, a picture parameter set, an adaptation parameter set, and the like.

The quantization parameter is a value used in quantization and inverse quantization, and may be a value mapped to a quantization step size.

A default matrix may refer to a specific quantization matrix that has been previously defined in an encoder and/or decoder. A default quantization matrix to be described later in this specification may be used as the same as a default matrix. A non-default matrix may refer to a quantization matrix that has not been previously defined in an encoder and/or decoder and is transmitted from the encoder to the decoder (i.e., transmitted/received by a user). A non-default quantization matrix to be described later in this specification can be used as the same as a non-default matrix.

FIG. 1 is a block diagram showing a configuration according to an embodiment of an image encoding apparatus to which the present invention is applied.

1 , the image encoding apparatus 100 includes a motion prediction module 111, a motion compensation module 112, an intra-prediction module 120, a switch 115, a subtractor 125, a transform module 130, a quantization module 140, an entropy encoding module 150, an inverse quantization (dequantization) module 160, an inverse transform module 170, an adder 175, a filter module 180, and a reference image buffer 190.

The image encoding apparatus 100 may encode an input image in intra mode or inter mode and output a bitstream. Intra prediction refers to prediction within a frame, while inter prediction refers to prediction between frames. In the case of intra mode, the switch 115 may switch to intra mode, while in the case of inter mode, the switch 115 may switch to inter mode. After generating a prediction block for an input block of the input image, the image encoding apparatus 100 may encode the difference between the input block and the prediction block. Here, the input image may refer to the original image.

In case of the intra mode, the intra prediction module 120 may generate a predicted block by performing spatial prediction based on pixel values of encoded blocks adjacent to the current block.

In the case of inter-frame mode, the motion prediction module 111 can search for an area that best matches the input block in the reference image stored in the reference image buffer 190 during the motion prediction process and obtain a motion vector based on the retrieved area. The motion compensation module 112 can generate a predicted block by performing motion compensation using a motion vector. Here, a motion vector is a 2-dimensional vector used in inter-frame prediction and can indicate the offset between the current block and a block in the reference image.

The subtractor 125 may generate a residual block based on the difference between the input block and the generated prediction block. The transform module 130 may output transform coefficients by performing a transform on the residual block. Next, the quantization module 140 may output quantized coefficients by quantizing the received transform coefficients using at least one of a quantization parameter and a quantization matrix. Here, the quantization matrix may be input to the encoder, and the input quantization matrix may be determined to be used in the encoder.

The entropy coding module 150 can output a bit stream by performing entropy coding based on the value calculated by the quantization module 140 or the coding parameter value calculated in the coding process. If entropy coding is applied, the codewords can be represented by allocating a small number of bits to codewords with a high probability of occurrence and a large number of bits to codewords with a low probability of occurrence, so as to reduce the size of the bit stream used to encode the codewords to be encoded. Therefore, the compression performance of the image encoding can be increased by entropy coding. The entropy coding module 150 can use coding methods such as exponential Golomb coding, context-adaptive variable length coding (CAVLC), and context-adaptive binary arithmetic coding (CABAC) for entropy coding.

The image encoding device (hereinafter referred to as an encoder) according to the embodiment of FIG. 1 performs inter-frame prediction encoding (i.e., inter-frame prediction encoding), and thus the currently encoded image needs to be decoded and stored so as to be used as a reference image. Therefore, the quantized coefficients are dequantized by the dequantization module 160 and inversely transformed by the inverse transform module 170. The dequantized and inversely transformed coefficients become a reconstructed residual block, and the reconstructed residual block is added to the prediction block by the adder 175, thereby generating a reconstructed block.

The reconstructed block experiences a filter module 180. The filter module 180 may apply one or more of a deblocking filter, sample adaptive offset (SAO), and an adaptive loop filter (ALF) to the reconstructed block or picture. The filter module 180 may also be referred to as an in-loop filter. The deblocking filter may remove block distortion that occurs at block boundaries. The SAO may add an appropriate offset value to pixel values to compensate for coding errors. The ALF may perform filtering based on a value obtained by comparing the reconstructed image with the original image. The reconstructed block that has passed through the filter module 180 may be stored in the reference image buffer 190.

FIG. 2 is a block diagram showing a configuration according to an embodiment of an image decoding apparatus to which the present invention is applied.

2 , the image decoding apparatus 200 includes an entropy decoding module 210 , an inverse quantization (dequantization) module 220 , an inverse transform module 230 , an intra prediction module 240 , a motion compensation module 250 , an adder 255 , a filter module 260 , and a reference image buffer 270 .

The image decoding apparatus 200 may receive a bitstream output from an encoder, decode the bitstream in intra mode or inter mode, and output a reconstructed image. In the case of intra mode, the switch may be switched to intra mode. In the case of inter mode, the switch may be switched to inter mode. The image decoding apparatus 200 may obtain a reconstructed residual block from the received bitstream, generate a prediction block, and generate a reconstructed block by adding the reconstructed residual block to the prediction block.

The entropy decoding module 210 may generate symbols including symbols in the form of quantized coefficients by performing entropy decoding on the input bitstream according to a probability distribution. The entropy decoding method is similar to the above-mentioned entropy encoding method.

If the entropy decoding method is applied, symbols may be represented by allocating a small number of bits to symbols having a high probability of occurrence and a large number of bits to symbols having a low probability of occurrence, so as to reduce the size of a bit stream per symbol.

The quantized coefficients may be subjected to inverse quantization based on a quantization parameter by the inverse quantization module 220 and may be subjected to inverse transformation by the inverse transformation module 230. As a result of the inverse quantization/inverse transformation of the quantized coefficients, a reconstructed residual block may be generated.

The quantization matrix used in inverse quantization is also called a scaling list. The inverse quantization module 220 can generate inverse quantized coefficients by applying the quantization matrix to the quantized coefficients.

Here, the inverse quantization module 220 may perform inverse quantization in response to the quantization applied by the encoder. For example, the inverse quantization module 220 may perform inverse quantization by applying the quantization matrix applied by the encoder to the quantized coefficients.

The image decoding apparatus 200 (hereinafter referred to as a decoder) may receive the quantization matrix used for inverse quantization from the bitstream, and a default matrix already included in the encoder and/or decoder may be used as the quantization matrix. The transmitted information about the quantization matrix may be received all at once, depending on the size of each quantization matrix or the size of the transform block to which the quantization matrix is applied by a sequence parameter set or a picture parameter set. For example, a 4x4 quantization matrix for a 4x4 transform block may be received, an 8x8 matrix for an 8x8 transform block may be received, a 16x16 matrix for a 16x16 transform block may be received, and a 32x32 matrix for a 32x32 transform block may be received.

In the case of intra mode, the intra prediction module 240 can generate a prediction block by performing spatial prediction using pixel values of decoded blocks around the current block. In the case of inter mode, the motion compensation module 250 can generate a prediction block by performing motion compensation using a motion vector and a reference image stored in the reference image buffer 270.

The adder 255 adds the reconstructed residual block and the prediction block together, and the added block can pass through the filter module 260. The filter module 260 can apply one or more of a deblocking filter, SAO, and ALF to the reconstructed block or reconstructed picture. The filter module 260 can output a reconstructed image (i.e., a restored image). The reconstructed image can be stored in the reference image buffer 270 and used for inter-frame prediction.

Meanwhile, the block partition information may include information about the depth of the unit. The depth information may indicate the number of times the unit is partitioned and/or the extent to which the unit is partitioned.

FIG. 3 is a conceptual diagram schematically illustrating an embodiment in which one unit is partitioned into a plurality of lower-level units.

Depth information can be used to hierarchically partition a unit or block based on a tree structure. The lower-level units of each partition may have depth information. The depth information may include information about the size of the lower-level unit, as it indicates the number of times the unit is partitioned and/or the degree to which the unit is partitioned.

3 , the highest node may be referred to as a root node, and the highest node may have a minimum depth value. Here, the highest node may have a depth of level 0 and may indicate a first unit that has not yet been partitioned.

A lower-level node having a depth of level 1 can indicate a cell partitioned once from the first cell, and a lower-level node having a depth of level 2 can indicate a cell partitioned twice from the first cell. For example, in 320 of FIG. 3 , cell “a” corresponding to node “a” is a cell partitioned once from the first cell, and cell “a” can have a depth of level 1.

The leaf nodes at level 3 can indicate cells partitioned three times from the first cell. For example, in 320 of FIG3 , cell “d” corresponding to node “d” is a cell partitioned three times from the first cell, and cell “d” can have a depth of level 3. Therefore, the leaf nodes at level 3 (i.e., the lowest nodes) can have the deepest depth.

The above descriptions illustrate exemplary encoding/decoding methods. Like other encoding/decoding processes, the quantization matrix used in the quantization and inverse quantization processes of the encoding/decoding method significantly affects coding efficiency. Therefore, improvements in quantization/inverse quantization must be made with coding efficiency in mind.

More specifically, conventionally, quantization matrices for all transforms are encoded/decoded without regard to the minimum and maximum sizes of available transform units. Furthermore, conventionally, quantization matrices are applied all at once, without mixing and using default matrices and non-default matrices depending on the size of the transform or the type of quantization matrix in a sequence, picture, or slice. Consequently, there are disadvantages in that the encoder has limited freedom in selecting quantization matrices, and coding efficiency is low because default matrices that do not need to be encoded/decoded must be encoded and transmitted.

As described above, according to the conventional method, when a quantization matrix is applied, the degree of freedom and encoding efficiency are low, and the degree of complexity is high.

In order to solve these problems, it is necessary to consider a method of effectively using a quantization matrix in order to improve encoding efficiency and reduce complexity in quantization/inverse quantization.

FIG4 is a flowchart schematically illustrating an image encoding method according to the present invention.

4 , in step S410 , the encoder determines information about the size of a transform unit of a current sequence or picture and encodes the information.

The information about the size of the transformation unit means at least one of a minimum size and a maximum size of the transformation unit. When encoding an image, the encoder can determine the minimum size and the maximum size of the transformation unit.

For example, the encoder can determine the minimum size of the square transformation unit as a 4x4 block or the maximum size of the square transformation unit as a 32x32 block. In addition, the encoder can determine the minimum size and maximum size of the square transformation unit as a 4x4 block and a 32x32 block, respectively. The encoder can perform encoding according to the minimum size and maximum size of the square transformation unit.

The encoder can perform entropy coding on the information about the size of the transform unit determined for the bitstream.For example, the encoder can encode the information about the size of the transform unit determined as a parameter set in the bitstream.

As described above, the information about the size of the transformation unit represents information about at least one of the minimum size and the maximum size of the transformation unit. Therefore, the encoder can encode the information about the minimum size and the maximum size of the transformation unit into the bitstream as the information about the size of the transformation unit. Here, the maximum size of the transformation unit can be specified using the difference between the maximum size of the transformation unit and the minimum size of the transformation unit.

Table 1 schematically shows an example of information on the size of a transform unit that has been entropy-coded as a sequence parameter set of a bitstream.

<Table 1>

As in the syntax elements illustrated in Table 1, after calculating Log2MinTrafoSize by applying the Log2 function to the minimum horizontal or vertical size of a square transform unit, the encoder can specify a value obtained by subtracting 2 from Log2MinTrafoSize using log2_min_transform_block_size_minus2. Furthermore, after calculating Log2MaxTrafoSize by applying the Log2 function to the maximum horizontal or vertical size of a square transform unit, the encoder can specify the difference between Log2MaxTrafoSize and Log2MinTrafoSize using log2_diff_max_min_transform_block_size. The encoder can encode log2_min_transform_block_size_minus2 and log2_diff_max_min_transform_block_size (i.e., syntax elements) into a bitstream and transmit the resulting bitstream to the decoder. In other words, the encoder can encode the values indicated by log2_min_transform_block_size_minus2 and log2_diff_max_min_transform_block_size and transmit the encoded values in the form of a bitstream.

The encoder can encode information about the quantization matrix in step S420. The encoder can encode information about the quantization matrix, including one or more of the following: (1) information about whether the quantization matrix has been used, (2) information about whether the quantization matrix exists, (3) information about whether the quantization matrix has been encoded and whether a default matrix has been used, (4) a predictive encoding method and a type of quantization matrix, (5) a reference quantization matrix ID (identifier), and (6) a difference between coefficient values of a previously encoded quantization matrix and coefficient values of a quantization matrix to be encoded in the quantization matrix.

Here, the encoder may encode information about the quantization matrix based on information about the size of the transform unit.

Hereinafter, a method for encoding information about a quantization matrix is described in detail with reference to the drawings and the following tables.

The information about the quantization matrix indicates the method determined or used by the encoder. For example, the encoder can determine whether to use a quantization matrix and can encode the information about whether the quantization matrix has been used as a parameter set. Therefore, the encoded information about whether the quantization matrix has been used indicates whether the quantization matrix determined by the encoder has been used.

Table 2 shows an example in which information on whether a quantization matrix has been used is encoded as a sequence parameter.

<Table 2>

As in the syntax of Table 2, the encoder can encode scaling_list_enabled_flag (i.e., information on whether a quantization matrix is used) as a sequence parameter set and transmit the encoded information to the decoder. When the value of scaling_list_enabled_flag is 1, it can indicate that the quantization matrix is used in the inverse quantization/scaling of transform coefficients for all sequences. When the value of scaling_list_enabled_flag is 0, it can indicate that the quantization matrix is not used in the inverse quantization/scaling of transform coefficients. Here, syntax can mean a syntax element.

After determining whether a quantization matrix exists, the encoder can encode information on whether the quantization matrix exists as a parameter set.

Table 3 shows an example in which information on whether a quantization matrix exists is encoded as a parameter set.

<Table 3>

As in the syntax of Table 3, the encoder can encode aps_scaling_list_data_present_flag (i.e., information on whether a quantization matrix exists) as a parameter set. In Table 3, an example in which information on whether a quantization matrix exists is encoded as an adaptive parameter set is illustrated, but the present invention is not limited thereto. For example, the encoder may encode information on whether a quantization matrix exists as another parameter set.

In Table 3, when the value of aps_scaling_list_data_present_flag is 1, it indicates that the quantization matrix exists in the adaptive parameter set. When the value of aps_scaling_list_data_present_flag is 0, it indicates that the quantization matrix does not exist in the adaptive parameter set. If the value of scaling_list_enabled_flag is 1 and the value of aps_scaling_list_data_present_flag is 0, this may mean that a default matrix is used when performing inverse quantization. In addition, information about whether a quantization matrix exists can exist in different parameter sets. For example, if sps_scaling_list_data_present_flag indicating whether a quantization matrix exists in a sequence and pps_scaling_list_data_present_flag indicating whether a quantization matrix exists in a picture are used, when the value of sps_scaling_list_data_present_flag is 1 and the value of pps_scaling_list_data_present_flag is 0, the quantization matrix corresponding to the sequence can be used when performing quantization/inverse quantization. That is, if a quantization matrix is transmitted through several parameter sets and the quantization matrix does not exist in some parameter sets, when performing quantization/inverse quantization, the quantization matrix that exists or does not exist in the active parameter set can be used. From the embodiments to be described later, the above can also be applied to content in which information on the presence or absence of a quantization matrix is encoded/decoded.

After determining whether to encode the quantization matrix and whether to use the default matrix, the encoder can encode information on whether the quantization matrix has been encoded and whether the default matrix has been used as a parameter set.

Table 4 shows an example in which information on whether a quantization matrix has been encoded and whether a default matrix has been used is encoded as a parameter set.

<Table 4>

As in the syntax of Table 4, the encoder can encode use_default_scaling_list_flag (i.e., information about whether the quantization matrix has been encoded and whether the default matrix has been used) as an adaptation parameter set. When the value of use_default_scaling_list_flag is 1, the quantization matrix is not encoded and thus the coefficient values of all quantization matrices are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of use_default_scaling_list_flag is 0, the quantization matrix is encoded and the default matrix defined in the encoder and/or decoder is not used.

Table 4 illustrates an example in which use_default_scaling_list_flag is encoded as an adaptive parameter set. This is merely an example for ease of description. In some embodiments, use_default_scaling_list_flag may be encoded as another parameter set.

The information about the quantization matrix can be determined by considering the size of the transform unit or the size of the transform block, the encoding mode, and the color component. In addition, the information about the quantization matrix can indicate whether the corresponding information is a luminance component (Y, luma) or a chrominance component (Cb, Cr, chroma).

For example, the encoder can determine at least one of encoding of the quantization matrix, whether to use a default matrix, and a predictive encoding method by using SizeID (i.e., information corresponding to the size of the quantization matrix) and MatrixID (i.e., information corresponding to the type of the quantization matrix). Here, SizeID can be interpreted as information about the quantization matrix corresponding to the size of the transform unit or information about the quantization matrix corresponding to the size of the transform block. In addition, SizeID used in this specification is the same as sizeID and sizeId, and MatrixID is the same as matrixID and matrixId.

Here, the encoder may use a table stored therein and/or a table stored in the decoder.

Table 5 shows an example of a table used to indicate the size of a transform block or the size of a quantization matrix corresponding to the transform block.

<Form 5>

In the example of Table 5, the SizeID value specifies the size of a transform unit, the size of a transform block, or the size of a quantization matrix.

Table 6 shows an example of a table of encoding modes of blocks in which quantization matrices are used, and types of quantization matrices mapped to color components.

<Table 6>

In the example of Table 6, the MatrixID value may indicate the encoding mode used in the quantization matrix and the type of the quantization matrix of the specified color component. Here, the encoding mode may mean the prediction mode.

Tables 7 and 8 are examples of default quantization matrix tables used to specify a default quantization matrix based on SizeID and MatrixID determined in Tables 5 and 6. Here, each value in the table means a value specified by ScalingList[SizeID][MatrixID][i].

<Form 7>

i 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ScalingList[0][0..2][i] 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ScalingList[0][3..5][i] 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16

<Table 8>

Table 7 relates to the default quantization matrix where the SizeID value is 0 (i.e., 4x4 blocks), while Table 8 relates to the default quantization matrix where the SizeID value is 1 (i.e., 8x8 blocks), 2 (i.e., 16x16 blocks), and 3 (i.e., 32x32 blocks). In Tables 7 and 8, the SizeID and MatrixID values are the values specified in Tables 5 and 6.

In Tables 7 and 8, "i" specifies the position of each coefficient in the quantization matrix. In the case of a quantization matrix, for example, in the case of a quantization matrix for a 16x16 block or a 32x32 block, quantization matrix values for all 16x16 blocks and 32x32 blocks are not specified, but quantization matrix coefficients for only 8x8 blocks can be specified, and unspecified quantization matrix coefficients can be derived based on the 8x8 blocks and used. Table 8 shows an example in which a default quantization matrix is specified for each 8x8 block. The quantization matrix coefficients for the 16x16 block or the 32x32 block can be interpolated and derived from the quantization matrix stored for each 8x8 block, or can be derived in a specific manner. If a quantization matrix of 16x16 size or 32x32 size is derived from an 8x8 size quantization matrix by interpolation, the interpolated values are not used, and instead, additional values can be used as quantization matrix coefficients at the DC position.

Meanwhile, if the quantization matrix is not used by considering the minimum and maximum sizes of the available transform units, the quantization matrices of the transform units of all sizes must be encoded. In this case, encoding efficiency may deteriorate and the complexity of calculation may increase.

To address these issues, the encoder may encode information about the quantization matrix by considering the size of the transform unit. For example, the encoder may limit SizeID based on the minimum size and the maximum size among multiple pieces of information about the size of the transform unit.

The encoder can perform one or more of encoding of a quantization matrix, encoding of information on whether a default matrix has been used, and encoding of information on the type of a prediction encoding method by using the restricted SizeID.

Table 9 shows an example of a syntax structure used when encoding of a quantization matrix is performed by limiting SizeID.

<Form 9>

As in the example of Table 9, the encoder can limit SizeID based on the minimum size and the maximum size among multiple information about the sizes of the transform unit, and perform one or more of encoding of the quantization matrix, encoding of information about whether a default matrix has been used, and encoding of information about the type of prediction encoding method according to the specific transform unit size.

For example, when the value of Log2MinTrafoSize is 3 and the value of Log2MaxTrafoSize is 4, the encoder can perform one or more of encoding of a quantization matrix corresponding to an 8x8 transform unit to a 16x16 transform unit, encoding of information about whether a default matrix has been used, and encoding of information about the type of predictive encoding method.

Meanwhile, in the example of Table 9, use_default_scaling_list_flag may not be encoded.

In addition, the encoder can limit SizeID based on the difference between the maximum size and the minimum size among multiple information about the size of the transform unit, and perform one or more of encoding of the quantization matrix, encoding of information about whether a default matrix has been used, and encoding of information about the type of prediction encoding method.

Table 10 schematically shows an example of a syntax structure used to encode pieces of information about a quantization matrix by limiting SizeID based on the difference between the maximum size and the minimum size among pieces of information about the size of a transform unit.

<Form 10>

In the syntax example of Table 10, SizeID is limited based on the difference between the maximum size and the minimum size among multiple pieces of information about the sizes of the transform unit. The encoder can limit SizeID based on the difference between the maximum size and the minimum size among multiple pieces of information about the sizes of the transform unit, and can encode one or more of information about the quantization matrix, information about whether a default matrix has been used, and information about the type of prediction encoding method only within the range of the size of a specific transform unit based on the limited SizeID.

In the example of Table 10, when the value of Log2MinTrafoSize is 3 and the value of Log2MaxTrafoSize is 4, one or more of encoding of a quantization matrix corresponding to an 8x8 transform unit to a 16x16 transform unit, encoding of information about whether a default matrix has been used, and encoding of information about the type of predictive encoding method can be performed.

Here, the difference between Log2MaxTrafoSize and Log2MinTrafoSize is the difference between the maximum size and the minimum size of the transform unit, and can be the same as log2_diff_max_min_transform_block_size. In addition, Log2MinTrafoSize-2 can be the same as log2_min_transform_block_size_minus2.

In the example of Table 10, use_default_scaling_list_flag may not be encoded.

Meanwhile, if default matrices and non-default matrices are not mixed and used according to the size or type of quantization matrix for each transform block (or unit) in a sequence, picture, or slice, the encoder's freedom in selecting quantization matrices is reduced. For example, in order to use a default matrix for a transform block of a specific size in a slice and a non-default matrix for another transform block of a specific size in the slice, the default matrix must be encoded and transmitted to the decoder. As a result, coding efficiency deteriorates.

In order to mix and use default matrices and non-default matrices according to each transform size or type of quantization matrix in a sequence, picture, or slice, the encoder can encode information about whether the quantization matrix has been encoded and information about whether the default matrix has been used as a parameter set based on SizeID.

Table 11 shows an example of a syntax structure that can be used when encoding information about a quantization matrix based on SizeID.

<Form 11>

As in the example of Table 11, the encoder can encode sid_use_default_scaling_list_flag[SizeID][MatrixID] (ie, information on whether the quantization matrix has been encoded and whether the default matrix has been used) as an adaptation parameter set based on SizeID. MatrixID indicates the type of a specific quantization matrix in Table 6.

When the value of sid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the quantization matrix corresponding to SizeID is not encoded, and the coefficient values of the quantization matrix corresponding to SizeID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of sid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to SizeID is encoded, and the default matrix defined in the encoder and/or decoder may not be used in the quantization matrix corresponding to SizeID.

In the example of Table 11, use_default_scaling_list_flag may not be encoded.

Furthermore, the encoder can encode information on whether a quantization matrix has been encoded and on whether a default matrix has been used as a parameter set based on SizeID.

Table 12 schematically shows an example of a syntax structure that can be used when encoding information about a quantization matrix using MatrixID.

<Form 12>

As in the example of Table 12, the encoder can encode mid_use_default_scaling_list_flag[SizeID][MatrixID] (ie, information on whether the quantization matrix has been encoded and whether the default matrix has been used) as an adaptive parameter set based on the MatrixID.

When the value of mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the quantization matrix corresponding to MatrixID is not encoded, and the coefficient values of the quantization matrix corresponding to MatrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to MatrixID is encoded, and the default matrix defined in the encoder and/or decoder is not used as the quantization matrix corresponding to MatrixID.

In the example of Table 12, use_default_scaling_list_flag may not be encoded.

Furthermore, the encoder can encode information on whether a quantization matrix has been encoded and whether a default matrix has been used as a parameter set based on SizeID and MatrixID.

Table 13 schematically shows an example of a syntax structure that can be used when SizeID and MatrixID are used to encode information about a quantization matrix.

<Form 13>

As in the example of Table 13, the encoder can encode sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] (ie, information on whether the quantization matrix has been encoded and whether the default matrix has been used) as an adaptation parameter set based on SizeID and MatrixID.

When the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the quantization matrix corresponding to SizeID and MatrixID is not encoded, and the coefficient values of the quantization matrix corresponding to SizeID and MatrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder.

When the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to SizeID and MatrixID is encoded, and the default matrix defined in the encoder and/or decoder is not used as the quantization matrix corresponding to SizeID and MatrixID.

In the example of Table 13, use_default_scaling_list_flag may not be encoded.

Meanwhile, unlike the example of Table 13, the encoder can encode information on whether the quantization matrix has been encoded and whether the default matrix has been used as a parameter set based on SizeID and MatrixID. The encoder can limit SizeID based on the minimum size and the maximum size among multiple pieces of information on the size of the transform unit, and perform one or more of encoding the quantization matrix, encoding the information on whether the default matrix has been used, and encoding the information on the type of the prediction encoding method based on the limited SizeID.

Table 14 schematically shows an example of another syntax structure that can be used when encoding information about a quantization matrix by using SizeID and MatrixID.

<Form 14>

In the example of Table 14, use_default_scaling_list_flag may not be encoded.

In addition, the encoder can limit SizeID based on the difference between the maximum size and the minimum value among multiple information about the size of the transform unit, and perform one or more of encoding of the quantization matrix, encoding of information about whether a default matrix has been used, and encoding of information about the type of prediction encoding method.

Table 15 schematically shows an example of another syntax structure that can be used when encoding information about a quantization matrix by using SizeID and MatrixID.

<Form 15>

In the example of Table 15, the difference between Log2MaxTrafoSize (specifying the maximum size of a transform unit) and Log2MinTrafoSize (specifying the minimum size of a transform unit) is the difference between the maximum and minimum sizes of a transform unit and is the same as log2_diff_max_min_transform_block_size. Log2MinTrafoSize-2 is the same as log2_min_transform_block_size_minus2.

In the example of Table 15, the encoder can encode information on whether the quantization matrix has been encoded and whether the default matrix has been used as parameters based on SizeID and MatrixID limited by Log2MaxTrafoSize-Log2MinTrafoSize+1.

In the example of Table 15, use_default_scaling_list_flag may not be encoded.

Meanwhile, information on whether information on the quantization matrix exists in a parameter set to be encoded or whether information on the quantization matrix is to be updated may be encoded as a parameter set and used in encoding/decoding.

Table 16 schematically shows an example of a syntax structure that can be used when encoding information on whether a quantization matrix exists.

<Form 16>

In the example of Table 16, the encoder can specify whether information on the quantization matrix exists in the parameters to be encoded by using the syntax element scaling_list_update_flag[SizeID][MatrixID].

For example, when the value of scaling_list_update_flag[SizeID][MatrixID] is 1, it can indicate that there is information about the quantization matrix corresponding to SizeID and MatrixID. When the value of scaling_list_update_flag[SizeID][MatrixID] is 1, it can indicate that the information about the quantization matrix corresponding to SizeID and MatrixID and previously encoded is updated with the information about the quantization matrix corresponding to SizeID and MatrixID in the parameter set to be encoded. This update can mean replacing the information about the quantization matrix that has been previously encoded with the information about the quantization matrix in the parameter set to be encoded.

When the value of scaling_list_update_flag[SizeID][MatrixID] is 0, it may indicate that there is no information about the quantization matrix corresponding to SizeID and MatrixID. When the value of scaling_list_update_flag[SizeID][MatrixID] is 0, it may indicate that information about the encoding matrix is not updated.

When the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the decoder does not know which quantization matrix it has to use to perform inverse quantization on the quantized transform coefficient corresponding to SizeID and MatrixID, because there is no information about the quantization matrix corresponding to SizeID and MatrixID in the parameter set, and the information about the quantization matrix has not been encoded. Therefore, when the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to SizeID and MatrixID may mean using a default matrix or not using a quantization matrix, because there is no information about the quantization matrix corresponding to SizeID and MatrixID.

In the example of Table 16, when the value of scaling_list_update_flag[SizeID][MatrixID] is 1, because scaling_list_update_flag[SizeID][MatrixID] is encoded based on SizeID and MatrixID, the encoder can encode one or more of information about the quantization matrix, information about whether a default matrix has been used, and information about the type of prediction encoding method.

When the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the encoder does not encode one or more of information about the quantization matrix, information about whether a default matrix is used, and information about the type of prediction encoding method. That is, the encoder may not encode unnecessary quantization matrices by using scaling_list_update_flag[SizeID][MatrixID].

Since it is not possible to mix and use default matrices and non-default matrices for each transform size or each quantization matrix type in a sequence, picture, or slice simply by using scaling_list_update_flag[SizeID][MatrixID], there is a disadvantage in that the degree of freedom when the encoder selects a quantization matrix is low.

Therefore, the encoder can encode sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] (ie, information on whether the quantization matrix has been encoded and whether the default matrix has been used) as a parameter set based on SizeID and MatrixID.

For example, in the example of Table 16, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the quantization matrix corresponding to SizeID and MatrixID is not encoded, and the coefficient value of the quantization matrix corresponding to SizeID and MatrixID can be determined to be the same as the default matrix coefficient value defined in the encoder and/or decoder. When the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to SizeID and MatrixID is encoded, and the default matrix defined in the encoder and/or decoder is not used as the quantization matrix corresponding to SizeID and MatrixID.

In the example of Table 16, use_default_scaling_list_flag may not be encoded.

In addition, the encoder can encode information about whether the quantization matrix has been encoded and whether the default matrix has been used in the parameter set based on SizeID and MatrixID. In addition, the encoder can use scaling_list_update_flag[SizeID][MatrixID] (i.e., such information indicating whether the information about the quantization matrix will be updated as the information about the quantization matrix corresponding to SizeID and MatrixID in the parameters to be encoded).

Table 17 schematically shows an example of a syntax structure that can be used when encoding information on a quantization matrix using SizeID and MatrixID as described above.

<Form 17>

In the example of Table 17, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0 and the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to SizeID and MatrixID is encoded. The previously encoded quantization matrix corresponding to SizeID and MatrixID is not updated to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be encoded, and the previously encoded quantization matrix corresponding to the encoded SizeID and MatrixID is used without change.

In addition, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0 and the value of scaling_list_update_flag[SizeID][MatrixID] is 1, the quantization matrix corresponding to SizeID and MatrixID is encoded, and the previously encoded quantization matrix corresponding to SizeID and MatrixID is updated to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be encoded.

In addition, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1 and the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the quantization matrix corresponding to SizeID and MatrixID is not encoded, and the coefficient value of the quantization matrix is determined to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder. The previously encoded quantization matrix corresponding to SizeID and MatrixID is not updated to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be encoded, and the encoder and decoder use the previously encoded quantization matrix corresponding to SizeID and MatrixID.

In addition, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1 and the value of scaling_list_update_flag[SizeID][MatrixID] is also 1, the quantization matrix corresponding to SizeID and MatrixID is not encoded, and the coefficient values of the quantization matrix are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. The previously encoded quantization matrix corresponding to SizeID and MatrixID is updated to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be encoded.

In the example of Table 17, use_default_scaling_list_flag may not be encoded.

Furthermore, after determining the type of a method of predicting and encoding a quantization matrix, the encoder can encode information on the method of predicting and encoding the quantization matrix into a parameter set.

Tables 18 and 19 schematically show examples of syntax that can be used when encoding the method of predicting and encoding the quantization matrix in a parameter set.

<Form 18>

<Form 19>

The encoder can encode pred_mode_flag (ie, information on a method of predicting and encoding a quantization matrix) to the adaptation parameter set as in the example of Table 18. scaling_list_pred_mode_flag described later in this specification can be interpreted as having the same meaning as pred_mode_flag.

For example, in the example of Table 18, when the value of pred_mode_flag is 1, the encoder can encode the quantization matrix according to the differential pulse code modulation (DPCM) method and the exponential Golomb coding method. When the value of pred_mode_flag is 0, the encoder can determine the coefficient values of the quantization matrix to be encoded so that they have the same values as the coefficient values of the previously encoded quantization matrix. Here, the coefficient values of the quantization matrix and the coefficient values of the previously encoded quantization matrix may be values within different quantization matrices.

If the value of pred_mode_flag is 0, the encoder can encode information on the reference quantization matrix ID of the quantization matrix to be encoded into the parameter set.

Therefore, as in the example of Table 18, the encoder can encode pred_matrix_id_delta (ie, the reference quantization matrix ID of the quantization matrix to be encoded) into the adaptation parameter set.

Scaling_list_pred_matrix_id_delta to be described in this specification can be interpreted as having the same meaning as pred_matrix_id_delta. Here, the encoder and the decoder can determine the value of RefMatrixID indicating the reference quantization matrix of the quantization matrix to be encoded by using pred_matrix_id_delta and Equation 1.

<Equation 1>

RefMatrixID=MatrixID-(1+pred_matrix_id_delta)

If the method for predicting and encoding a quantization matrix is a method for encoding a quantization matrix based on DPCM and the Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of a previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded as a parameter set. Here, the coefficient values of the previously encoded quantization matrix may be the coefficient values within the quantization matrix to be encoded. In other words, the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded may be values within the same quantization matrix.

Therefore, the encoder can encode delta_coef (i.e., the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) as an adaptive parameter set, as in the example of Table 19. delta_coef described later in this specification can be interpreted as having the same meaning as scaling_list_delta_coef.

The encoder can mix and use the default quantization matrix and the non-default quantization matrix in a sequence, a picture, or a slice by using the following method, and can prevent unnecessary quantization matrices from being transmitted.

If the method for predicting and encoding the quantization matrix is a method of determining a default matrix so that the default matrix is the same as the quantization matrix already included in the encoder and previously encoded (pred_mode_flag=0), the encoder can encode information about whether the default matrix has been used as a parameter set by using the reference quantization matrix ID of the quantization matrix to be encoded.

Therefore, as in the example of Table 18, the encoder can encode pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set. Here, the encoder and decoder can determine the RefMatrixID indicating the reference quantization matrix or the default matrix of the quantization matrix to be encoded by using pred_matrix_id_delta and Equation 2, and determine whether to use the default matrix.

<Equation 2>

RefMatrixID=MatrixID-pred_matrix_id_delta

In Equation 2, if the value of RefMatrixID is the same as the value of MatrixID, the coefficient value of the quantization matrix corresponding to SizeID and RefMatrixID is determined to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder. Here, the default matrix means the default matrix specified by SizeID and RefMatrixID.

In addition, when the value of pred_matrix_id_delta is 0, the value of RefMatrixID becomes the same as the value of MatrixID. If the value of RefMatrixID is different from the value of MatrixID, the encoder can determine the quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be encoded. In this case, the encoder can determine the coefficient values of the quantization matrix to be encoded so that they have the same values as the coefficient values of the reference quantization matrix.

If the size of the quantization matrix corresponding to SizeID is included in the minimum size and maximum size of the transform unit available to the decoder, the reference quantization matrix of the quantization matrix to be encoded and whether to use the default matrix can be determined by using the above method. If the size of the quantization matrix corresponding to SizeID is not included in the minimum size and maximum size of the transform unit available to the decoder, the method for encoding the quantization matrix corresponding to SizeID may not be determined to be the same as the default matrix. When one or more of information about the quantization matrix, information about whether the quantization matrix has been used, and information about the type of predictive encoding method are encoded based on SizeID and the difference between the maximum size of the transform unit and the minimum size of the transform unit, the determination process can be performed.

After determining whether to use the quantization matrix, the encoder can encode information on whether the quantization matrix has been used as a parameter set.

Table 20 schematically shows an example in which information on whether a quantization matrix has been used is encoded as a parameter set.

<Form 20>

As in the example of Table 20, the encoder can encode scaling_list_enable_flag (ie, information on whether the quantization matrix has been used) as a parameter set.

In the example of Table 20, when the value of scaling_list_enable_flag is 1, a quantization matrix such as a default matrix or a non-default matrix can be used in quantization/dequantization. When the value of scaling_list_enable_flag is 0, no quantization matrix is used in quantization/dequantization, or the same quantization matrix can be used for all coefficient values. Here, all coefficient values can be 16.

Furthermore, if the method for predicting and encoding a quantization matrix is a method for encoding a quantization matrix based on DPCM and the Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of a previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded as a parameter set. Here, the coefficient values of the previously encoded quantization matrix may be the coefficient values within the quantization matrix to be encoded. In other words, the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded may be values within the same quantization matrix.

Table 21 schematically shows an example of a syntax structure that can be used when encoding information on a quantization matrix by using a difference between coefficient values of a previously encoded quantization matrix and coefficient values of a quantization matrix to be encoded.

<Form 21>

In the example of Table 21, delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) is encoded as a parameter set.

In the example of Table 21, the coefficient values of the quantization matrix can be calculated using Equation 3.

<Equation 3>

Nextcoef=(nextcoef+delta_coef+256)%256

If nextcoef (i.e., the coefficient value of the quantization matrix calculated using Equation 3) is the same as (1) the specific value and (2) the first value of the quantization matrix, the coefficient value of the quantization matrix can be determined to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder.

That is, if the value of nextcoef is identical to (1) a specific value and (2) the first value of the quantization matrix, the corresponding quantization matrix can be used as a default matrix.

Here, the specific value may be 0. In addition, the default matrix may be a default matrix corresponding to SizeID and MatrixID. Therefore, if nextcoef (i.e., the coefficient value of the quantization matrix) is the same as 0 and the coefficient value of the quantization matrix corresponds to the first value of the quantization matrix, encoding of the difference between the corresponding quantization matrix and the quantization matrix can be stopped.

If the method for predicting and encoding a quantization matrix is a method for encoding a quantization matrix using DPCM and the Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of a previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded as a parameter set. Here, the coefficient values of the previously encoded quantization matrix may be the coefficient values within the quantization matrix to be encoded. In other words, the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded may be values within the same quantization matrix.

Table 22 schematically shows an example of a syntax structure when the difference between the coefficient values of a previously encoded quantization matrix and the coefficient values of a quantization matrix to be encoded is used.

<Form 22>

In the example of Table 22, delta_coef (i.e., the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) is encoded as a parameter set. In the example of Table 22, if nextcoef (i.e., the coefficient value of the quantization matrix calculated using Equation 3) is the same as a specific value and is the first value of the quantization matrix, the coefficient value of the quantization matrix can be determined to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder.

That is, if the value of nextcoef is the same as (1) the specific value and (2) the first value of the quantization matrix, the quantization matrix can be used as a default matrix. Here, the specific value may be 0, and the coefficient value of the quantization matrix calculated using Equation 3 may be a coefficient value of a quantization matrix having a quantization matrix size of 4x4 and 8x8 or a transform size.

Also, the first value of the quantization matrix may be a value using scaling_list_dc_coef_minus8, and the specific value may be a value corresponding to scaling_list_dc_coef_minus8+8.

Here, scaling_list_dc_coef_minus8 may refer to the first value of a quantization matrix having a size of 16x16 or a quantization matrix having a size of 32x32. That is, scaling_list_dc_coef_minus8 may refer to the coefficient value of the quantization matrix used for the DC matrix coefficient and may refer to the DC matrix coefficient. In this specification, the DC matrix coefficient exists in the quantization matrix used when performing inverse quantization, and the DC matrix coefficient may refer to the quantization matrix coefficient used for the DC transform coefficient within the transform block.

For example, when sizeID is 2, scaling_list_dc_coef_minus8[sizeID-2][matrixID] may mean the coefficient value of the quantization matrix of the DC matrix coefficient in the quantization matrix having a size of 16×16 or a transform size. When sizeID is 3, scaling_list_dc_coef_minus8[sizeID-2][matrixID] may mean the coefficient value of the quantization matrix of the DC matrix coefficient in the quantization matrix having a size of 32×32 or a transform size.

In addition, the aforementioned default matrix may mean a default matrix corresponding to SizeID and MatrixID. As described above, if the coefficient value nextcoef of the quantization matrix is the same as 0 and is the first value of the quantization matrix, encoding of the difference between the corresponding quantization matrix and the quantization matrix can be stopped.

If this method is used, it does not matter whether code scaling_list_dc_coef_minus8 (ie, coefficient values of the quantization matrix for DC matrix coefficients) is encoded, and encoding of information on whether a default matrix has been used can be performed differently according to the size of the quantization matrix or the transform size.

Meanwhile, an encoding/decoding method for determining whether to use a quantization matrix of a default matrix by using coefficient values of the quantization matrix has a disadvantage in that complexity in encoding/decoding processing of the coefficient values of the quantization matrix increases.

The following method provides a method for determining whether to use a default matrix using a reference quantization matrix ID in image encoding/decoding. Therefore, if the following method is used, the computational complexity can be reduced when encoding/decoding a quantization matrix.

Tables 23 and 24 schematically show examples of syntax structures that can be used when a reference quantization matrix ID is used.

<Form 23>

<Form 24>

First, the encoder can encode information about whether a quantization matrix exists as a parameter set.

As in the example of Table 23, the encoder can encode scaling_list_present_flag (i.e., information about whether a quantization matrix exists in the bitstream) as a parameter set. For example, if the quantization matrix does not exist and the quantization matrix is determined to be the default quantization matrix, the encoder can encode the value of scaling_list_present_flag as 0. If the quantization matrix exists, the encoder can encode the value of scaling_list_present_flag as 1.

The encoder can determine the type of predictive coding method used for the quantization matrix and encode information about the determined method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set.

As in the example of Table 23, the encoder can encode scaling_list_pred_mode_flag (i.e., information specifying a method for predicting and encoding a quantization matrix) as a parameter set. For example, if the coefficient values of the quantization matrix are encoded according to the DPCM and Exponential Golomb coding methods by scanning the quantization matrix to predict and encode the quantization matrix, the encoder encodes the value of scaling_list_pred_mode_flag to 1. In addition, if the reference quantization matrix and the quantization matrix to be encoded are determined to have the same value, or the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix, the encoder can encode the value of scaling_list_pred_mode_flag to 0.

Here, determining the matrix or coefficient values so that they have the same value may mean using a quantization matrix prediction method that copies coefficient values of a specific quantization matrix to coefficient values of a quantization matrix to be encoded.

If the value of scaling_list_pred_mode_flag is 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded and information on whether a default matrix has been used as a parameter set. Here, the parameter set may be an adaptive parameter set.

As in the example of Table 23, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_matrix_id_delta (ie, the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set.

Here, the encoder can determine the value of scaling_list_pred_matrix_id_delta (ie, quantization matrix ID) by using matrixID indicating a quantization matrix to be encoded, RefMatrixID indicating a reference quantization matrix or a default matrix, and Equation 4.

<Equation 4>

scaling_list_pred_matrix_id_delta=matrixID–RefMatrixID

If the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder, the encoder makes the value of RefMatrixID the same as the value of matrixID by encoding the value of scaling_list_pred_matrix_id_delta to 0. Here, the default matrix can mean the default matrix corresponding to sizeID and matrixID.

If the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the reference quantization matrix (that is, determined to be the same as the coefficient values of the previously encoded quantization matrix), the encoder can encode the value of scaling_list_pred_matrix_id_delta to a non-zero value so that the value of RefMatrixID is different from the value of matrixID. Here, the value of scaling_list_pred_matrix_id_delta can be a positive integer.

If the method for predicting and encoding the quantization matrix is a method for encoding the quantization matrix according to the DPCM and the Exponential Golomb coding method so as to predict and encode the coefficients in the quantization matrix, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix as a parameter set. Here, the parameter set encoded by the difference may be an adaptive parameter set.

As in the example of Table 24, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the encoder can encode scaling_list_dc_coef_minus8 (ie, DC matrix coefficients) as a parameter set.

As in the example of Table 24, the encoder can encode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix) as a parameter set. In Tables 23 and 24, an example in which information about the quantization matrix is encoded as an adaptive parameter set has been illustrated, but the present invention is not limited thereto. For example, the encoder can encode information about the quantization matrix as another parameter set (i.e., a parameter set including at least one of a sequence parameter set and a picture parameter set).

As described above, the conventional quantization matrix encoding/decoding method has a disadvantage in that encoding efficiency is deteriorated because unnecessary information is encoded/decoded when predicting the quantization matrix.

However, in the present invention, when the quantization matrix is encoded/decoded by performing encoding/decoding of the quantization matrix differently depending on whether a reference quantization matrix exists, encoding efficiency can be improved.

Tables 25 and 26 schematically show examples of syntax structures that can be used when encoding/decoding of a quantization matrix is performed differently depending on whether a reference quantization matrix exists.

<Form 25>

<Form 26>

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the example of Table 25, the encoder can encode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag as 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag as 1.

After determining the type of method for predicting and encoding the quantization matrix, if the value of matrixID is greater than 0, the encoder can encode information about the method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded may be an adaptive parameter set.

As in the example of Table 25, the encoder can encode scaling_list_pred_mode_flag (i.e., information specifying a method for predicting and encoding a quantization matrix) as a parameter set only when the value of matrixID is greater than 0. If the quantization matrix is encoded according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix to predict and encode the coefficients within the quantization matrix, the encoder encodes the value of scaling_list_pred_mode_flag to 1. In addition, if the reference quantization matrix is determined to have the same value as the quantization matrix to be encoded, the encoder can encode the value of scaling_list_pred_mode_flag to 0. Here, determining the matrices so that they have the same value may mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the value of matrixID is 0, the value of scaling_list_pred_mode_flag becomes true as in the example of Table 23. Therefore, the encoder does not encode the value of scaling_list_pred_mode_flag and can encode the quantization matrix according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix.

If the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is greater than 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded as a parameter set. Here, the parameter set encoded with the reference quantization matrix ID may be an adaptive parameter set.

As in the example of Table 25, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set only when the value of matrixID is greater than 0. Here, the encoder and decoder can determine the value of scaling_list_pred_matrix_id_delta (i.e., the quantization matrix ID) by using matrixID indicating the quantization matrix to be encoded, RefMatrixID indicating the reference quantization matrix, and Equation 5.

<Equation 5>

scaling_list_pred_matrix_id_delta=matrixID-(RefMatrixID+1)

When the value of matrixID is 0, the first quantization matrix is indicated for each sizeID. Since the quantization matrix can only be predicted from the quantization matrix with the same sizeID that has been previously encoded, there is no reference quantization matrix with the same sizeID for the first quantization matrix of each sizeID. Therefore, prediction of the quantization matrix, such as the matrix copy method, cannot be performed. As a result, only when the value of matrixID is greater than 0, the encoder can encode scaling_list_pred_matrix_id_delta as the reference quantization matrix ID, determine RefMatrixID based on the encoded reference quantization matrix ID, and determine the coefficient values of the quantization matrix to be encoded so that they have the same values as the coefficient values of the reference quantization matrix.

Determining the coefficient values of the quantization matrix to be encoded so that they have the same values as the coefficient values of the reference quantization matrix may mean a quantization matrix prediction method that determines the reference quantization matrix (corresponding to RefMatrixID) as the reference quantization matrix of the quantization matrix to be encoded, and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the method for predicting and encoding a quantization matrix is a method for predicting and encoding coefficients within the quantization matrix by scanning the quantization matrix according to the DPCM and Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded within the quantization matrix as a parameter set. Here, the parameter set into which the difference is encoded may be an adaptive parameter set.

As in the example of Table 26, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the encoder can encode scaling_list_dc_coef_minus8 (ie, DC matrix coefficients) as a parameter set.

As in the example of Table 26, the encoder can encode scaling_list_delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) as a parameter set.

In addition, the encoder can encode information about whether the default matrix has been used by using scaling_list_delta_coef used to calculate scaling_list_dc_coef_minus8 or nextCoef. That is, the encoder can encode the value of scaling_list_dc_coef_minus8 so that it becomes -8 to instruct the decoder to use the default matrix, and can encode scaling_list_delta_coef so that the first nextCoef value becomes 0 to instruct the decoder to use the default matrix.

Meanwhile, the method of encoding/decoding a quantization matrix in which whether to use a default matrix is determined by using the coefficient values of the quantization matrix has a disadvantage in that it increases the complexity of the processing of encoding/decoding the coefficient values of the quantization matrix. In addition, there is a disadvantage in that coding efficiency is deteriorated because unnecessary information is encoded/decoded when predicting the quantization matrix.

However, the present invention can reduce the complexity of calculation when encoding/decoding a quantization matrix because it determines whether to use a default matrix by using the ID of a reference quantization matrix in image encoding/decoding. In addition, the present invention can improve the encoding efficiency when encoding/decoding a quantization matrix by encoding/decoding the quantization matrix differently depending on whether a reference quantization matrix exists.

Tables 27 and 28 schematically show examples of syntax structures that can be used when the ID of the reference quantization matrix is used.

<Form 27>

<Form 28>

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the example of Table 27, the encoder can encode scaling_list_present_flag (i.e., information specifying whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag as 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag as 1.

After determining the type of predictive coding method for the quantization matrix, the encoder can encode information about the method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set.

As in the example of Table 27, the encoder can encode scaling_list_pred_mode_flag (i.e., information about the prediction encoding method of the quantization matrix) as a parameter set. For example, if the quantization matrix is encoded according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix to predict and encode the coefficients in the quantization matrix, the encoder can encode the value of scaling_list_pred_mode_flag to 1. If the reference quantization matrix and the quantization matrix to be encoded are determined to have the same value, or if the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix, the encoder can encode the value of scaling_list_pred_mode_flag to 0. Here, determining these values so that they have the same value may mean using a quantization matrix prediction method that copies the coefficient values of a specific quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is greater than 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded and information on whether to use a default matrix as a parameter set. Here, the parameter set encoded with the information on the reference quantization matrix ID and whether to use a default matrix may be an adaptive parameter set.

As in the example of Table 27, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_matrix_id_delta (ie, the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set only when the value of matrixID is greater than 0.

Here, the encoder can determine scaling_list_pred_matrix_id_delta (ie, quantization matrix ID) by using matrixID indicating a quantization matrix to be encoded, RefMatrixID indicating a reference quantization matrix or a default matrix, and Equation 6.

<Equation 6>

scaling_list_pred_matrix_id_delta=matrixID–RefMatrixID

If the coefficient values of the quantization matrix to be encoded have been determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder, the encoder can encode the value of scaling_list_pred_matrix_id_delta to 0 so that the value of RefMatrixID is the same as the value of matrixID. Here, the default matrix means the default matrix corresponding to sizeID and matrixID.

If the coefficient values of the quantization matrix to be encoded are determined to be the same as those of the reference quantization matrix, the encoder can encode the value of scaling_list_pred_matrix_id_delta as non-0 so that the value of RefMatrixID and the value of matrixID are different from each other.

In addition, when the value of scaling_list_pred_mode_flag is 0, it indicates that the method for predicting and encoding the quantization matrix is performed to determine the quantization matrix to be the same as the reference quantization matrix or the default matrix. In this case, the quantization matrix can be predicted from a previously encoded quantization matrix with the same sizeID or the default matrix.

When the value of matrixID is 0, it means the first quantization matrix for each sizeID. Therefore, when the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is 0, there is no reference quantization matrix with the same sizeID value for the first quantization matrix for each sizeID. Therefore, quantization matrix prediction such as the matrix copy method cannot be performed on the first quantization matrix for each sizeID.

In this case, the encoder can derive the value of scaling_list_pred_matrix_id_delta as 0 without encoding scaling_list_pred_matrix_id_delta. When the value of scaling_list_pred_matrix_id_delta is 0, the coefficient values of the quantization matrix to be encoded corresponding to sizeID and matrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder because the value of RefMatrixID is the same as the value of matrixID. Here, the default matrix can mean the default matrix corresponding to sizeID and matrixID.

If the method for predicting and encoding a quantization matrix is a method for encoding a quantization matrix by scanning according to a DPCM and an exponential Golomb coding method so as to predict and encode coefficients in the quantization matrix, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix as a parameter set. Here, the parameter set encoded by the difference may be an adaptive parameter set.

As in the example of Table 28, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the encoder can encode scaling_list_dc_coef_minus8 (ie, DC matrix coefficients) as a parameter set.

As in the example of Table 28, scaling_list_delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix) can be encoded as a parameter set.

In conventional quantization matrix encoding/decoding methods, when a quantization matrix is transmitted, all coefficients within the matrix and the DC matrix coefficients are encoded/decoded. In this case, improvement in coding efficiency is limited because prediction and encoding/decoding are not performed on the DC matrix coefficients.

In contrast, if prediction and encoding/decoding are performed on DC matrix coefficients within a quantization matrix, encoding efficiency can be improved.

Here, the present invention provides a method for predicting DC matrix coefficients from adjacent AC coefficients by using high correlation between adjacent coefficients, instead of predicting the DC matrix coefficients from a constant 8. The present invention can improve encoding efficiency through this method.

Tables 29 and 30 schematically show examples of syntax structures that can be used when predicting DC matrix coefficients by using correlations between adjacent coefficients.

<Form 29>

<Form 30>

In the examples of Tables 29 and 30, the encoding/decoding sequence of the quantization matrix is made the same as the restoration sequence of the quantization matrix. In this case, the storage space for storing DC matrix coefficients can be reduced. In addition, in the examples of Tables 29 and 30, when indicating whether to use the default matrix, only the syntax element "scaling_list_delta_coef" can be used instead of using several syntax elements.

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the example of Table 28, the encoder can encode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag as 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag as 1.

After determining the type of method for predicting and encoding the quantization matrix, the encoder can encode information about the method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set.

As in the example of Table 29, the encoder can encode scaling_list_pred_mode_flag (i.e., information about a method for predicting and encoding a quantization matrix) as a parameter set. For example, if the quantization matrix is encoded according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix to predict and encode the coefficients in the quantization matrix, the encoder can encode the value of scaling_list_pred_mode_flag as 1. If the reference quantization matrix is determined to have the same value as the quantization matrix to be encoded, the encoder can encode the value of scaling_list_pred_mode_flag as 0. Here, determining these values so that they have the same value can mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the value of scaling_list_pred_mode_flag is 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded as a parameter set. Here, the parameter set encoded with the reference quantization matrix ID may be an adaptive parameter set.

As in the example of Table 29, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set. Here, the encoder can determine scaling_list_pred_matrix_id_delta (i.e., the quantization matrix ID) by using matrixID indicating the quantization matrix to be encoded, RefMatrixID indicating the reference quantization matrix, and the following equation 7.

<Equation 7>

scaling_list_pred_matrix_id_delta=matrixID-(RefMatrixID+1)

Determining the coefficient values of the quantization matrix to be encoded so that they have the same values as the coefficient values of the reference quantization matrix can mean a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be encoded, and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the method for predicting and encoding a quantization matrix is a method for predicting and encoding coefficients within the quantization matrix by scanning the quantization matrix according to the DPCM and Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded within the quantization matrix as a parameter set. Here, the parameter set into which the difference is encoded may be an adaptive parameter set.

As in the example of Table 30, the encoder can encode scaling_list_delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) as a parameter set.

Here, the encoder can encode information on whether to use the default matrix by using scaling_list_delta_coef used to calculate nextCoef. For example, the encoder can encode scaling_list_delta_coef so that the first nextCoef value becomes 0 in order to instruct the decoder to use the default matrix.

As in the example of Table 30, the encoder can encode scaling_list_dc_coef_res (i.e., the difference between the coefficient values of the quantization matrix corresponding to the DC matrix coefficient) as a parameter set. Here, if the size of the quantization matrix to be encoded is a 16x16 (sizeID=2) or 32x32 (sizeID=3) quantization matrix and the default matrix is not used, scaling_list_dc_coef_res can be encoded as (useDefaultScalingMatrixFlag=0).

In the example of Table 30, the value of scaling_list_dc_coef_res of a 16x16-sized or 32x32-sized quantization matrix for encoding the DC matrix coefficient alone can be calculated by using the difference between the value of the DC matrix coefficient and the matrix coefficient existing at the DC position.

Meanwhile, the method for encoding/decoding a quantization matrix that determines whether to use a default matrix by using the coefficient values of the quantization matrix has the disadvantage of increasing the complexity of processing the coefficient values of the quantization matrix for encoding/decoding. In addition, conventionally, when the quantization matrix is transmitted, all coefficients within the matrix and the DC matrix coefficients are encoded/decoded. In this case, improvement in coding efficiency is limited because prediction and encoding/decoding are not performed on the DC matrix coefficients.

In the present invention, whether to use a default matrix is determined by using the ID of a reference quantization matrix during image encoding/decoding. This reduces the computational complexity of encoding/decoding the quantization matrix. Furthermore, the present invention improves coding efficiency by predicting and encoding/decoding the DC matrix coefficients within the quantization matrix. Furthermore, coding efficiency can be improved by predicting the DC matrix coefficients from adjacent AC coefficients using the high correlation between the adjacent AC coefficients, rather than predicting a constant 8.

Tables 31 and 32 schematically show examples of syntax structures that can be used when all of the aforementioned features are applied.

<Form 31>

<Form 32>

In the examples of Tables 31 and 32, the encoding/decoding order of the quantization matrix is made the same as the restoration order of the quantization matrix. Therefore, the memory space used to store DC matrix coefficients can be reduced. In addition, in the examples of Tables 31 and 32, when indicating whether to use the default matrix, instead of using several syntax elements, only the syntax element scaling_list_delta_coef can be used.

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the example of Table 31, the encoder can encode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag as 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag as 1.

After determining the type of predictive coding method for the quantization matrix, the encoder can encode information about the method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set.

As in the example of Table 31, the encoder can encode scaling_list_pred_mode_flag (i.e., information specifying a method for predicting and encoding a quantization matrix) as a parameter set. For example, if the quantization matrix is encoded according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix to predict and encode the coefficients in the quantization matrix, the encoder can encode the value of scaling_list_pred_mode_flag as 1. In addition, if the reference quantization matrix and the quantization matrix to be encoded are determined to have the same value or if the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix, the encoder can encode the value of scaling_list_pred_mode_flag as 0. Here, determining these values so that they have the same value can mean using a quantization matrix prediction method that copies the coefficient values of a specific quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the value of scaling_list_pred_mode_flag is 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded and information on whether to use a default matrix as a parameter set. Here, the parameter set on which encoding is performed may be an adaptive parameter set.

As in the example of Table 31, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_matrix_id_delta (ie, the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set.

Here, the encoder and the decoder can determine the value of scaling_list_pred_matrix_id_delta (ie, quantization matrix ID) by using matrixID indicating a quantization matrix to be encoded, RefMatrixID indicating a reference quantization matrix or a default matrix, and Equation 8.

<Equation 8>

scaling_list_pred_matrix_id_delta=matrixID–RefMatrixID

If the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder, the encoder can encode the value of scaling_list_pred_matrix_id_delta to 0 so that the value of RefMatrixID is the same as the value of matrixID. Here, the default matrix means the default matrix corresponding to sizeID and matrixID.

If the value of scaling_list_pred_matrix_id_delta is 0, the encoder can encode the value of scaling_list_pred_matrix_id_delta as a non-zero value so that the value of RefMatrixID is different from the value of matrixID.

If the method for predicting and encoding a quantization matrix is a method for predicting and encoding coefficients in a quantization matrix by scanning a quantization matrix encoded according to a DPCM and an exponential Golomb coding method, the encoder can encode the difference between the coefficient values of a previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix as a parameter set. Here, the parameter set encoded as the difference may be an adaptive parameter set.

As in the example of Table 32, the encoder can encode scaling_list_delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) as a parameter set.

As in the example of Table 32, the encoder can encode scaling_list_dc_coef_res (i.e., the difference between the coefficient values of the quantization matrix corresponding to the DC matrix coefficient) as a parameter set. Here, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3) and the default matrix is not used, scaling_list_dc_coef_res can be encoded as (useDefaultScalingMatrixFlag=0).

The value of scaling_list_dc_coef_res of a 16×16 sized quantization matrix or a 32×32 sized quantization matrix for separately encoding a DC matrix coefficient can be calculated by using a difference between a value of the DC matrix coefficient and a matrix coefficient existing at a DC position.

Meanwhile, in conventional quantization matrix encoding/decoding methods, quantization matrices are copied by using the size of the quantization matrix used when performing quantization and inverse quantization, rather than the size of the quantization matrix used when performing encoding/decoding. Therefore, quantization matrices are copied from a limited number of quantization matrices. As a result, improvements in coding efficiency are limited when encoding/decoding quantization matrices.

However, in the present invention, encoding efficiency can be improved and the degree of freedom in predicting a quantization matrix can be increased because the quantization matrix is predicted from a quantization matrix having the same size as a quantization matrix when encoding/decoding is performed.

Tables 33 and 34 schematically show examples of syntax structures that can be used when a quantization matrix is predicted from a quantization matrix having the same size as a quantization matrix when encoding/decoding is performed.

<Form 33>

<Form 34>

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the examples of Tables 33 or 34, the encoder can encode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag to 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag to 1.

After determining the type of predictive encoding method used for the quantization matrix, the encoder can encode information about the method for predicting and encoding the quantization matrix as a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set. For example, as in the examples of Tables 33 or 34, the encoder can encode scaling_list_pred_mode_flag (i.e., information about the method for predicting and encoding the quantization matrix) as a parameter set. For example, if the quantization matrix is encoded using DPCM and Exponential Golomb coding by scanning the quantization matrix to predict and encode the coefficients in the quantization matrix, the encoder can encode scaling_list_pred_mode_flag as 1. If the reference quantization matrix and the quantization matrix to be encoded are determined to have the same value, the encoder can encode scaling_list_pred_mode_flag as 0. Here, determining these values so that they have the same value can mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

In addition, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded as a parameter set. Here, at least one of the information specifying the size of the reference quantization matrix of the quantization matrix to be encoded and the information specifying the reference quantization matrix can be encoded as the parameter set as ID information (identifier) about the reference quantization matrix. The encoded parameter set can be an adaptive parameter set.

For example, as in the example of Table 33, if the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the reference quantization matrix, the encoder can encode scaling_list_pred_size_matrix_id_delta (i.e., ID information of the reference quantization matrix of the quantization matrix to be encoded) as a parameter set. Here, the value of scaling_list_pred_size_matrix_id_delta (i.e., ID information of the quantization matrix) can be determined by using RefSizeID (i.e., the size of the reference quantization matrix of the quantization matrix to be encoded), RefMatrixID indicating the reference quantization matrix, and Equation 9.

<Equation 9>

scaling_list_pred_size_matrix_id_delta=6*(RefSizeID-sizeID)+(RefMatrixID%6)

For another example, as in the example of Table 34, if the coefficient value of the quantization matrix to be encoded is determined to be the same as the coefficient value of the reference quantization matrix, the encoder can encode scaling_list_pred_size_id_delta and scaling_list_pred_size_matrix_id_delta (i.e., ID information of the reference quantization matrix of the quantization matrix to be encoded) as a parameter set. Here, the value of scaling_list_pred_size_id_delta can be determined by using RefSizeID and Equation 10, and the value of scaling_list_pred_matrix_id_delta can be determined by using RefMatrixID indicating the reference quantization matrix of the quantization matrix to be encoded and Equation 11.

<Equation 10>

scaling_list_pred_size_id_delta=sizeID–RefSizeID

<Equation 11>

scaling_list_pred_matrix_id_delta=matrixID–RefMatrixID

Determining the coefficient values of the quantization matrix to be encoded to be the same as the coefficient values of the reference quantization matrix may mean using a method of copying the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

Therefore, it is not allowed to predict the quantization matrix only from quantization matrices with the same sizeID, but through the example of Table 33 or Table 34, the quantization matrix can be predicted from quantization matrices with the same matrix size but different sizeID when performing encoding/decoding.

Furthermore, in the examples of Table 33 or Table 34, the range of values of the syntax elements may be limited to specific values. For example, in the examples of Table 33 or Table 34, scaling_list_pred_size_matrix_id_delta may be limited to values ranging from 0 to 17, scaling_list_pred_size_id_delta may be limited to values ranging from 0 to 2, and scaling_list_pred_matrix_id_delta may be limited to values ranging from 0 to 5.

Furthermore, in the example of Table 33 or Table 34, the encoder may not predict a quantization matrix from a quantization matrix having a larger size than a quantization matrix to be encoded.

In addition, the encoder can classify the quantization matrix into DC matrix coefficients and AC matrix coefficients according to the size of each quantization matrix, and predict the quantization matrix for the DC matrix coefficients and AC matrix coefficients. For example, a quantization matrix with an 8x8 size can be classified into DC matrix coefficients and AC matrix coefficients and then predicted, and both the DC matrix coefficients and the AC matrix coefficients can be predicted in relation to the quantization matrix with the remaining size. In other words, when prediction is performed based on a quantization matrix with an 8x8 size, the encoder can predict the value at the corresponding position by determining the value corresponding to the position of the DC matrix coefficient in the 8x8 size quantization matrix as the DC matrix coefficient of the quantization matrix to be encoded. If prediction is performed based on a quantization matrix with a 16x16 or 32x32 size, the encoder can also predict the DC matrix coefficient of the quantization matrix.

Meanwhile, if the method for predicting and encoding a quantization matrix is a method for predicting and encoding coefficients in a quantization matrix by scanning a quantization matrix encoded according to a DPCM and an exponential Golomb coding method, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix as a parameter set. Here, the parameter set may be an adaptive parameter set.

Table 35 shows an example of a syntax structure that can be used when predicting coefficients in a quantization matrix by using coefficient values of a quantization matrix that has been previously encoded in the quantization matrix.

<Form 35>

As in the example of Table 35, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the encoder can encode scaling_list_dc_coef_minus8 (ie, information about DC matrix coefficients) as a parameter set.

As in the example of Table 35, the encoder can encode scaling_list_delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) as a parameter set.

In addition, the encoder can encode information about whether to use the default matrix by using scaling_list_delta_coef used to derive the value of scaling_list_dc_coef_minus8 or nextCoef. For example, the encoder can encode the value of scaling_list_dc_coef_minus8 as -8 to instruct the decoder to use the default matrix, and can encode scaling_list_delta_coef so that the first nextCoef value is 0 to instruct the decoder to use the default matrix.

In other words, the method of encoding/decoding a quantization matrix in which the coefficient values of the quantization matrix are used to determine whether to use a default matrix has the disadvantage of increasing the complexity of the processing of encoding/decoding the coefficient values of the quantization matrix. Furthermore, there is the disadvantage of deteriorating coding efficiency because unnecessary information is encoded/decoded when predicting the quantization matrix. Furthermore, the quantization matrix is copied by using the size of the quantization matrix used when performing quantization and inverse quantization, rather than the size of the quantization matrix used when performing encoding/decoding. Since the quantization matrix is copied from a limited number of quantization matrices, the improvement in coding efficiency when encoding/decoding the quantization matrix is limited.

In the present invention, whether to use a default matrix can be determined by using the ID of a reference quantization matrix during image encoding/decoding. Therefore, the complexity of calculations when encoding/decoding the quantization matrix can be reduced. Furthermore, encoding efficiency can be improved and the degree of freedom in predicting the quantization matrix can be increased because, when encoding/decoding the quantization matrix, the quantization matrix is predicted based on a quantization matrix of the same size as the quantization matrix.

Tables 36 and 37 schematically show examples of syntax structures that can be used when predicting a quantization matrix by using the ID of a reference quantization matrix and by using a quantization matrix having the same size as when encoding/decoding the quantization matrix.

<Form 36>

<Form 37>

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the examples of Tables 36 or 37, the encoder can encode scaling_list_present_flag (i.e., information about whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag as 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag as 1.

After determining the type of predictive coding method for the quantization matrix, the encoder can encode information about the method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set.

As in the examples of Table 36 or Table 37, the encoder can encode scaling_list_pred_mode_flag (i.e., information specifying a method for predicting and encoding a quantization matrix) as a parameter set. For example, if the quantization matrix is encoded according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix to predict and encode the coefficients in the quantization matrix, the encoder can encode the value of scaling_list_pred_mode_flag to 1. In addition, if the reference quantization matrix and the quantization matrix to be encoded are determined to have the same value, or if the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix, the encoder can encode the value of scaling_list_pred_mode_flag to 0. Here, determining these values so that they have the same value may mean using a quantization matrix prediction method that copies the coefficient values of a specific quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the value of scaling_list_pred_mode_flag is 0, the encoder can encode the reference quantization matrix ID of the quantization matrix to be encoded as a parameter set. Here, at least one of information specifying the size of the reference quantization matrix of the quantization matrix to be encoded and information specifying the reference quantization matrix can be encoded as ID information about the reference quantization matrix in the parameter set. The encoded parameter set may be an adaptive parameter set. Furthermore, the ID or the parameter set into which the ID information is encoded may be an adaptive parameter set.

For example, as in the example of Table 36, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_size_matrix_id_delta (i.e., ID information of the reference quantization matrix of the quantization matrix to be encoded) as a parameter set. Here, the encoder can determine scaling_list_pred_size_matrix_id_delta (i.e., ID information of the quantization matrix) by using RefSizeID and RefMatrixID indicating the reference quantization matrix or the default matrix and Equation 12.

<Equation 12>

scaling_list_pred_size_matrix_id_delta=6*(RefSizeID-sizeID)+(RefMatrixID%6)

For another example, as in Table 37, if the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the reference quantization matrix, or if the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix, the encoder can encode scaling_list_pred_size_id_delta and scaling_list_pred_size_matrix_id_delta (i.e., ID information of the reference quantization matrix of the quantization matrix to be encoded) as a parameter set. Here, the encoder can derive the value of scaling_list_pred_size_id_delta by using RefSizeID and Equation 13, and can derive the value of scaling_list_pred_matrix_id_delta by using RefMatrixID indicating the reference quantization matrix or the default matrix of the quantization matrix to be encoded and Equation 14.

<Equation 13>

scaling_list_pred_size_id_delta=sizeID–RefSizeID

<Equation 14>

scaling_list_pred_matrix_id_delta=matrixID–RefMatrixID

If the coefficient values of the quantization matrix to be encoded are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder, the encoder can encode the value of scaling_list_pred_matrix_id_delta to 0 so that the value of RefMatrixID and the value of matrixID are the same. Here, the default matrix means the default matrix corresponding to sizeID and matrixID.

If the coefficient values of the quantization matrix to be encoded are determined to be the same as those of the reference quantization matrix, the encoder can encode the value of scaling_list_pred_matrix_id_delta as a non-zero value so that the value of RefMatrixID and the value of matrixID are different from each other.

Therefore, through the example of Table 36 or Table 37, the quantization matrix can be predicted from the quantization matrix having the same sizeID, and the quantization matrix can be predicted from the quantization matrix having the same matrix size but different sizeID when encoding/decoding is performed.

In addition, in the examples of Table 36 or Table 37, the ranges of the values of scaling_list_pred_size_matrix_id_delta, scaling_list_pred_size_id_delta, and scaling_list_pred_matrix_id_delta may be limited. For example, scaling_list_pred_size_matrix_id_delta may be limited to values ranging from 0 to 17, scaling_list_pred_size_id_delta may be limited to values ranging from 0 to 2, and scaling_list_pred_matrix_id_delta may be limited to values ranging from 0 to 5.

Furthermore, prediction of the quantization matrix may not be performed based on a quantization matrix having a larger size than a quantization matrix to be encoded.

When predicting a quantization matrix, the method of predicting the quantization matrix can be performed differently by considering the size of the matrix. For example, when predicting based on a quantization matrix having an 8x8 size, the encoder can predict the value at the corresponding position by determining the value corresponding to the position of the DC matrix coefficient in the 8x8 quantization matrix as the DC matrix coefficient. If prediction is performed based on a quantization matrix having a 16x16 or 32x32 size, the encoder can also predict the DC matrix coefficient.

Meanwhile, if the method for predicting and encoding the quantization matrix is a method for predicting and encoding the coefficients in the quantization matrix by scanning the quantization matrix according to the DPCM and Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix as a parameter set. Here, the parameter set encoded by the difference may be an adaptive parameter set.

Table 38 shows an example of a syntax structure that can be used when predicting coefficients in a quantization matrix by using coefficient values of a quantization matrix that has been previously encoded in the quantization matrix.

<Form 38>

As in the example of Table 38, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the encoder can encode scaling_list_dc_coef_minus8 (ie, information specifying DC matrix coefficients) as a parameter set.

As in the example of Table 38, the encoder can encode scaling_list_delta_coef (ie, the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) as a parameter set.

In conventional quantization matrix encoding/decoding methods, the coefficient values of the quantization matrix are encoded by ignoring the coefficient values that frequently appear when encoding/decoding the first coefficient in the quantization matrix. Therefore, in conventional quantization matrix encoding/decoding methods, the improvement of coding efficiency is limited.

In the present invention, the first coefficient in the quantization matrix can be predicted and encoded/decoded by using a frequently occurring coefficient value. In addition, in the present invention, if the first coefficient value or DC matrix coefficient value of the default matrix is defined as 16, or the first coefficient value or DC matrix coefficient value of the non-default matrix is distributed around 16, then the first coefficient value or DC matrix coefficient value in the quantization matrix to be encoded/decoded can be predicted by a constant of 16 and then encoded/decoded. In this case, the present invention can improve encoding efficiency.

Tables 39 and 40 schematically show examples of syntax structures that can be used when considering the first coefficient in the quantization matrix.

<Form 39>

<Form 40>

First, the encoder can encode information indicating whether a quantization matrix exists as a parameter set.

As in the example of Table 39, the encoder can encode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) as a parameter set. For example, if there is no quantization matrix and all quantization matrices are determined to be default quantization matrices, the encoder can encode the value of scaling_list_present_flag as 0. If there is an encoded quantization matrix, the encoder can encode the value of scaling_list_present_flag as 1.

After determining the type of predictive coding method for the quantization matrix, the encoder can encode information about the method for predicting and encoding the quantization matrix into a parameter set. Here, the parameter set into which the information about the method for predicting and encoding the quantization matrix is encoded can be an adaptive parameter set.

As in the example of Table 39, the encoder can encode scaling_list_pred_mode_flag (i.e., information about a method for predicting and encoding a quantization matrix) as a parameter set. For example, if the quantization matrix is encoded according to the DPCM and Exponential Golomb coding method by scanning the quantization matrix to predict and encode the coefficients in the quantization matrix, the encoder can encode the value of scaling_list_pred_mode_flag to 1. In addition, if the reference quantization matrix and the quantization matrix to be encoded are determined to have the same value, the encoder can encode the value of scaling_list_pred_mode_flag to 0. Here, determining these values so that they have the same value may mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be encoded.

If the value of scaling_list_pred_mode_flag is 0, the encoder can encode the reference quantization matrix ID of the quantization matrix as a parameter set. Here, the parameter set into which the reference quantization matrix ID is encoded may be an adaptive parameter set.

As in the example of Table 39, if the value of scaling_list_pred_mode_flag is 0, the encoder can encode scaling_list_pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be encoded) as a parameter set. Here, the encoder can determine scaling_list_pred_matrix_id_delta (i.e., the quantization matrix ID) by using matrixID indicating the quantization matrix to be encoded, RefMatrixID indicating the reference quantization matrix, and Equation 15.

<Equation 15>

scaling_list_pred_matrix_id_delta=matrixID-(RefMatrixID+1)

Determining the coefficient values of the quantization matrix to be encoded so that they have the same values as the coefficient values of the reference quantization matrix can mean using coefficient values of the reference quantization matrix copied to the coefficient values of the quantization matrix to be encoded.

If the method for predicting and encoding a quantization matrix is a method for predicting and encoding coefficients within the quantization matrix by scanning the quantization matrix according to the DPCM and Exponential Golomb coding method, the encoder can encode the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded within the quantization matrix as a parameter set. Here, the parameter set into which the difference is encoded may be an adaptive parameter set.

As in the example of Table 40, if the size of the quantization matrix to be encoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the encoder can encode scaling_list_dc_coef_minus16 (i.e., the coefficient value of the quantization matrix corresponding to the DC matrix coefficient) as a parameter set. Here, the value of scaling_list_dc_coef_minus16 indicates the DC matrix coefficient calculated assuming a prediction value of 16.

As in the example of Table 40, the encoder can encode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded in the quantization matrix) as a parameter set. As in the example of Table 40, the encoder can set "nextCoef=16", that is, set the predicted value of the first coefficient value to 16.

In addition, the encoder can determine whether to use the default matrix by using scaling_list_delta_coef used to calculate scaling_list_dc_coef_minus16 or nextCoef. That is, the encoder can encode the value of scaling_list_dc_coef_minus16 to -16 to instruct the decoder to use the default matrix, and can encode scaling_list_delta_coef so that the value of the first nextCoef becomes 0 to instruct the decoder to use the default matrix.

In the embodiments of the examples of the above and following tables and Tables 39 and 40, the encoder can set nextCoef to 16, and the value of scaling_list_dc_coef_minus16 can mean the DC matrix coefficient calculated assuming the prediction value is 16. In addition, in the embodiments of the above and following tables, the encoder can encode the value of scaling_list_dc_coef_minus16 as -16 to instruct the decoder to use the default matrix.

An example of the operation of an encoder for encoding information about a quantization matrix and signaling the encoded information has been described so far. Hereinafter, an example in which a decoder decodes information about a quantization matrix and obtains a quantization matrix is described by using an example of the aforementioned table.

FIG. 5 is a flowchart schematically illustrating an example of the operation of a decoder for decoding information about a quantization matrix and performing decoding by using the decoded information.

5 , the decoder decodes information about the size of a transformation unit and determines the size of the transformation unit based on the decoded information in step S510 .

The decoder performs entropy decoding on the information about the size of the transform unit from the received bitstream.The decoder can decode the information about the size of the transform unit from the parameter set in the bitstream.

For example, the decoder may decode information about the minimum size and the maximum size of the transform unit from the bitstream.

As in the example of Table 1, the decoder can decode the minimum size in the horizontal or vertical direction of a square transform unit to which the Log2 function has been applied by using the syntax element "log2_min_transform_block_size_minus2" in the bitstream. In addition, the decoder can decode the difference between the maximum size in the horizontal or vertical direction of a square transform unit to which the Log2 function has been applied and the minimum size in the horizontal or vertical direction of the square transform unit by using the syntax element "log2_diff_max_min_transform_block_size" in the bitstream.

The decoder can determine the minimum size and maximum size of the decoded transform unit. Here, the maximum size of the transform unit can be determined by the difference between the decoded maximum size and the minimum value, and the decoded minimum size.

For example, the decoder can calculate Log2MinTrafoSize by adding 2 to the decoded log2_min_transform_block_size_minus2, and determine the value calculated using 1<<Log2MinTrafoSize as the minimum size in the horizontal or vertical direction of the square transform unit. The decoder can calculate Log2MaxTrafoSize based on the value of the decoded log2_diff_max_min_transform_block_size and the value obtained by adding 2 to the decoded log2_min_transform_block_size_minus2, and determine the value calculated using 1<<Log2MaxTrafoSize as the maximum size in the horizontal or vertical direction of the square transform unit.

Here, the minimum size of the transform unit may mean a value calculated using Log2MinTrafoSize or 1<<Log2MinTrafoSize, and the maximum size of the transform unit may mean a value calculated using Log2MaxTrafoSize or 1<<Log2MaxTrafoSize.

The decoder decodes information about the quantization matrix in step S520. The decoder can decode information about the quantization matrix, including one or more of the following: (1) information about whether the quantization matrix has been used, (2) information about whether the quantization matrix exists, (3) information about whether the quantization matrix has been decoded and whether a default matrix has been used, (4) information about the type of method for predicting and decoding the quantization matrix, (5) information about the reference quantization matrix ID, and (6) information about the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix. Here, the information about the quantization matrix may depend on the size of the transform unit.

First, the decoder can determine whether a quantization matrix has been used by decoding information about whether a quantization matrix has been used from a parameter set. As in the example of Table 2, the decoder can decode scaling_list_enabled_flag (i.e., information about whether a quantization matrix has been used) from a sequence parameter set. Here, when the value of scaling_list_enabled_flag is 1, the decoder can use the quantization matrix used in the inverse quantization/scaling of transform coefficients for the entire sequence. When the value of scaling_list_enabled_flag is 0, the decoder may not use the quantization matrix used in the inverse quantization/scaling of transform coefficients.

The decoder can determine whether a quantization matrix exists by decoding information about whether a quantization matrix exists from a parameter set. As in the example of Table 3, the decoder can decode aps_scaling_list_data_present_flag (i.e., information about whether a quantization matrix exists) from an adaptive parameter set. For example, when the value of aps_scaling_list_data_present_flag is 1, it means that a quantization matrix exists in the adaptive parameter set. When the value of aps_scaling_list_data_present_flag is 0, it means that a quantization matrix does not exist in the adaptive parameter set. If scaling_list_enabled_flag is 1 and aps_scaling_list_data_present_flag is 0, it can mean that a default matrix is used when performing inverse quantization. In addition, although an example has been illustrated in which information about whether a quantization matrix exists is decoded from an adaptive parameter set, the present invention is not limited thereto. The decoder can decode information about whether a quantization matrix exists from another parameter set.

The decoder can determine whether the quantization matrix has been decoded and whether the default matrix has been used by decoding information about whether the quantization matrix has been decoded and whether the default matrix has been used from the parameter set. As in the example of Table 4, the decoder can decode use_default_scaling_list_flag (i.e., information about whether the quantization matrix has been decoded and whether the default matrix has been used) from the adaptive parameter set. For example, when the value of use_default_scaling_list_flag is 1, the quantization matrix is not decoded, and the coefficient values of all quantization matrices can be determined to be the same as the coefficient values of the default quantization matrix defined in the encoder and/or decoder. When the value of use_default_scaling_list_flag is 0, the quantization matrix is decoded, and the default matrix defined in the encoder and/or decoder may not be used.

The decoder can determine one or more of whether to decode a quantization matrix, whether to use a default matrix, and whether to perform predictive coding by using SizeID and MatrixID.

As in the examples of Tables 5 and 6, the value of SizeID can specify the quantization matrix according to the size of the transform unit or the size of the quantization matrix by using a table, while the value of MatrixID can specify the encoding mode in which the quantization matrix is used and the type of quantization matrix corresponding to the color component.

Meanwhile, Tables 7 and 8 can be used to indicate the default quantization matrix.

If the minimum size and maximum size of the available transform units are not considered, the quantization matrices of the transform units of all sizes must be decoded, which deteriorates the coding efficiency and increases the complexity of the calculation.

According to the present invention, information about a quantization matrix can be decoded by considering the size of a transform unit.

In the example of Table 9, the SizeID corresponding to the size of each transform unit is limited based on the minimum size and the maximum size of the transform unit among multiple information about the transform unit, and based on the limited SizeID, one or more of decoding of the quantization matrix, decoding of information about whether a default matrix has been used, and decoding of information about the type of prediction and decoding methods are performed.

As in the example of Table 9, SizeID can be limited based on the minimum size and maximum size of the transform unit among multiple information about the transform unit, and one or more of the information about whether a quantization matrix or a default matrix has been used and the information about the type of prediction decoding method can be decoded only in relation to a transform unit having a specific size.

For example, if the value of Log2MinTrafoSize specifying the minimum size of the transform unit is 3 and the value of Log2MaxTrafoSize specifying the maximum size of the transform unit is 4, the decoder can perform one or more of decoding of quantization matrices corresponding to transform units ranging from 8x8 size to 16x16 size, decoding of information about whether a default matrix has been used, and decoding of information about the type of predictive decoding method.

In the example of Table 9, use_default_scaling_list_flag may not be decoded.

In addition, unlike in this example, the decoder may limit the SizeID based on the difference between the maximum size and the minimum value of the transform unit, and based on the limited SizeID, perform one or more of decoding of the quantization matrix, decoding of information about whether a default matrix has been used, and decoding of information about the type of predictive decoding method.

As in the example of Table 10, the decoder can limit SizeID based on the difference between the minimum size and the maximum size of the transform unit, and perform one or more of decoding of the quantization matrix, decoding of information about whether a default matrix has been used, and decoding of information about the type of predictive decoding method on only transform units having a specific size (i.e., only a specific size of the transform unit).

For example, if the value of Log2MinTrafoSize specifying the minimum size of the transform unit is 3 and the value of Log2MaxTrafoSize specifying the maximum size of the transform unit is 4, the decoder can perform one or more of decoding of quantization matrices corresponding to transform units ranging from 8x8 size to 16x16 size, decoding of information about whether a default matrix has been used, and decoding of information about the type of predictive decoding method.

Here, the difference between Log2MaxTrafoSize and Log2MinTrafoSize is the difference between the maximum size and the minimum size of the transform unit and can be specified by log2_diff_max_min_transform_block_size. In addition, Log2MinTrafoSize-2 is the same as log2_min_transform_block_size_minus2.

In the example of Table 10, use_default_scaling_list_flag may not be decoded.

Meanwhile, if the default matrix and the non-default matrix are not mixed and used according to the size of each transform block or the type of quantization matrix in a sequence, picture, or slice, the degree of freedom when the encoder selects the quantization matrix is reduced. For example, if a default matrix for a specific transform size within a slice is used and a non-default matrix for another specific transform size within the slice is used, coding efficiency may be degraded because the default matrix must be encoded and transmitted.

In the present invention, a default matrix and a non-default matrix can be mixed and used according to the size of each transform block or the type of quantization matrix in a sequence, a picture, or a slice.

For example, the decoder can decode information about whether the quantization matrix has been decoded and whether the default matrix has been used from the parameter set based on SizeID. As in the example of Table 11, the decoder can decode sid_use_default_scaling_list_flag[SizeID][MatrixID] (i.e., information specifying whether the quantization matrix has been decoded and whether the default matrix has been used) from the adaptive parameter set based on SizeID. For example, when the value of sid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the decoder does not decode the quantization matrix corresponding to SizeID, and the coefficient values of the quantization matrix corresponding to SizeID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of sid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the decoder can decode the quantization matrix corresponding to SizeID, but does not use the default matrix defined in the encoder and/or decoder as the quantization matrix corresponding to SizeID.

Meanwhile, in the example of Table 11, use_default_scaling_list_flag may not be decoded.

Furthermore, the decoder may decode information on whether a quantization matrix has been decoded and whether a default matrix has been used from a parameter set based on MatrixID instead of SizeID.

As in the example of Table 12, the decoder can decode mid_use_default_scaling_list_flag[SizeID][MatrixID] (i.e., information specifying whether the quantization matrix has been decoded and whether the default matrix has been used) from the adaptive parameter set based on MatrixID. For example, when the value of mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the decoder does not decode the quantization matrix corresponding to MatrixID, and the coefficient values of the quantization matrix corresponding to MatrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of sid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the decoder decodes the quantization matrix corresponding to MatrixID, but does not use the default matrix defined in the encoder and/or decoder as the quantization matrix corresponding to MatrixID.

In the example of Table 12, use_default_scaling_list_flag may not be decoded.

Furthermore, the decoder can decode information on whether a quantization matrix has been decoded and whether a default matrix has been used from a parameter set based on SizeID and MatrixID by considering both SizeID and MatrixID, rather than only SizeID or only MatrixID.

As in the example of Table 13, the decoder can decode sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] (i.e., information specifying whether the quantization matrix has been decoded and whether the default matrix has been used) from the adaptation parameter set based on SizeID and MatrixID. For example, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the decoder does not decode the quantization matrix corresponding to SizeID and MatrixID, and the coefficient values of the quantization matrix corresponding to SizeID and MatrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the decoder decodes the quantization matrix corresponding to SizeID and MatrixID and does not use the default matrix defined in the encoder and/or decoder as the quantization matrix corresponding to SizeID and MatrixID.

In the example of Table 13, use_default_scaling_list_flag may not be decoded.

Meanwhile, as in the example of Table 14, the decoder limits SizeID according to the minimum size and maximum size of the transform unit, and based on the limited SizeID, performs one or more of decoding of the quantization matrix, decoding of information on whether a default matrix has been used, and decoding of information on the type of predictive decoding method. In addition, the decoder can decode information on whether the quantization matrix has been decoded and information on whether the default matrix has been used from the parameter set based on SizeID and MatrixID.

In the example of Table 14, use_default_scaling_list_flag may not be decoded.

As in the example of Table 15, the decoder can limit SizeID based on the difference between the maximum size and the minimum size of the transform unit among multiple pieces of information about the transform unit, and based on the limited SizeID, perform one or more of decoding the quantization matrix, decoding information on whether a default matrix is used, and decoding information on the type of predictive decoding method. For example, the difference between Log2MaxTrafoSize and Log2MinTrafoSize is the difference between the maximum size and the minimum size of the transform unit and is the same as log2_diff_max_min_transform_block_size, while Log2MinTrafoSize-2 is the same as log2_min_transform_block_size_minus2. In addition, the decoder can decode information on whether the quantization matrix has been decoded and whether the default matrix has been used from the parameter set based on SizeID and MatrixID.

In the example of Table 15, use_default_scaling_list_flag may not be decoded.

In addition, as in the example of Table 16, the decoder can determine whether information about the quantization matrix exists in the parameter set to be decoded or whether the quantization matrix is to be updated based on scaling_list_update_flag[SizeID][MatrixID] in the parameter set. For example, scaling_list_update_flag[SizeID][MatrixID] having a value of 1 indicates that information about the quantization matrix specified by SizeID and MatrixID exists in the parameter set to be decoded, or indicates that information about the quantization matrix corresponding to SizeID and MatrixID and previously decoded should be updated with information about the quantization matrix corresponding to SizeID and MatrixID in the parameter set to be decoded. Here, updating the information about the quantization matrix can mean replacing the information about the previously decoded quantization matrix with the information about the quantization matrix in the parameter set to be decoded. In addition, scaling_list_update_flag[SizeID][MatrixID] having a value of 0 indicates that the quantization matrix corresponding to SizeID and MatrixID does not exist in the parameter set to be decoded, or that information about the previously decoded quantization matrix is not to be updated. For example, when the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the decoder does not know which quantization matrix should be used for the inverse quantization of the coefficients of the quantization matrix specified by SizeID and MatrixID because the quantization matrix corresponding to SizeID and MatrixID does not exist in the parameter set and the information about the quantization matrix has not yet been decoded. Therefore, when the value of scaling_list_update_flag[SizeID][MatrixID] is 0, it is possible to instruct the use of a default matrix as the quantization matrix corresponding to SizeID and MatrixID or not to use a quantization matrix because the information about the quantization matrix corresponding to SizeID and MatrixID does not exist in the parameter set to be decoded.

Here, scaling_list_update_flag[SizeID][MatrixID] is decoded based on the SizeID and MatrixID corresponding to the size of each transform unit. Therefore, when the value of scaling_list_update_flag[SizeID][MatrixID] is 1, the decoder can perform one or more of decoding the quantization matrix, decoding the information on whether the default matrix has been used, and decoding the information on the type of prediction decoding method. When the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the decoder does not perform one or more of decoding the quantization matrix, decoding the information on whether the default matrix has been used, and decoding the information on the type of prediction decoding method. That is, the decoder may not decode unnecessary quantization matrices based on the indication of scaling_list_update_flag[SizeID][MatrixID].

Meanwhile, there is a disadvantage in that the degree of freedom in selecting a quantization matrix is low because the default matrix and the non-default matrix are not mixed and used according to the size of each transform block or the type of the quantization matrix in a sequence, picture or fragment by using only scaling_list_update_flag[SizeID][MatrixID]. Therefore, the decoder can decode sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] (i.e., information about whether the quantization matrix has been decoded and whether the default matrix has been used) from the parameter set based on SizeID and MatrixID. For example, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1, the decoder does not decode the quantization matrix specified by SizeID and MatrixID, and the coefficient values of the quantization matrix corresponding to SizeID and MatrixID are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. When the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0, the decoder decodes the quantization matrix specified by SizeID and MatrixID, and does not use the default matrix defined in the encoder and/or decoder as the quantization matrix corresponding to SizeID and MatrixID.

In the example of Table 16, use_default_scaling_list_flag may not be decoded.

In addition, as in the example of Table 17, the decoder can decode information about whether the quantization matrix has been decoded and whether the default matrix has been used from the parameter set based on SizeID and MatrixID. In addition, scaling_list_update_flag[SizeID][MatrixID] about information updated to the quantization matrix corresponding to SizeID and MatrixID can be used in the parameters to be decoded.

For example, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0 and the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the decoder decodes the quantization matrix corresponding to SizeID and MatrixID, does not update the previously decoded quantization matrix corresponding to SizeID and MatrixID to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be decoded, and uses the previously decoded quantization matrix corresponding to SizeID and MatrixID.

In addition, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 0 and the value of scaling_list_update_flag[SizeID][MatrixID] is 1, the decoder decodes the quantization matrix corresponding to SizeID and MatrixID, and updates the previously decoded quantization matrix corresponding to SizeID and MatrixID to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be decoded.

In addition, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1 and the value of scaling_list_update_flag[SizeID][MatrixID] is 0, the decoder does not decode the quantization matrix corresponding to SizeID and MatrixID, determines the coefficient values of the quantization matrix to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder, does not update the quantization matrix corresponding to SizeID and MatrixID and previously decoded to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be decoded, and uses the previously decoded quantization matrix corresponding to SizeID and MatrixID.

In addition, when the value of sid_mid_use_default_scaling_list_flag[SizeID][MatrixID] is 1 and the value of scaling_list_update_flag[SizeID][MatrixID] is 1, the decoder does not decode the quantization matrix corresponding to SizeID and MatrixID, determines the coefficient values of the quantization matrix to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder, and updates the quantization matrix corresponding to SizeID and MatrixID and previously decoded to the quantization matrix corresponding to SizeID and MatrixID in the parameters to be decoded.

In the example of Table 17, use_default_scaling_list_flag may not be decoded.

In addition, the decoder can decode information about the method of predicting and decoding the quantization matrix from the parameter set. And can determine the type of prediction decoding method used for the quantization matrix based on the decoded information. As in the example of Table 18, the decoder can decode pred_mode_flag (i.e., information about the method of predicting and decoding the quantization matrix) from the adaptive parameter set. For example, when the value of pred_mode_flag is 1, the decoder can decode the quantization matrix according to the exponential Golomb method and the inverse differential pulse code modulation (DPCM) method. When the value of pred_mode_flag is 0, the decoder determines the coefficient values of the quantization matrix to be the same as the coefficient values of the previously decoded quantization matrix. Here, the coefficient values of the quantization matrix and the coefficient values of the previously decoded quantization matrix can be values in different quantization matrices, and the previously decoded quantization matrix can mean a reference quantization matrix.

If the value of pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded from the parameter set. As in the example of Table 18, the decoder can decode pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be decoded) from the adaptation parameter set. Here, the decoder can determine the RefMatrixID indicating the reference quantization matrix of the quantization matrix to be decoded by using pred_matrix_id_delta and Equation 16.

<Equation 16>

RefMatrixID=MatrixID-(1+pred_matrix_id_delta)

If the method for predicting and decoding the quantization matrix is a method for decoding the quantization matrix based on the Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded from the parameter set. Here, the coefficient values of the previously decoded quantization matrix can be the coefficient values of the quantization matrix to be decoded. As in the example of Table 19, the decoder can decode delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded) from the adaptive parameter set.

Meanwhile, the default quantization matrix and the non-default quantization matrix can be mixed and used in a sequence, a picture, or a slice by using the following method, and reception of an unnecessary quantization matrix can be prevented.

For example, if the method used to predict and decode the quantization matrix is a method of determining the quantization matrix as the same as the quantization matrix included in the decoder and previously decoded (pred_mode_flag=0), the decoder can use the reference quantization matrix ID of the quantization matrix to be decoded from the parameter set to decode information about whether the default quantization matrix has been used.

As in the example of Table 18, the decoder can decode pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be decoded) from the parameter set. Here, the decoder can determine RefMatrixID (i.e., information specifying the reference quantization matrix or default matrix of the quantization matrix to be decoded, and information on whether the default matrix has been used) by using pred_matrix_id_delta and Equation 17.

<Equation 17>

RefMatrixID=MatrixID-pred_matrix_id_delta

For example, when the value of RefMatrixID is the same as the value of MatrixID, the coefficient values of the quantization matrix corresponding to SizeID and RefMatrixID are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. Here, the default matrix means the default matrix corresponding to SizeID and RefMatrixID. In addition, when the value of pred_matrix_id_delta is 0, the value of RefMatrixID becomes the same as the value of MatrixID. If the value of RefMatrixID is different from the value of MatrixID, the quantization matrix corresponding to RefMatrixID is determined to be the reference quantization matrix of the quantization matrix to be decoded, and the coefficient values of the quantization matrix to be decoded are determined to be the same as the coefficient values of the reference quantization matrix.

If the size of the quantization matrix corresponding to SizeID is included in the minimum size and maximum size available to the decoder, the reference quantization matrix of the quantization matrix to be decoded and whether the default matrix has been used can be determined by the above method. If the size of the quantization matrix corresponding to SizeID is not included in the minimum size and maximum size of the transform unit available to the decoder, the quantization matrix corresponding to SizeID may not be determined to be the same as the default matrix. If one or more of decoding of the quantization matrix, decoding of information on whether the default matrix has been used, and decoding of information on the type of predictive decoding method are performed based on the difference between the maximum size and the minimum value of the transform unit among multiple pieces of information about the transform unit, the above determination processing for SizeID can be performed.

After determining whether the quantization matrix has been used, the decoder can decode information on whether the quantization matrix has been used from the parameter set.

As in the example of Table 20, the decoder can decode scaling_list_enable_flag (i.e., information about whether a quantization matrix is used) from the parameter set. Here, when the value of scaling_list_enable_flag is 1, the decoder can use a quantization matrix (such as a default matrix or a non-default matrix) in inverse quantization. When the value of scaling_list_enable_flag is 0, the decoder does not use the quantization matrix, or can use a quantization matrix with all the same coefficient values in inverse quantization. Here, all coefficient values can be 16.

Furthermore, if the method for predicting and decoding a quantization matrix is a method for decoding a quantization matrix based on an inverse DPCM and an exponential Golomb coding method, the decoder can decode the difference between the coefficient values of a previously decoded quantization matrix and the coefficient values of a quantization matrix to be decoded from a parameter set. The coefficient values of the previously decoded quantization matrix may be the coefficient values of the quantization matrix to be decoded. In other words, the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded may be values of the same quantization matrix.

As in the example of Table 21, the decoder can decode delta_coef (i.e., the difference between the coefficient value of the previously decoded quantization matrix and the coefficient value of the quantization matrix to be decoded) from the parameter set. As in the example of Table 21, if the coefficient value "nextcoef" of the quantization matrix (1) is the same as the specific value and (2) is the first value of the quantization matrix, the coefficient value of the corresponding quantization matrix can be determined to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder by using Equation 18.

<Equation 18>

nextcoef=(nextcoef+delta_coef+256)%256

That is, if the coefficient value "nextcoef" of the quantization matrix (1) is the same as a specific value and (2) is the first value of the quantization matrix, the decoder can use the corresponding quantization matrix as a default matrix. Here, the specific value may be 0. In addition, the default matrix may mean a default matrix specified by SizeID and MatrixID. Therefore, if the coefficient value "nextcoef" of the quantization matrix is the same as 0 and is the first value of the quantization matrix, the decoder can stop decoding the difference between the corresponding quantization matrix and the quantization matrix.

Meanwhile, if the method for predicting and decoding the quantization matrix is a method for decoding the quantization matrix based on the inverse DPCM and exponential Golomb coding method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded from the parameter set. The coefficient values of the previously decoded quantization matrix may be the coefficient values of the quantization matrix to be decoded. In other words, the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded may be values of the same quantization matrix.

As in the example of Table 22, the decoder can decode delta_coef (i.e., the difference between the coefficient value of the previously decoded quantization matrix and the coefficient value of the quantization matrix to be decoded) from the parameter set. For example, as in the example of Table 22, if the coefficient value "nextcoef" of the quantization matrix calculated using Equation 18 (i.e., (nextcoef+delta_coef+256)%256) is the same as the specific value and is the first value of the quantization matrix, the decoder can determine the coefficient value of the corresponding quantization matrix to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder. That is, if nextcoef (1) is the same as the specific value and (2) is the first value of the quantization matrix, the decoder can use the corresponding quantization matrix as the default matrix. Here, the specific value may be 0, and the coefficient value of the quantization matrix calculated using (nextcoef+delta_coef+256)%256 may be the coefficient value of a quantization matrix having a size of 4x4 or 8x8.

Also, the first value of the quantization matrix may be a value using scaling_list_dc_coef_minus8, and the specific value may be a value corresponding to scaling_list_dc_coef_minus8+8.

scaling_list_dc_coef_minus8 can mean the first value of a quantization matrix having a size of 16x16 or 32x32, which may mean a DC matrix coefficient value.

When the value of sizeID is 2, scaling_list_dc_coef_minus8[sizeID-2][matrixID] can correspond to a DC matrix coefficient value having a size of 16x16. Here, 16x16 can be the size of a transform block corresponding to the quantization matrix. When the size of SizeID is 3, scaling_list_dc_coef_minus8[sizeID-2][matrixID] can correspond to a DC matrix coefficient value in a quantization matrix having a size of 32x32. Here, the size of 32x32 can be the size of a transform block corresponding to the quantization matrix. In each case, the default matrix can mean a default matrix corresponding to SizeID and MatrixID. Therefore, if the coefficient value "nextcoef" of the quantization matrix is the same as 0 and is the first value of the quantization matrix, the decoder can stop decoding the difference between the corresponding quantization matrix and the quantization matrix (i.e., the difference between the coefficient values).

The decoder can differently perform decoding of whether to decode scaling_list_dc_coef_minus8 (ie, DC matrix coefficient value) and information on whether a default matrix has been used, according to the size of the quantization matrix or the transform size, by using this method.

The disadvantage of the method for encoding/decoding quantization matrices that uses quantization matrix coefficient values to determine whether to use a default matrix is that it increases the complexity of processing the coefficient values of the encoding/decoding quantization matrix. In contrast, the present invention can determine whether to use a default matrix by using a reference quantization matrix ID during image encoding/decoding. Therefore, the computational complexity of encoding/decoding quantization matrix processing can be reduced.

First, the decoder can decode information indicating whether a quantization matrix exists from the parameter set. As in the example of Table 23, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from the parameter set. For example, when the value of scaling_list_present_flag is 0, it means that there is no quantization matrix and the quantization matrix is determined as the default quantization matrix. When the value of scaling_list_present_flag is 1, it means that an encoded quantization matrix exists.

The decoder can decode information about the method for predicting and decoding the quantization matrix from a parameter set and, based on the decoded information, determine the type of prediction decoding method used for the quantization matrix. Here, the parameter set from which the information about the prediction decoding method is decoded may be an adaptive parameter set. As in the example of Table 23, the decoder can decode scaling_list_pred_mode_flag (i.e., information about the method for predicting and decoding the quantization matrix) from the parameter set. For example, when scaling_list_pred_mode_flag has a value of 1, the decoder predicts and decodes the coefficients within the quantization matrix by scanning the quantization matrix decoded using the Exponential Golomb coding and inverse DPCM methods. When scaling_list_pred_mode_flag has a value of 0, the decoder determines the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix, or determines the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the default matrix. Determining these values so that they have the same values may mean using a quantization matrix prediction method that copies the coefficient values of a specific quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded and information on whether the default matrix has been used from the parameter set. Here, the parameter set from which the reference quantization matrix ID and information are decoded may be an adaptive parameter set.

That is, as in the example of Table 23, the decoder can decode scaling_list_pred_matrix_id_delta (i.e., information specifying the reference quantization matrix ID of the quantization matrix to be decoded, and information on whether a default matrix has been used) from the parameter set. Here, the decoder can determine the RefMatrixID indicating the reference quantization matrix or the default matrix of the quantization matrix to be decoded by using scaling_list_pred_matrix_id_delta and Equation 19.

<Equation 19>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta

If the value of RefMatrixID is the same as the value of matrixID, the coefficient value of the quantization matrix to be decoded corresponding to sizeID and matrixID can be determined to be the same as the coefficient value of the default matrix defined in the encoder and/or decoder. Here, the default matrix can be a default matrix corresponding to sizeID and matrixID. Referring to Equation 19, when the value of scaling_list_pred_matrix_id_delta is 0, it means that the value of RefMatrixID is the same as the value of matrixID.

If the value of RefMatrixID is different from the value of matrixID, the decoder can determine the quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded, and determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix may mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded, and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded. Here, the value of scaling_list_pred_matrix_id_delta can be a positive integer value.

If the method for predicting and decoding a quantization matrix is a method for predicting and decoding coefficients in a quantization matrix by scanning according to an Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of a previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix from a parameter set. Here, the parameter set from which the decoder decodes the difference may be an adaptive parameter set.

As in the example of Table 24, if the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the decoder can decode scaling_list_dc_coef_minus8 (i.e., DC matrix coefficient) from the parameter set. In addition, as in the example of Table 24, the decoder can decode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix) from the parameter set. In the examples of Tables 23 and 24, an example in which information about the quantization matrix is decoded from an adaptive parameter set has been illustrated, but the present invention is not limited thereto. The decoder can decode information about the quantization matrix from another parameter set (i.e., a parameter set including at least one of a sequence parameter set and a picture parameter set).

As described above in the example of the encoder, in the conventional quantization matrix encoding/decoding method, encoding efficiency deteriorates because unnecessary information is encoded/decoded when predicting the quantization matrix. However, in the present invention, encoding efficiency can be improved when encoding/decoding the quantization matrix because encoding/decoding of the quantization matrix can be performed differently depending on whether a reference quantization matrix exists.

More specifically, the decoder can decode information indicating whether a quantization matrix exists from the parameter set. As in the example of Table 25, the decoder can decode scaling_list_present_flag (i.e., information about whether a quantization matrix exists in the bitstream) from the parameter set. For example, when the value of scaling_list_present_flag is 0, it means that there is no quantization matrix and all quantization matrices are determined to be default quantization matrices. When the value of scaling_list_present_flag is 1, it means that a coded quantization matrix exists.

In addition, when the value of matrixID is greater than 0, the decoder can decode information about the method of predicting and encoding the quantization matrix from the parameter set and determine the type of predictive decoding method used for the quantization matrix based on the decoded information. Here, the parameter set from which the information about the predictive decoding method is decoded may be an adaptive parameter set.

For example, as in the example of Table 25, when the value of matrixID is greater than 0, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from the parameter set. In the example of Table 25, when the value of scaling_list_pred_mode_flag is 1, the decoder can predict and decode the coefficients within the quantization matrix by scanning the quantization matrix decoded according to the Exponential Golomb coding and inverse DPCM method. When the value of scaling_list_pred_mode_flag is 0, the decoder can determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Here, determining these values so that they have the same values may mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

Furthermore, in the example of Table 25, the value of scaling_list_pred_mode_flag becomes true when the value of matrixID is 0. Therefore, the decoder does not decode scaling_list_pred_mode_flag, and can decode the quantization matrix by scanning the quantization matrix according to the inverse DPCM and exponential Golomb coding method.

If the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is greater than 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded from the parameter set. Here, the parameter set from which the reference quantization matrix ID is decoded may be an adaptive parameter set.

For example, as in the example of Table 25, when the value of matrixID is greater than 0, the decoder can decode scaling_list_pred_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be decoded) from the parameter set. Here, RefMatrixID indicating the reference quantization matrix of the quantization matrix to be decoded can be determined by using scaling_list_pred_matrix_id_delta and Equation 20.

<Equation 20>

RefMatrixID=matrixID-(1+scaling_list_pred_matrix_id_delta)

In the example of Table 25, matrixID with a value of 0 indicates the first quantization matrix for each sizeID. Quantization matrices can be predicted only from previously decoded quantization matrices with the same sizeID, and quantization matrix prediction using a method such as matrix copying cannot be performed for the first quantization matrix for each sizeID because there is no reference quantization matrix with the same sizeID value. Therefore, when the value of matrixID is greater than 0, the decoder can decode scaling_list_pred_matrix_id_delta (i.e., reference quantization matrix ID), determine the quantization matrix corresponding to RefMatrixID as the reference quantization matrix for the quantization matrix to be decoded based on the decoded reference quantization matrix ID, and determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix can mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix for the quantization matrix to be decoded and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the method for predicting and decoding a quantization matrix is a method for predicting and decoding coefficients in a quantization matrix by scanning according to an Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix from a parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

For example, as in the example of Table 26, when the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the decoder can decode scaling_list_dc_coef_minus8 (i.e., DC matrix coefficients) from the parameter set. In addition, as in the example of Table 26, the decoder can decode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded) from the parameter set.

In addition, the decoder can determine whether the default matrix is used by using scaling_list_delta_coef used to calculate scaling_list_dc_coef_minus8 or nextCoef. For example, if the value of scaling_list_dc_coef_minus8 is decoded as -8, the decoder can determine the corresponding quantization matrix as the default matrix. When the value of the first nextCoef calculated by decoding scaling_list_delta_coef is 0, the decoder can determine the corresponding quantization matrix as the default matrix.

As described above in the example of the encoder, the method of encoding/decoding a quantization matrix in which the coefficient values of the quantization matrix are used to determine whether a default matrix has been used has the disadvantage that it increases the complexity of processing the coefficient values of the quantization matrix for encoding/decoding. In addition, coding efficiency is deteriorated because unnecessary information is encoded/decoded when predicting the quantization matrix. However, in the present invention, in image encoding/decoding, the complexity of calculations when encoding/decoding the quantization matrix can be reduced because it can be determined based on the reference quantization matrix ID whether a default matrix has been used, and the coding efficiency of the encoding/decoding quantization matrix can be improved because the quantization matrix is encoded/decoded differently depending on whether a reference quantization matrix exists.

More specifically, first, the decoder decodes information indicating whether a quantization matrix exists from a parameter set. As in the example of Table 27, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from the parameter set. For example, when the value of scaling_list_present_flag is 0, it indicates that no quantization matrix exists and all quantization matrices are determined to be default quantization matrices. When the value of scaling_list_present_flag is 1, it indicates the encoded quantization matrix.

In addition, the decoder can decode information about the method of predicting and decoding the quantization matrix from the parameter set, and can determine the type of prediction decoding method used for the quantization matrix based on the decoded information. Here, the parameter set from which the information about the prediction decoding method is decoded can be an adaptive parameter set.

More specifically, as in the example of Table 27, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from a parameter set. For example, when the value of scaling_list_pred_mode_flag is 1, the decoder can predict and decode coefficients within a quantization matrix by scanning the quantization matrix decoded according to the Exponential Golomb coding and inverse DPCM methods. When the value of scaling_list_pred_mode_flag is 0, the decoder can determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix, or determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the default matrix. Here, determining these values so that they have the same values may mean using a quantization matrix prediction method that copies the coefficient values of a specific quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is greater than 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded and the information on whether the default matrix has been used from the parameter set. Here, the parameter set from which the reference quantization matrix ID and the information on whether the default matrix has been used are decoded may be an adaptive parameter set.

In this case, as in the example of Table 27, when the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is greater than 0, the decoder can decode scaling_list_pred_matrix_id_delta (i.e., the reference quantization matrix ID indicating the quantization matrix to be decoded and information on whether the default matrix has been used) from the parameter set. Here, RefMatrixID indicating the reference quantization matrix or the default matrix of the quantization matrix to be decoded can be determined by using scaling_list_pred_matrix_id_delta and Equation 21.

<Equation 21>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta

If the value of RefMatrixID is equal to the value of matrixID, the coefficient values of the quantization matrix to be decoded corresponding to sizeID and matrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. Here, the default matrix means the default matrix corresponding to sizeID and matrixID. According to Equation 21, when the value of scaling_list_pred_matrix_id_delta is 0, it means that the value of RefMatrixID is the same as the value of matrixID.

If the value of RefMatrixID is different from the value of matrixID, the quantization matrix corresponding to RefMatrixID is determined as the reference quantization matrix of the quantization matrix to be decoded, and the coefficient values of the quantization matrix to be decoded are determined to be the same as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded to be the same as the coefficient values of the reference quantization matrix may mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

Here, when the value of scaling_list_pred_mode_flag is 0, it indicates that the method of predicting and decoding the quantization matrix is to determine the quantization matrix as the same as the previously decoded quantization matrix. In this case, the quantization matrix can be predicted from the previously decoded quantization matrix with the same sizeID.

When the value of matrixID is 0, the first quantization matrix is indicated for each sizeID. If the value of scaling_list_pred_mode_flag is 0 and the value of matrixID is 0, prediction of the quantization matrix using a method such as matrix copy cannot be performed on the first quantization matrix for each sizeID because there is no reference quantization matrix with the same sizeID. In this case, the encoder does not encode scaling_list_pred_matrix_id_delta and derives the value of scaling_list_pred_matrix_id_delta as 0. When the value of scaling_list_pred_matrix_id_delta is 0, the coefficient values of the quantization matrix to be decoded corresponding to sizeID and matrixID are determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder because the value of RefMatrixID is the same as the value of matrixID. Here, the default matrix means the default matrix corresponding to sizeID and matrixID.

If the method for predicting and decoding the decoded quantization matrix is a method for predicting and decoding coefficients in the quantization matrix by scanning based on the Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix from the parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

For example, as in the example of Table 28, if the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the decoder can decode scaling_list_dc_coef_minus8 (i.e., DC matrix coefficients) from the parameter set. As in the example of Table 28, the decoder can decode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded) from the parameter set.

As described above in the encoder example, in conventional quantization matrix encoding/decoding methods, when a quantization matrix is transmitted, all coefficients within the matrix and the DC matrix coefficients are encoded/decoded. This limits improvements in coding efficiency because the DC matrix coefficients are not predicted and encoded/decoded. In the present invention, the DC matrix coefficients within the quantization matrix can be predicted and encoded/decoded, thereby improving coding efficiency. For example, in the examples of Tables 29 and 30, coding efficiency can be improved because the DC matrix coefficients are not predicted from the constant 8, but rather predicted from adjacent AC coefficients by utilizing the high correlation between adjacent coefficients. Furthermore, in the examples of Tables 29 and 30, the storage space required to store the DC matrix coefficients can be reduced because the encoding/decoding sequence of the quantization matrix is made the same as the recovery sequence of the quantization matrix. Furthermore, in the examples of Tables 29 and 30, whether a default matrix is used can be indicated using the syntax element "scaling_list_delta_coef" rather than using several syntax elements.

More specifically, the decoder can decode information indicating whether a quantization matrix exists from the parameter set. For example, as in the example of Table 29, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from the parameter set. Then, when the value of scaling_list_present_flag is 0, it indicates that no quantization matrix exists and thus all quantization matrices are determined to be default quantization matrices. When the value of scaling_list_present_flag is 1, it indicates that a coded quantization matrix exists.

The decoder can decode information about the method of predicting and decoding the quantization matrix from the parameter set, and can determine the type of prediction decoding method of the quantization matrix based on the decoded information. Here, the parameter set from which the information about the method of predicting and decoding the quantization matrix is decoded can be an adaptive parameter set.

More specifically, as in the example of Table 29, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from a parameter set. For example, when the value of scaling_list_pred_mode_flag is 1, the decoder can predict and decode coefficients in the quantization matrix by scanning according to the Exponential Golomb coding and inverse DPCM method. When the value of scaling_list_pred_mode_flag is 0, the decoder can determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Here, determining these values so that they have the same values can mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded from the parameter set. Here, the parameter set from which the reference quantization matrix ID is decoded may be an adaptive parameter set.

More specifically, as in the example of Table 29, the decoder can decode scaling_list_pred_matrix_id_delta (ie, the reference quantization matrix ID of the quantization matrix to be decoded) from the parameter set. Here, RefMatrixID indicating the reference quantization matrix of the quantization matrix to be decoded can be determined by using scaling_list_pred_matrix_id_delta and Equation 22.

<Equation 22>

RefMatrixID=matrixID-(1+scaling_list_pred_matrix_id_delta)

The decoder can determine the quantization matrix corresponding to RefMatrixID as a reference quantization matrix for the quantization matrix to be decoded, and determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix may mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix for the quantization matrix to be decoded, and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the method for predicting and decoding the decoded quantization matrix is a method for predicting and decoding coefficients in the quantization matrix by scanning based on the Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix from the parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

For example, as in the example of Table 30, the decoder can decode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix) from the parameter set. Here, the encoder can determine whether the default matrix is used by using scaling_list_delta_coef used to calculate nextCoef. That is, when the value of the first nextCoef calculated by decoding scaling_list_delta_coef is 0, the decoder can determine that the corresponding quantization matrix is the default matrix.

In addition, as in the example of Table 30, the decoder can decode scaling_list_dc_coef_res (i.e., the difference between the coefficient values of the quantization matrix corresponding to the DC matrix coefficient) from the parameter set. Here, when the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3) and the default matrix is not used, scaling_list_dc_coef_res can be decoded from (useDefaultScalingMatrixFlag=0).

In relation to a quantization matrix having a size of 16×16 or 32×32 whose DC matrix coefficient is separately decoded, a DC matrix coefficient can be calculated according to Equation 23 by using a value of scaling_list_dc_coef_res and a sum of matrix coefficients existing at a DC position.

<Equation 23>

ScalingFactor[2][matrixID][0][0]=scaling_list_dc_coef_res[0][matrixID]+ScalingFactor[2][matrixID][0][0]where matrixID=0..5

ScalingFactor[3][matrixID][0][0]=scaling_list_dc_coef_res[1][matrixID]+ScalingFactor[3][matrixID][0][0]where matrixID=0..1

In Equation 23, ScalingFactor[2] represents a quantization matrix with a size of 16x16, and ScalingFactor[3] represents a quantization matrix with a size of 32x32. In addition, ScalingFactor[2][matrixID][0][0] represents the DC matrix coefficient within the quantization matrix with a size of 16x16 corresponding to matrixID. ScalingFactor[3][matrixID][0][0] represents the DC matrix coefficient within the quantization matrix with a size of 32x32 corresponding to matrixID.

Meanwhile, the method for encoding/decoding a quantization matrix that uses the coefficient values of the quantization matrix to determine whether a default matrix is being used has the disadvantage that it increases the complexity of processing the coefficient values of the quantization matrix for encoding/decoding. In addition, when the quantization matrix is transmitted, all coefficients within the quantization matrix and the DC matrix coefficients are encoded/decoded. In this case, the improvement in coding efficiency is limited because the DC matrix coefficients are not predicted and encoded/decoded.

In the present invention, in image encoding/decoding, by determining whether a default matrix has been used based on a reference quantization matrix ID, the complexity when encoding/decoding the quantization matrix can be reduced. In addition, by predicting and encoding/decoding the DC matrix coefficient within the quantization matrix, the coding efficiency can be improved. For example, in the examples of Tables 31 and 32, the coding efficiency can be improved by predicting the DC matrix coefficient in the quantization matrix from adjacent AC coefficients based on the high correlation between adjacent coefficients, rather than predicting the DC matrix coefficient from a constant 8. In addition, in the examples of Tables 31 and 32, the storage space used to store the DC matrix coefficient can be reduced because the encoding/decoding sequence of the quantization matrix is made the same as the recovery sequence of the quantization matrix. In addition, in the examples of Tables 31 and 32, it is possible to indicate whether the default matrix has been used by the syntax element "scaling_list_delta_coef" instead of using several syntax elements.

More specifically, the decoder can decode information indicating whether a quantization matrix exists from a parameter set. As in the example of Table 31, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from a parameter set, which is encoded as a parameter set. Here, when the value of scaling_list_present_flag is 0, it indicates that no quantization matrix exists and thus all quantization matrices are determined to be default quantization matrices. When the value of scaling_list_present_flag is 1, it indicates that an encoded quantization matrix exists.

The decoder can decode information about the method of predicting and decoding the quantization matrix from the parameter set, and can determine the type of prediction decoding method of the quantization matrix based on the decoded information. Here, the parameter set from which the information about the prediction decoding method is decoded can be an adaptive parameter set.

For example, as in the example of Table 31, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from a parameter set. In the example of Table 31, when the value of scaling_list_pred_mode_flag is 1, the decoder can predict and decode coefficients in the quantization matrix by scanning the quantization matrix decoded according to the Exponential Golomb coding and inverse DPCM method. When the value of scaling_list_pred_mode_flag is 0, the coefficient values of the quantization matrix to be decoded can be determined to be the same as the coefficient values of the reference quantization matrix, or the coefficient values of the quantization matrix to be decoded can be determined to be the same as the coefficient values of the default matrix. Here, determining these values so that they have the same value can mean using a quantization matrix prediction method that copies the coefficient values of a specific quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded and information on whether a default matrix has been used from the parameter set. Here, the decoded parameter set may be an adaptive parameter set.

More specifically, as in the example of Table 31, the decoder can decode scaling_list_pred_matrix_id_delta (i.e., information about the reference quantization matrix ID of the quantization matrix to be decoded and whether a default matrix has been used) from the parameter set. Here, the RefMatrixID indicating the reference quantization matrix or the default matrix of the quantization matrix to be decoded can be determined by using scaling_list_pred_matrix_id_delta and Equation 24.

<Equation 24>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta

If the value of RefMatrixID is the same as the value of matrixID, the coefficient values of the quantization matrix to be decoded corresponding to sizeID and matrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. Here, the default matrix represents the default matrix corresponding to sizeID and matrixID. In addition, in Equation 24, when the value of scaling_list_pred_matrix_id_delta is 0, it means that the value of RefMatrixID is the same as the value of matrixID. When the value of RefMatrixID is different from the value of matrixID, the quantization matrix corresponding to RefMatrixID can be determined as the reference quantization matrix of the quantization matrix to be decoded, and the coefficient values of the quantization matrix to be decoded are determined to be the same as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded to be the same as the coefficient values of the reference quantization matrix can mean using such a quantization matrix prediction method, which determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded, and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the method for predicting and decoding the decoded quantization matrix is a method for predicting and decoding the coefficients in the quantization matrix by scanning the quantization matrix according to the Exponential Golomb coding and inverse DPCM method, then the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix from the parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

In addition, as in the example of Table 32, the decoder can decode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix) from the parameter set. As in the example of Table 32, the decoder can decode scaling_list_dc_coef_res (i.e., the difference between the coefficient values of the quantization matrix corresponding to the DC matrix coefficient) from the parameter set. Here, when the size of the quantization matrix to be decoded is a 16x16 (sizeID=2) or 32x32 (sizeID=3) quantization matrix and the default matrix is not used, scaling_list_dc_coef_res can be decoded from (useDefaultScalingMatrixFlag=0).

In relation to a quantization matrix having a 16×16 size or a quantization matrix having a 32×32 size whose DC matrix coefficient is separately decoded, a DC matrix coefficient can be calculated according to Equation 25 by using the value of scaling_list_dc_coef_res and the sum of coefficients of a matrix existing at a DC position.

<Equation 25>

ScalingFactor[2][matrixID][0][0]=scaling_list_dc_coef_res[0][matrixID]+ScalingFactor[2][matrixID][0][0]where matrixID=0..5

ScalingFactor[3][matrixID][0][0]=scaling_list_dc_coef_res[1][matrixID]+ScalingFactor[3][matrixID][0][0]where matrixID=0..1

In Equation 25, ScalingFactor[2] represents a quantization matrix of 16x16 size, and ScalingFactor[3] represents a quantization matrix of 32x32 size. In addition, ScalingFactor[2][matrixID][0][0] represents the DC matrix coefficient within the quantization matrix of 16x16 size corresponding to the corresponding matrixID, and ScalingFactor[3][matrixID][0][0] represents the DC matrix coefficient within the quantization matrix of 32x32 size corresponding to the corresponding matrixID.

As described above in the example related to the encoder, in conventional quantization matrix encoding/decoding methods, the quantization matrix is copied by using the size of the quantization matrix when performing quantization and inverse quantization (rather than using the size of the quantization matrix when performing encoding/decoding). Therefore, the encoding efficiency of the quantization matrix is limited because the quantization matrix must be copied from a limited number of quantization matrices. However, in the present invention, the encoding efficiency can be improved and the degree of freedom of predicting the quantization matrix can be increased because the quantization matrix can be predicted from a quantization matrix having the same size as the quantization matrix when performing encoding/decoding.

More specifically, the decoder can decode information indicating whether a quantization matrix exists from the parameter set. As in the examples of Tables 33 and 34, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from the parameter set. For example, when the value of scaling_list_present_flag is 0, it indicates that no quantization matrix exists and thus all quantization matrices are determined to be default quantization matrices. When the value of scaling_list_present_flag is 1, it indicates that a coded quantization matrix exists.

In addition, the decoder can decode information about the method of predicting and decoding the quantization matrix from the parameter set, and can determine the type of prediction decoding method of the quantization matrix based on the decoded information. Here, the parameter set from which the information about the prediction decoding method is decoded can be an adaptive parameter set.

More specifically, as in the examples of Tables 33 and 34, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from a parameter set. For example, when the value of scaling_list_pred_mode_flag is 1, the decoder can predict and decode coefficients in the quantization matrix by scanning the quantization matrix decoded according to the Exponential Golomb coding and inverse DPCM methods. When the value of scaling_list_pred_mode_flag is 0, the decoder can determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Here, determining these values so that they have the same values can mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded from the parameter set. Here, the ID information (identifier) about the reference quantization matrix can include one or more of the size of the reference quantization matrix of the quantization matrix to be decoded and the reference quantization matrix. In addition, the parameter set from which the reference quantization matrix ID is decoded may be an adaptive parameter set.

For example, as in the example of Table 33, the decoder can decode scaling_list_pred_matrix_id_delta (i.e., ID information about the reference quantization matrix of the quantization matrix to be decoded) from the parameter set. Here, RefSizeID (i.e., the size of the reference quantization matrix of the quantization matrix to be decoded) and RefMatrixID indicating the reference quantization matrix can be determined by using scaling_list_pred_size_matrix_id_delta and Equation 26.

<Equation 26>

RefSizeID=sizeID-(scaling_list_pred_size_matrix_id_delta/6)

RefMatrixID=scaling_list_pred_size_matrix_id_delta%6

In addition, as in the example of Table 34, the decoder can decode scaling_list_pred_size_id_delta and scaling_list_pred_size_matrix_id_delta (i.e., ID information of the reference quantization matrix of the quantization matrix to be decoded) from the parameter set. Here, RefSizeID can be determined by using the value of scaling_list_pred_size_id_delta and Equation 27, and RefMatrixID indicating the reference quantization matrix of the quantization matrix to be decoded can be determined by using scaling_list_pred_matrix_id_delta and Equation 28.

<Equation 27>

RefSizeID=sizeID-scaling_list_pred_size_id_delta

<Equation 28>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta

The coefficient values of the quantization matrix to be decoded can also be determined by the coefficient values of the reference quantization matrix whose sizeID is equal to RefSizeID and whose matrixID is equal to RefMatrixID. That is, the decoder can copy the reference quantization matrix to the quantization matrix to be decoded. Determining the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix can mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefSizeID and RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded, and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

Through the examples of Tables 33 and 34, the quantization matrix can be predicted from the quantization matrix having the same sizeID, and can also be predicted from the quantization matrix having the same matrix size when performing encoding/decoding but having a different sizeID.

Furthermore, in the examples of Tables 33 and 34, the values of scaling_list_pred_size_matrix_id_delta, scaling_list_pred_size_id_delta, and scaling_list_pred_matrix_id_delta may be limited to values within a specific range. For example, scaling_list_pred_size_matrix_id_delta may be limited to values within a range of 0 to 17, scaling_list_pred_size_id_delta may be limited to values within a range of 0 to 2, and scaling_list_pred_matrix_id_delta may be limited to values within a range of 0 to 5.

Furthermore, in the examples of Tables 33 and 34 , the decoder may not predict the quantization matrix to be decoded from a quantization matrix having a larger size than the quantization matrix to be decoded.

In addition, in the examples of Tables 33 and 34, when the quantization matrix to be decoded is predicted from a quantization matrix having an 8x8 size, the decoder can predict the value at the corresponding position by determining the value corresponding to the position of the DC matrix coefficient within the 8x8 size quantization matrix as the DC matrix coefficient. In addition, when the quantization matrix to be decoded is predicted from a quantization matrix having a 16x16 or 32x32 size, the decoder can also predict the DC matrix coefficient.

Meanwhile, if the method for predicting and decoding a quantization matrix is a method for predicting and decoding coefficients within a quantization matrix by scanning a quantization matrix according to an Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded within the quantization matrix from a parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

More specifically, as in the example of Table 35, if the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the decoder can decode scaling_list_dc_coef_minus8 (ie, DC matrix coefficient) from the parameter set.

Furthermore, as in the example of Table 35, the decoder can decode scaling_list_delta_coef (ie the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be encoded) from the parameter set.

In addition, the decoder can determine whether the default matrix has been used by using scaling_list_delta_coef used to calculate scaling_list_dc_coef_minus8 or nextCoef. That is, if the value of scaling_list_dc_coef_minus8 is decoded as -8, the corresponding quantization matrix can be determined as the default matrix. If the value of the first nextCoef calculated by decoding scaling_list_delta_coef is 0, the corresponding quantization matrix can be determined as the default matrix.

As described above in the example of the encoder, in the conventional quantization matrix encoding/decoding method, the complexity in the processing of the coefficient values of the encoding/decoding quantization matrix is increased because the coefficient values of the quantization matrix are used to determine whether a default matrix has been used. In addition, the quantization matrix is copied from a limited number of quantization matrices because the quantization matrix is copied by using the size of the quantization matrix when quantization and inverse quantization are performed (instead of using the size of the quantization matrix when encoding/decoding is performed). However, in the present invention, by determining whether a default matrix has been used based on a reference quantization matrix ID, the complexity of calculation when encoding/decoding the quantization matrix can be reduced. In addition, in the present invention, by predicting the quantization matrix from a quantization matrix having the same size as the quantization matrix when encoding/decoding is performed, the coding efficiency can be improved and the degree of freedom of predicting the quantization matrix can be increased.

More specifically, the decoder can decode information indicating whether a quantization matrix exists from the parameter set. As in the examples of Tables 36 and 37, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from the parameter set. For example, when the value of scaling_list_present_flag is 0, it indicates that there is no quantization matrix, and thus all quantization matrices can be determined as default quantization matrices. When the value of scaling_list_present_flag is 1, it indicates that a coded quantization matrix exists.

The decoder can decode information about a method of predicting and decoding a quantization matrix from a parameter set, and can determine the type of method of predicting and decoding a quantization matrix based on the decoded information. Here, the decoded parameter set may be an adaptive parameter set.

As in the examples of Tables 36 and 37, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from a parameter set. Here, when the value of scaling_list_pred_mode_flag is 1, the decoder can decode the quantization matrix by scanning according to the Exponential Golomb coding and inverse DPCM method so as to predict and decode the coefficients in the quantization matrix. When the value of scaling_list_pred_mode_flag is 0, the decoder can determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix, or determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the default matrix. Here, determining these values so that they have the same values can mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded and information on whether a default matrix has been used from the parameter set. Here, the ID information (identifier) about the reference quantization matrix can include one or more of the size of the reference quantization matrix of the quantization matrix to be decoded and the reference quantization matrix. In addition, the decoded parameter set can be an adaptive parameter set.

For example, as in the example of Table 36, the decoder can decode scaling_list_pred_size_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be decoded and information on whether the default matrix has been used) from the parameter set. Here, RefSizeID and RefMatrixID indicating the reference quantization matrix can be determined by using scaling_list_pred_size_matrix_id_delta and Equation 29.

<Equation 29>

RefSizeID=sizeID-(scaling_list_pred_size_matrix_id_delta/6)

RefMatrixID=scaling_list_pred_size_matrix_id_delta%6

In addition, as in the example of Table 37, the decoder can decode scaling_list_pred_size_id_delta and scaling_list_pred_size_matrix_id_delta (i.e., the reference quantization matrix ID of the quantization matrix to be decoded and information on whether the default matrix is used) from the parameter set. Here, RefSizeID can be determined by using the value of scaling_list_pred_size_id_delta and Equation 30, and RefMatrixID indicating the reference quantization matrix or the default matrix of the quantization matrix to be decoded can be determined by using the value of scaling_list_pred_matrix_id_delta and Equation 31.

<Equation 30>

RefSizeID=sizeID-scaling_list_pred_size_id_delta

<Equation 31>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta

If the value of RefMatrixID is equal to the value of matrixID, the coefficient values of the quantization matrix to be decoded corresponding to sizeID and matrixID can be determined to be the same as the coefficient values of the default matrix defined in the encoder and/or decoder. Here, the default matrix represents the default matrix corresponding to sizeID and matrixID. In addition, in Equation 31, when the value of scaling_list_pred_matrix_id_delta is 0, it means that the value of RefMatrixID is equal to the value of matrixID.

If the value of RefMatrixID is different from the value of matrixID, the quantization matrix corresponding to RefSizeID and RefMatrixID is determined as the reference quantization matrix of the quantization matrix to be decoded, and the coefficient values of the quantization matrix to be decoded can be determined to be the same as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded to be the same as the coefficient values of the reference quantization matrix may mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefSizeID and RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

According to the example of Table 36 or 37, the quantization matrix can be predicted from the quantization matrix having the same sizeID, and the quantization matrix can also be predicted from the quantization matrix having the same matrix size when performing encoding/decoding but having a different sizeID.

Furthermore, in the examples of Tables 36 or 37, the values of scaling_list_pred_size_matrix_id_delta, scaling_list_pred_size_id_delta, and scaling_list_pred_matrix_id_delta may be limited to values within a specific range. For example, scaling_list_pred_size_matrix_id_delta may be limited to values within a range of 0 to 17, scaling_list_pred_size_id_delta may be limited to values within a range of 0 to 2, and scaling_list_pred_matrix_id_delta may be limited to values within a range of 0 to 5.

Furthermore, in the example of Table 36 or 37, the decoder may not predict a quantization matrix from a quantization matrix having a larger size than a quantization matrix to be decoded.

In addition, when prediction is performed from a quantization matrix having an 8x8 size, the decoder can predict the value at the corresponding position by determining the value corresponding to the position of the DC matrix coefficient within the 8x8 size quantization matrix as the DC matrix coefficient. In addition, when prediction is performed from a quantization matrix having a 16x16 size or a 32x32 size, the decoder can also predict the DC matrix coefficient.

Meanwhile, if the method for predicting and decoding a quantization matrix is a method for predicting and decoding coefficients within a quantization matrix by scanning a quantization matrix according to an Exponential Golomb coding and inverse DPCM method, the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded within the quantization matrix from a parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

As in the example of Table 38, if the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the decoder can decode scaling_list_dc_coef_minus8 (ie, DC matrix coefficients) from the parameter set.

As in the example of Table 38, the decoder can decode scaling_list_delta_coef (ie the difference between the coefficient values of the previously encoded quantization matrix and the coefficient values of the quantization matrix to be encoded) from the parameter set.

As described above in the example of the encoder, in the conventional quantization matrix encoding/decoding method, the improvement of encoding efficiency is limited because the coefficient value of the quantization matrix is encoded by not considering the frequently occurring coefficient value when encoding/decoding the first coefficient in the quantization matrix. However, in the present invention, encoding efficiency can be improved because the first coefficient in the quantization matrix can be predicted and encoded/decoded using the frequently occurring coefficient value. If the first coefficient value or DC matrix coefficient value of the default matrix is defined as 16 and the first coefficient value or DC matrix coefficient value of the non-default matrix is distributed based on 16, if the first coefficient value or DC matrix coefficient value in the quantization matrix to be encoded/decoded is encoded/decoded by predicting the first coefficient value or DC matrix coefficient value from the constant 16, encoding efficiency can be improved.

More specifically, the decoder can decode information indicating whether a quantization matrix exists from the parameter set. As in the example of Table 39, the decoder can decode scaling_list_present_flag (i.e., information indicating whether a quantization matrix exists in the bitstream) from the parameter set. For example, when the value of scaling_list_present_flag is 0, it indicates that there is no quantization matrix and thus all quantization matrices can be determined as default quantization matrices. When the value of scaling_list_present_flag is 1, it indicates that a coded quantization matrix exists.

In addition, the decoder can decode information about the method of predicting and decoding the quantization matrix from the parameter set, and can determine the type of predictive decoding method used for the quantization matrix based on the decoded information. Here, the parameter set from which the information about the predictive encoding method is decoded can be an adaptive parameter set.

As in the example of Table 39, the decoder can decode scaling_list_pred_mode_flag (i.e., information about a method of predicting and decoding a quantization matrix) from a parameter set. For example, when the value of scaling_list_pred_mode_flag is 1, the decoder decodes the quantization matrix by scanning according to the Exponential Golomb coding and inverse DPCM method to predict and decode coefficients in the quantization matrix. When the value of scaling_list_pred_mode_flag is 0, the decoder determines the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Here, determining these values so that they have the same values can mean using a quantization matrix prediction method that copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded.

If the value of scaling_list_pred_mode_flag is 0, the decoder can decode the reference quantization matrix ID of the quantization matrix to be decoded from the parameter set. Here, the parameter set from which the reference quantization matrix ID is decoded may be an adaptive parameter set.

In addition, as in the example of Table 39, the decoder can decode scaling_list_pred_matrix_id_delta (ie, the reference quantization matrix ID of the quantization matrix to be decoded) from the parameter set. Here, RefMatrixID indicating the reference quantization matrix of the quantization matrix to be decoded can be determined by using scaling_list_pred_matrix_id_delta and Equation 32.

<Equation 32>

RefMatrixID=matrixID-(1+scaling_list_pred_matrix_id_delta)

The decoder can determine the quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded, and determine the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix. Determining the coefficient values of the quantization matrix to be decoded so that they have the same values as the coefficient values of the reference quantization matrix may mean using a quantization matrix prediction method that determines the reference quantization matrix corresponding to RefMatrixID as the reference quantization matrix of the quantization matrix to be decoded and copies the coefficient values of the reference quantization matrix to the coefficient values of the quantization matrix to be decoded. Here, the value of scaling_list_pred_matrix_id_delta can be a positive integer value.

If the method for predicting and decoding the decoded quantization matrix is a method for predicting and decoding the coefficients in the quantization matrix by scanning the quantization matrix according to the Exponential Golomb coding and inverse DPCM method, then the decoder can decode the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded in the quantization matrix from the parameter set. Here, the parameter set from which the difference is decoded may be an adaptive parameter set.

As in the example of Table 40, the decoder can decode scaling_list_delta_coef (i.e., the difference between the coefficient values of the previously decoded quantization matrix and the coefficient values of the quantization matrix to be decoded) from the parameter set. Here, the decoder can set the predicted value of the first coefficient value to 16, as in nextCoef=16.

In addition, as in the example of Table 40, if the size of the quantization matrix to be decoded is 16x16 (sizeID=2) or 32x32 (sizeID=3), the decoder can decode scaling_list_dc_coef_minus16 (i.e., the coefficient value of the quantization matrix corresponding to the DC matrix coefficient) from the parameter set. The value of scaling_list_dc_coef_minus16 means the DC matrix coefficient calculated assuming that the prediction value is 16.

In addition, the decoder can determine whether the default matrix is used by using scaling_list_delta_coef used to calculate scaling_list_dc_coef_minus16 or nextCoef. For example, if the value of scaling_list_dc_coef_minus16 is decoded as -16, the corresponding quantization matrix can be determined as the default matrix. If the first nextCoef value calculated by decoding scaling_list_delta_coef is 0, the corresponding quantization matrix can be determined as the default matrix.

In the examples of these tables and the examples of Tables 39 and 40, nextCoef can be set to 16 and the value of scaling_list_dc_coef_minus16 can mean the DC matrix coefficient calculated assuming that the prediction value is 16. If the value of scaling_list_dc_coef_minus16 is decoded as -16, the decoder can determine the corresponding quantization matrix as the default matrix.

The embodiments of encoding/decoding and transmission/reception of information on a quantization matrix according to the present invention have been described so far with reference to tables and drawings.

In the examples of Tables 18 and 19, the examples of Tables 20 and 21, the examples of Tables 23 and 24, the examples of Tables 25 and 26, the examples of Tables 27 and 28, the examples of Tables 29 and 30, the examples of Tables 31 and 32, the examples of Tables 33 and 34, the examples of Tables 36 and 38, the examples of Tables 37 and 38, and the examples of Tables 39 and 40, examples of the grammatical structure according to the present invention have been described with reference to two tables, but this is only for convenience of description, and the present invention is not limited to these examples.

For example, in the example of the syntax structure, scaling_list_pred_mode_flag is illustrated to indicate a method of predicting a quantization matrix. When the value of scaling_list_pred_mode_flag is 0, the quantization matrix is obtained by matrix copying, and when the value of scaling_list_pred_mode_flag is 1, the quantization matrix is obtained by predicting the matrix coefficients from the previous matrix coefficients within the quantization matrix.

For example, in the examples of Tables 23 and 24, when the value of scaling_list_pred_mode_flag is 1, the quantization matrix is obtained by obtaining the syntax of the quantization matrix (that is, the syntax of the scaling list "scaling_list"). However, this can be solved in a single syntax structure. It should be noted that constructing two or more syntax structures using one syntax structure having the same meaning does not change the content of the present invention, but falls within the scope of the present invention.

Table 41 shows an example in which two syntax structures of Tables 23 and 24 are formed into one syntax structure. Similar to the examples of Tables 23 and 24, the encoder can encode information about the quantization matrix of Table 41 as a parameter set including at least one of a sequence parameter set and a picture parameter set, and the decoder can decode information about the quantization matrix of Table 41 from the parameter set including at least one of a sequence parameter set and a picture parameter set.

<Form 41>

As described above, the examples of Tables 23 and 24 are the same as the example of Table 41 except that the number of grammatical structures is two or one.

As in the example of Table 41, the encoder can indicate the prediction mode of the matrix through scaling_list_pred_mode_flag. For example, when copying between quantization matrices, the value of scaling_list_pred_mode_flag is determined to be 0 and encoded. When the coefficients of the matrix are predicted and encoded in the quantization matrix, the value of scaling_list_pred_mode_flag is determined to be 1 and encoded. As described above, copying the quantization matrix means using the default quantization matrix as the quantization matrix to be encoded or using the reference quantization matrix as the quantization matrix to be encoded. As described above, the method of predicting the coefficients of the matrix means the method of predicting and encoding the coefficients in the quantization matrix.

If copying of the quantization matrix is performed (scaling_list_pred_mode_flag==0), scaling_list_pred_matrix_id_delta is transmitted. As described above, scaling_list_pred_matrix_id_delta specifies a reference quantization matrix or a default quantization matrix used to derive the currently encoded quantization matrix.

For example, if the quantization matrix to be encoded is determined to be the default quantization matrix, the value of scaling_list_pred_matrix_id_delta can be determined to be 0 and encoded. In other words, this corresponds to the case where the quantization matrix to be currently encoded is inferred from the default quantization matrix. The default quantization matrix can be specified by Tables 7 and 8.

If the quantization matrix to be currently encoded is determined from the reference quantization matrix, the value of scaling_list_pred_matrix_id_delta can be determined to a value other than 0 and encoded. That is, this corresponds to the case where the quantization matrix to be currently encoded (i.e., ScalingList) is determined from the reference quantization matrix as in Equation 33.

<Equation 33>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta[sizeID][matrixID]

ScalingList[sizeID][matrixID][i]＝ScalingList[sizeID][RefMatrixId][i]

In Equation 33, the value of scaling_list_pred_matrix_id_delta is specified by sizeID and matrixID, and the index 'i' specifies the position of the coefficient within the quantization matrix.

If prediction and encoding are performed within the quantization matrix (scaling_list_pred_mode_flag == 1), matrix coefficients for a 4x4 quantization matrix, matrix coefficients for an 8x8 quantization matrix, matrix coefficients for a 16x16 quantization matrix including a DC matrix coefficient, and matrix coefficients for a 32x32 quantization matrix including a DC matrix coefficient can be encoded. Here, the total number of matrix coefficients to be encoded can be calculated using coefNum=Min(64,(1<<(4+(sizeId<<1)))). In addition, each of the 16x16 quantization matrix and the 32x32 quantization matrix can be downsampled to an 8x8 quantization matrix and encoded.

The decoder can decode the syntax elements of table 41 from the bitstream, perform inverse quantization on the decoded syntax elements, and reconstruct the image using these results.

As in the example of Table 41, the decoder can determine the prediction mode of the matrix indicated by the received scaling_list_pred_mode_flag. For example, when the value of scaling_list_pred_mode_flag is 0, the decoder can perform a copy between quantization matrices. When the value of scaling_list_pred_mode_flag is 1, the decoder can predict the matrix coefficients in the quantization matrix. Therefore, the decoder can obtain the (inverse) quantization matrix to be used in inverse quantization. It should be noted that in this specification, the quantization matrix to be encoded applied in the case of quantization and the quantization matrix to be decoded applied in the case of inverse quantization are both referred to as quantization matrices, but this is only for ease of description. The matrix applied to quantization and the matrix applied to inverse quantization can have an inverse relationship, and the quantization matrix used in inverse quantization can be referred to as a scaling list.

As described above, the copy of the quantization matrix means determining a default quantization matrix as the quantization matrix to be decoded or determining a reference quantization matrix as the quantization matrix to be decoded. As described above, the method of predicting coefficients of a matrix means a method of predicting and decoding coefficients in a quantization matrix.

If copying of the quantization matrix is performed (scaling_list_pred_mode_flag==0), the decoder specifies a reference quantization matrix or a default quantization matrix used to derive a quantization matrix to be currently decoded.

For example, when the value of scaling_list_pred_matrix_id_delta is 0, the decoder can determine the quantization matrix to be decoded as the default quantization matrix. That is, the quantization matrix to be currently decoded can be inferred from the default quantization matrix. The default quantization matrix can be specified by Tables 7 and 8.

When the value of scaling_list_pred_matrix_id_delta is non-zero, the decoder can determine the quantization matrix to be currently decoded from the reference quantization matrix. That is, the quantization matrix to be currently decoded, ie, ScalingList, can be determined from the reference quantization matrix as in Equation 34.

<Equation 34>

RefMatrixID=matrixID-scaling_list_pred_matrix_id_delta[sizeID][matrixID]

ScalingList[sizeID][matrixID][i]＝ScalingList[sizeID][RefMatrixId][i]

In Equation 34, the value of scaling_list_pred_matrix_id_delta is specified by sizeID and matrixID, and the index 'i' specifies the position of the coefficient within the quantization matrix.

If prediction and decoding within the quantization matrix are performed (scaling_list_pred_mode_flag == 1), the decoder can decode matrix coefficients for a 4x4 quantization matrix, matrix coefficients for an 8x8 quantization matrix, matrix coefficients for a 16x16 quantization matrix including a DC matrix coefficient, and matrix coefficients for a 32x32 quantization matrix including a DC matrix coefficient. Here, the total number of decoded matrix coefficients can be calculated using coefNum=Min(64,(1<<(4+(sizeId<<1)))). Here, since each of the 16x16 quantization matrix and the 32x32 quantization matrix is downsampled to an 8x8 quantization matrix when encoding, the 8x8 quantization matrix can be restored to a 16x16 quantization matrix and a 32x32 quantization matrix by upsampling or interpolating the 8x8 quantization matrix. Furthermore, if upsampling or interpolation is used, the DC matrix coefficients do not use interpolated values, but can be replaced with values derived from additional signaled values (such as scaling_list_dc_coef_minus8).

The embodiments of the syntax structure and examples of encoding and decoding using the syntax structure have been described so far with reference to tables. In the aforementioned examples, examples of encoding and decoding have been described using the syntax structure, but the present invention is not limited thereto. For example, only the syntax structure table may be used in encoding or decoding.

FIG6 is a flowchart schematically illustrating an example of a method of performing inverse quantization according to the present invention.

6 , the decoder can obtain an identifier indicating whether a quantization matrix exists in a parameter set at step S610. The information indicating whether a quantization matrix exists in a parameter set may be scaling_list_present_flag in the example of the aforementioned table.

Here, the presence of the quantization matrix in the parameter set includes information about the presence of the quantization matrix in the parameter set (e.g., scaling_list_pred_mode_flag, scaling_list_pred_matrix_id_delta, scaling_list_dc_coef_minus8, and scaling_list_delta_coef). In addition, before obtaining the identifier indicating whether the quantization matrix exists, scaling_list_enable_flag (i.e., an identifier indicating whether the quantization matrix is used) can be obtained. If the quantization matrix is used by obtaining scaling_list_enable_flag, an identifier indicating whether the quantization matrix exists can be obtained.

Here, the parameter set may be a sequence parameter set or a picture parameter set through which information on a quantization matrix is transmitted.

The decoder can determine whether the quantization matrix exists in the parameter set based on the identifier in step S620. For example, when the value of scaling_list_present_flag is 1, the decoder can determine that the quantization matrix exists in the parameter set. When the value of scaling_list_present_flag is 0, the decoder can determine that the quantization matrix does not exist in the parameter set.

If the quantization matrix does not exist in the parameter set as a result of the determination (i.e., if it is determined that the quantization matrix does not exist in the parameter set), the decoder may not use the quantization matrix in inverse quantization in step S630, may use a quantization matrix with the same matrix coefficient 16 in inverse quantization (i.e., a flat matrix), or may determine all quantization matrices as default quantization matrices in inverse quantization.

If the quantization matrix exists in the parameter set as a result of the determination (i.e., if it is determined that the quantization matrix exists in the parameter set), the decoder may obtain information about the quantization matrix according to the size of each quantization matrix or the type of the default quantization matrix in step S640. Here, the type of the quantization matrix may include at least one of a quantization matrix for inverse quantization of a transform coefficient of an intra residual block, a quantization matrix for inverse quantization of a transform coefficient of an inter residual block, a quantization matrix for inverse quantization of a transform coefficient of a luma residual block, and a quantization matrix for inverse quantization of a transform coefficient of a chroma residual block, or a combination thereof.

The decoder can perform inverse quantization in step S650 by using the obtained quantization matrix. If the quantization matrix does not exist in the parameter set, the decoder can perform inverse quantization without using the quantization matrix determined in step S630, or can perform inverse quantization so that a quantization matrix with the same matrix coefficient of 16 (i.e., a flat matrix) is performed in the inverse quantization, or all quantization matrices are used as default quantization matrices in the inverse quantization. The prediction of the coefficients of the quantization matrix and the use of the default quantization matrix have been described above in conjunction with the aforementioned embodiments. If the quantization matrix exists in the parameter set, the decoder can obtain the corresponding quantization matrix and use the obtained quantization matrix in the inverse quantization. The decoder can reconstruct the image based on the inverse quantized signal described above with reference to FIG2.

6, an example in which the encoder transmits an identifier indicating whether a quantization matrix exists is illustrated, but this is merely an example of the present invention. As described above, if information about the quantization matrix is transmitted, information indicating whether a quantization matrix exists may not be transmitted in addition.

7 is a diagram schematically illustrating an example of a method of obtaining information about a quantization matrix when a quantization matrix exists in a parameter set, and performing inverse quantization by using the information. The method of FIG7 may correspond to (1) a method including steps S640 and S650 of FIG6 , and (2) a method of obtaining a quantization matrix and performing inverse quantization using the obtained quantization matrix, although an additional indicator indicating whether a quantization matrix exists is not transmitted, a quantization matrix exists in a parameter set, and the encoder transmits information about the quantization matrix. Method (1) is the same as method (2) except whether information about whether a quantization matrix exists is transmitted through an additional identifier. In FIG7 , the decoder can decode information about the quantization matrix from a parameter set including at least one of a sequence parameter set and a picture parameter set.

In the example of FIG7, in order to reduce the complexity when encoding/decoding the quantization matrix, if the ID value of the reference quantization matrix used to predict the quantization matrix to be decoded is the same as the ID value of the quantization matrix to be decoded, the decoder does not decode the quantization matrix to be decoded, but can use the quantization matrix already included in the decoder when performing inverse quantization. Here, the quantization matrix already included in the decoder may be a default quantization matrix.

More specifically, referring to Figure 7, if the quantization matrix exists in the parameter set, the decoder can determine the method for predicting the quantization matrix in step S710. The presence of the quantization matrix in the parameter set includes the presence of information about the quantization matrix in the parameter set (e.g., scaling_list_pred_mode_flag, scaling_list_pred_matrix_id_delta, scaling_list_dc_coef_minus8, and scaling_list_delta_coef).

Referring to the aforementioned example, a method for predicting a quantization matrix can be determined based on the value of the syntax element "pred_mode_flag" received from the encoder. To clarify that the prediction method is used for the quantization matrix, pred_mode_flag may be represented as scaling_list_pred_mode_flag in the aforementioned example, etc. The method for predicting the quantization matrix indicated by pred_mode_flag may be any of the following: (1) a method of using a quantization matrix already included in the decoder without change and (2) a method of receiving a value of a quantization matrix and performing inverse DPCM between coefficient values of the quantization matrix in the quantization matrix.

For example, when the value of pred_mode_flag is 0, the decoder can use the quantization matrix included therein (i.e., the decoded quantization matrix (or reference matrix) or the default matrix). When the value of pred_mode_flag is 1, the decoder can predict and decode the coefficients in the quantization matrix based on the received information.

If the method for predicting the quantization matrix is a method of using the quantization matrix already included in the decoder without change, the decoder can obtain ID information about the quantization matrix in step S720. The ID information of the quantization matrix is information about the quantization matrix already included in the decoder, and the ID information can correspond to scaling_list_pred_matrix_id_delta, pred_matrix_id_delta, etc. described in the above example.

The decoder can determine in step S730 whether the quantization matrix specified by the ID information is the same as the quantization matrix to be currently decoded. pred_matrix_id_delta specifies the reference quantization matrix used to derive the quantization matrix. To clarify that pred_matrix_id_delta is for the quantization matrix, pred_matrix_id_delta can be expressed as scaling_list_pred_matrix_id_delta as in the above example.

When the value of scaling_list_pred_matrix_id_delta is 0, the decoder can use the default quantization matrix specified by the information on the quantization matrix (SizeID and/or MatrixID) as the quantization matrix to be decoded.

When the value of scaling_list_pred_matrix_id_delta is non-zero, the decoder can derive the quantization matrix to be decoded from the decoded reference quantization matrix, because the matrixID specifying the quantization matrix to be decoded (or the type of quantization matrix) and the RefMatrixID specifying the reference quantization matrix have the relationship "scaling_list_pred_matrix_id_delta = matrixID - RefMatrixID" with reference to the aforementioned example.

If, as a result of the determination in step S730, the quantization matrix specified by the quantization matrix ID information is determined to be not the same as the quantization matrix to be decoded (i.e., !scaling_list_pred_matrix_id_delta == 0 or matrixID != RefMatrixID), the decoder can use the quantization matrix ID information to determine the quantization matrix to be used when performing inverse quantization in step S740. In this case, the decoder can determine the quantization matrix to be used when performing inverse quantization based on the quantization matrix ID information "scaling_list_pred_matrix_id_delta" as in the aforementioned table.

If, as a result of the determination in step S730, the quantization matrix specified by the quantization matrix ID information is determined to be the same as the quantization matrix to be decoded (i.e., scaling_list_pred_matrix_id_delta == 0 or matrixID == RefMatrixID), the decoder can use the default quantization matrix included therein in step S750. Here, the default quantization matrix can be determined by using Tables 7 and 8.

If the method used to predict the quantization matrix in step S710 is a method using an inverse DPCM method between the coefficient values of the quantization matrix, the decoder can initialize the coefficient values of the quantization matrix in step S760. For example, the decoder can initialize the coefficient value "nextcoef" of the quantization matrix by setting the coefficient value to a constant. The constant set when initializing the coefficient value "nextcoef" can be either 8 or 16, as in the example of the aforementioned table.

The decoder can decode the differences between the coefficients in the quantization matrix received from the encoder at step S770. The differences between the coefficients in the quantization matrix can be specified by a syntax element such as delta_coef. To clarify that this syntax element is for the quantization matrix, delta_coef can be referred to as scaling_list_delta_coef as in the example of the previous table.

The decoder can derive the coefficient values of the quantization matrix at step S780. The decoder can derive the coefficient values of the quantization matrix to be decoded (i.e., the current quantization matrix) by adding the difference between the coefficients in the quantization matrix to the coefficient values of the previously decoded quantization matrix. For example, the decoder can derive the coefficient values of the current quantization matrix by using the relationship "nextcoef = (nextcoef = delta_coef + 256) % 256" as in the aforementioned equation.

The decoder can determine whether the quantization matrix has been derived in step S790. If it is determined as a result of the determination that the quantization matrix has not been derived (ie, if all coefficient values within the quantization matrix have not been decoded), the decoder returns to step S770 and performs subsequent steps.

The decoder can perform inverse quantization by using the obtained quantization matrix at step S650.

Meanwhile, although not clearly described in the example of FIG. 7 , when deriving coefficient values of a quantization matrix, a DC matrix coefficient of a quantization matrix having a specific size may be first derived as in the aforementioned embodiment.

FIG8 is a diagram schematically illustrating another example of a method of obtaining information about a quantization matrix when a quantization matrix exists in a parameter set and performing inverse quantization by using the information. The method of FIG8 may correspond to (1) a method including steps S640 and S650 of FIG6 , and (2) a method of obtaining a quantization matrix and performing inverse quantization using the obtained quantization matrix, although an additional indicator indicating whether a quantization matrix exists is not transmitted, a quantization matrix exists in a parameter set, and the encoder transmits information about the quantization matrix. Method (1) is the same as method (2) except for whether information about whether a quantization matrix exists is transmitted by an additional identifier.

In the example of FIG. 8 , in order to prevent transmission of unnecessary quantization matrices, if the first value of the quantization matrix to be decoded is a specific value, the decoder does not decode the quantization matrix to be decoded and can use a default quantization matrix already included therein when performing inverse quantization.

8 , if a quantization matrix exists in a parameter set, the decoder can determine a method for predicting the quantization matrix in step S810. The existence of the quantization matrix in the parameter set includes the existence of information on the quantization matrix in the parameter set.

If the method for predicting the quantization matrix is a method of using the quantization matrix already included in the decoder without change, the decoder can obtain ID information on the quantization matrix in step S820.

The ID information of the quantization matrix is information about a quantization matrix that can be identified in the decoder, and the ID information can correspond to scaling_list_pred_matrix_id_delta, pred_matrix_id_delta, etc. that have been described in the aforementioned example.

The decoder can determine a quantization matrix to be used when performing inverse quantization by using the ID information of the quantization matrix in step S830. The decoder can determine a quantization matrix indicated by ID information such as scaling_list_pred_matrix_id_delta or pred_matrix_id_delta.

If the method used to predict the quantization matrix in step S810 is a method using an inverse DPCM method between the coefficient values of the quantization matrix, the decoder can initialize the coefficient values of the quantization matrix in step S840. For example, the decoder can initialize the coefficient value "nextcoef" of the quantization matrix by setting the coefficient value to a constant. The constant set when initializing the coefficient value "nextcoef" can be either 8 or 16, as in the example of the aforementioned table.

The decoder can decode the difference between the coefficients in the quantization matrix received from the encoder at step S850. The difference between the coefficients in the quantization matrix can be specified by a syntax element such as delta_coef.

The decoder can derive the coefficient values of the quantization matrix at step S860. The decoder can derive the coefficient values of the quantization matrix to be decoded (i.e., the current quantization matrix) by adding the difference between the coefficients in the quantization matrix to the coefficient values of the previously decoded quantization matrix. For example, the decoder can derive the coefficient values of the current quantization matrix by using the relationship "nextcoef = (nextcoef = delta_coef + 256) % 256" as in the aforementioned equation.

The decoder can determine whether the derived coefficient is the first coefficient value of the quantization matrix or whether the derived coefficient is the same as a specific value at step S870. Here, the specific value may be 0.

If, as a result of the determination in step S870, the derived coefficient is determined to be the first coefficient value of the quantization matrix and is identical to the specific value, the decoder can determine to use the default quantization matrix included therein in inverse quantization in step S880.

If the derived coefficient is determined not to be the first coefficient value of the quantization matrix and is not the same as the specific value as a result of the determination in step S870, the decoder checks whether all the difference values of the coefficients in the quantization matrix have been decoded in step S890. If, as a result of the check, not all the difference values are determined to be decoded, the decoder can return to step S850 and perform the subsequent steps.

The decoder can perform inverse quantization by using the obtained quantization matrix at step S650.

In the aforementioned embodiment, the information about the quantization matrix means the quantization matrix or the information about the quantization matrix that can be derived. Here, the information about the quantization matrix that can be derived can mean information about whether a default matrix has been used, the type of predictive encoding/decoding method, the reference quantization matrix ID, the reference quantization matrix, etc.

In the above exemplary systems, although the methods have been described based on flowcharts in the form of a series of steps or blocks, the present invention is not limited to the order of these steps, and some steps may be performed in a different order than other steps or may be performed simultaneously with other steps. In addition, it will be understood by those skilled in the art that the steps shown in the flowcharts are not exclusive, and the steps may include additional steps, or one or more steps in the flowcharts may be deleted without affecting the scope of the present invention.

Claims (6)

1. A video encoding apparatus, comprising: The quantization module is configured to determine the quantization matrix to be used in quantization and perform quantization; and The entropy coding module is configured to encode information about the quantization matrix based on the prediction scheme of the quantization matrix. The prediction scheme for the quantization matrix is either the prediction scheme between the coefficients in the quantization matrix or the quantization matrix copying scheme. The quantization matrix has a size of 4×4, 8×8, 16×16, or 32×32. If the prediction scheme of the quantization matrix is determined to be a prediction scheme between the coefficients in the quantization matrix, the flag information is set to 1; if the prediction scheme of the quantization matrix is determined to be a quantization matrix copying scheme, the flag information is set to 0. When the prediction scheme for the quantization matrix is a quantization matrix copying scheme, the quantization matrix is determined based on the identification information. If the quantization matrix is determined to be the default quantization matrix, then this identifier is set to 0; if this identifier is used to determine the reference quantization matrix, then this identifier is not set to 0. When the identifier is not 0, the coefficient values of the quantization matrix are determined to be the same as the coefficient values of the reference quantization matrix derived using the identifier. The quantization matrix is specified based on the prediction mode, color component type, and size of the block using the quantization matrix. The identifier information indicates the difference between matrixID and RefMatrixID, where matrixID indicates the prediction mode used in the quantization matrix to be encoded and the color component type of the quantization matrix, and RefMatrixID indicates the prediction mode used in the reference quantization matrix and the color component type of the reference quantization matrix. The quantization matrix (ScalingList[sizeID][matrixID][i]) to be encoded is determined from the reference quantization matrix (ScalingList[sizeID][RefMatrixId][i]) using the following equation: ScalingList[sizeID][matrixID][i]=ScalingList[sizeID][RefMatrixId][i]. 2. The video encoding apparatus of claim 1, wherein the identification information is used for a first function of deriving a reference quantization matrix and a second function of indicating that the quantization matrix is determined as the default quantization matrix. 3. The video encoding apparatus according to claim 1, wherein if the size of the quantization matrix is 16×16 or 32×32, then when the prediction scheme of the quantization matrix is a prediction scheme between the coefficients in the quantization matrix, the information about the quantization matrix includes the DC matrix coefficients. 4. A video decoding device, comprising: The entropy decoding module is configured to decode the quantization matrix based on the prediction scheme of the quantization matrix; and The inverse quantization module is configured to perform inverse quantization using the quantization matrix. The prediction scheme for the quantization matrix is either the prediction scheme between the coefficients in the quantization matrix or the quantization matrix copying scheme. The quantization matrix has a size of 4×4, 8×8, 16×16, or 32×32. When the flag information is 1, the prediction scheme for the quantization matrix is determined to be the prediction scheme between the coefficients in the quantization matrix; when the flag information is 0, the prediction scheme for the quantization matrix is determined to be the quantization matrix copying scheme. When the prediction scheme for the quantization matrix is a quantization matrix copying scheme, the quantization matrix is determined based on the identification information. When the identifier is 0, the quantization matrix is determined as the default quantization matrix; when the identifier is not 0, it is used to determine the reference quantization matrix. When the identifier is not 0, the coefficient values of the quantization matrix are determined to be the same as the coefficient values of the reference quantization matrix derived using the identifier. The quantization matrix is specified based on the prediction mode, color component type, and size of the block using the quantization matrix. The identifier information indicates the difference between matrixID and RefMatrixID. matrixID indicates the prediction mode used in the quantization matrix to be decoded and the color component type of that quantization matrix, while RefMatrixID indicates the prediction mode used in the reference quantization matrix and the color component type of that reference quantization matrix. The quantization matrix (ScalingList[sizeID][matrixID][i]) to be decoded is determined from the reference quantization matrix (ScalingList[sizeID][RefMatrixId][i]) using the following equation: ScalingList[sizeID][matrixID][i]=ScalingList[sizeID][RefMatrixId][i]. 5. The video decoding apparatus of claim 4, wherein the identification information is used for a first function of deriving a reference quantization matrix and a second function of indicating that the quantization matrix is determined as the default quantization matrix. 6. The video decoding apparatus according to claim 5, wherein when the prediction scheme of the quantization matrix is a prediction scheme between the coefficients in the quantization matrix, if the size of the quantization matrix is 16×16 or 32×32, the entropy decoding module uses the DC matrix coefficients to decode the quantization matrix.