WO2007033551A1 - A loop filtering method for use in image encoding process - Google Patents

Abstract

A loop filtering method for use in image encoding process includes: determination step of the block effect value, for determining the block effect value of the coding block according to the amount of the edge area similar point of coding block to be filtered; judgement step of the real edge of image, for judging whether the edge of the coding block is the real edge of image according to the pixel difference value of the two edge sides of the coding blocks; filtering step, for filtering the coding block in the filtering mode corresponding the block effect value of the coding block when the edge of the coding block is not the real edge of image. By said steps, the S/N ratio can be increased by about 0.08db, and the code rate can be decreased by about 1.5%.

Description

 Loop filtering method in image encoding processing

 The present invention relates to the field of image coding processing technologies, and in particular, to a loop filtering method in image coding processing.

Background technique

 With the development of multimedia technology and the rapid promotion of multimedia applications, the H.264 video image compression standard developed by the standard development working group JVT formed by the two standards organizations of MPEG and ITU, with its advanced technical features and better compression Performance has been widely used in conference TV, videophone, streaming media, HD DVD, video surveillance, digital TV, 3G and other fields.

 The compression processing framework of H.264 is shown in Figure 1. The basic processing unit is 16 X 16 macroblocks, which uses multi-frame reference, intra prediction, multi-macroblock mode, 4X4 integer transform and quantization, loop filtering, 1/ 4 pixel motion prediction, CAVLC (context-based variable length coding algorithm) and CABAC (context-based arithmetic coding algorithm) entropy coding and other advanced technologies, its compression efficiency is higher than MPEG-2, H.263, MPEG-4 ASP More than one.

 In addition, China Digital Audio Video Codec Standards Working Group AVS has organized a series of standards similar to the MPEG standard since 2002, including video coding standards, audio coding standards, system standards, digital copyright protection DRM standards, etc. In part, the AVS parti system standard and the AVS part2 video standard were released in December 2003, and the AVS part7 video standard was released in December 2004.

 In video coding standards such as H.264 and AVS, the images need to be block-processed, and each block will have block effects in different degrees after transformation and quantization. The block effect is mainly caused by the quantization error caused by the quantization block processing. The block effect has two different expressions depending on the content of the image within the block range, mainly trapezoidal noise and lattice noise. This type of noise will make the edges of the image noticeable and even blocky.

The trapezoidal noise appears at the strong edges of the image. Since many high frequency coefficients of the DCT (Discrete Cosine Transform) are quantized to zero, the strong edges cannot be fully digitized in the transform domain, and the continuity of the strong edges passing through the boundary of the coded block cannot be obtained due to the block processing of the image. Guaranteed, so that jagged noise appears at the strong edges of the image, making visually unnatural edges of the data block, Called trapezoidal noise.

 The lattice noise appears in a flat area of the image. In the flat region of the image, if the brightness is increasing or decreasing, the rounding may occur due to quantization rounding, which may result in a transform domain.

The DC (direct current) coefficient crosses the decision threshold of the adjacent quantization level, causing a sudden change in the brightness of the adjacent two coded blocks in the reconstructed image, so that the sheet-like contour appears visually, which is called lattice noise.

 In order to avoid the block effect, before the image is encoded and stored as the reference frame of the next frame, the image needs to be deblocked. In the MPEG family of standards, post-filtering is commonly used to overcome blockiness. In H.264, the loop-filter is used to overcome the block effect. Compared with the post-processing filter, the former does not need a special buffer to pre-store the current frame, so the hardware implementation is easier. Furthermore, the loop filter is located in the prediction loop and can directly affect the prediction frame. Therefore, it is possible to reduce the residual coefficient.

 The following describes the implementation of the loop filtering used in AVS part2, including: First, calculate the block effect value and the pixel difference value, and judge:

 The block effect value Bs is calculated according to the macroblock coding information, and if the macroblock is of the intra coding type, Bs=2, if the macroblock is of an inter coding type, and the motion vector and the reference frame have differences at the coding block boundary, then Bs =l, otherwise Bs=0;

 Creating a threshold table of pixel difference values of two adjacent pixels according to the quantization step QP, and comparing the difference value of the adjacent pixel pairs at the coding block boundary with the threshold table;

 Secondly, the corresponding filtering process can be performed - if the blockiness value of one edge of the current filtering process is 2, and the pixel difference of the pixel pair at the boundary of the encoding block is smaller than the value defined in the threshold table, the pairwise filter is used. The pixel values corresponding to the window are averaged to generate two pairs of new pixel values;

 If the block effect value of one edge of the current filtering process is 1, and the pixel difference of the pixel pair at the boundary of the encoding block is smaller than the value defined in the threshold table, the difference filtering method is used to increase or decrease the original pixel value by one. The difference, which produces two pairs of new pixel values;

 If the blockiness value is 0, or if the pixel difference of the pixel pair at the boundary of the coding block is greater than the value defined in the threshold table, no filtering is performed.

It can be seen that the above-mentioned existing loop filtering process neglects that the block effect in the flat region is easier. The fact that it is perceived by the human eye, therefore, does not perform large-intensity smoothing filtering on flat areas. Moreover, in the above method, the filter operator has only three levels (0, 1, 2), and since the filter operator is too single, it is difficult to achieve a good filtering effect, and thus the corresponding method is limited.

Summary of the invention

 In view of the above problems in the prior art, an object of the present invention is to provide a loop filtering method in image encoding processing, thereby achieving good deblocking effect in a flat region and adapting to more deblocking occasions. .

 In order to achieve the above object, the present invention provides a loop filtering method in an image encoding process, including:

 a block effect value determining step of counting the number of similar points in the boundary region of the coded block to be filtered, and determining a block effect value of the coded block according to the number of similar points;

 The image real edge judging step determines whether the edge of the encoding block is the real edge of the image according to the pixel difference value of the pixel points on both sides of the encoding block edge and the pixel difference value of the pixel point inside the encoding block;

 In the filtering step, when the coding block edge is not the real edge of the image, the coding block is filtered by using a filtering method corresponding to the block effect value of the coding block.

 The loop filtering method in the image encoding process described above, wherein, in the block effect value determining step, when the number of similar points is less than the first predetermined value, the block effect value is determined to be 0, and the number of similar points is greater than or equal to the first When a predetermined value is less than the second predetermined value, the blockiness value is determined to be 1, and when the number of similarities is greater than or equal to the second predetermined value, the blockiness value is determined to be 2.

 The loop filtering method in the image encoding process described above, wherein, in the block effect value determining step, when the encoding block is an intra-coded block, the determined block-effect value is incremented by one.

 The loop filtering method in the image encoding processing described above, wherein the filtering effect is not performed when the blockiness value is 0;

 The filtering processing method corresponding to the block effect value of 3 is to filter the pixel values by the corresponding filtering window to generate three pairs of new pixel values;

 The filtering processing method corresponding to the block effect value of 2 is to filter the pixel values by the corresponding filtering window to generate two pairs of new pixel values;

 The filter processing method corresponding to the block effect value is differential filtering, which generates 2 pairs of new pixel values.

a loop filtering method in the image encoding process described above, wherein the similarity point refers to a boundary A point in the region where the pixel difference is less than the flatness threshold.

 The loop filtering method in the image encoding process described above, wherein the number of similar points is the sum of the number of similar points on the same side and the sides of the coded block edge.

 The loop filtering method in the image encoding process described above, wherein the flatness threshold is obtained by calculating a lookup table index based on a QP average value of two blocks.

 The loop filtering method in the image encoding process described above, wherein, in the image real edge determining step, when the difference between the pixel pairs at the boundary of the encoding block is less than a predetermined threshold, it is determined that the encoding block is not the real image edge.

 It can be seen from the above technical solution provided by the present invention that the loop filtering implementation method adopted by the present invention can increase the signal-to-noise ratio by about 0.08 db and the code rate by about 1.5%. At the same time, since the loop filtering algorithm provided by the present invention is improved in design for flat region filtering, it has a good effect on the deblocking effect of the flat region.

 The filtering sequence is extended in the invention, so that the filtering operator is further refined and more suitable for different deblocking occasions.

 The present invention does not produce a phenomenon of smoothing the real edge for the texture region since the true edge is checked before filtering.

 In addition to the above advantages, the present invention can also implement parallel processing at the macroblock level, that is, it is possible to perform filtering processing on multiple edges simultaneously in the same macroblock.

DRAWINGS

 Figure 1 is a schematic diagram of a H.264 compression processing framework;

 2 is a flow chart of the method according to the present invention;

 Figure 3 is a schematic diagram of a code block boundary;

 Figure 4 is a schematic diagram of the boundary pixel values required for an 8-tap filter on a vertical boundary.

detailed description

 It is an object of the present invention to provide a loop filtering method which can effectively remove blockiness, improve the subjective quality of the decoded image, and objectively increase the peak signal to noise ratio and decrease the code rate.

A specific implementation manner of the method provided by the present invention will be described below with reference to the accompanying drawings, wherein the coding block is an 8×8 coding block, and the method is similar for other coding blocks (such as a 4×4 coding block). As shown in FIG. 2, the method of the present invention specifically includes the following processing: First, calculate the block effect value strength;

 Step 21: Calculate the number of similar points in the boundary area of the coding block rmm;

The similarity point is a pair of points whose pixel value difference is smaller than the flatness threshold. The flatness threshold can be obtained from the QP average QP _{a of the} two coded blocks. The number of similar points is the sum of the number of similar points on the same side and the two sides of the coding block edge. As shown in FIG. 3, Ln Hn Rn Kn (0<=η<=7) is 32 located at the boundary of the coding block. For each point, rmm is calculated by the following formula - 2 ((abs(L _n -H„)<rM)?l:0) +∑ (( bs(H _n - R„) < Th2) ?1:0)

₇ " ⁼ "= (1)

+j ((abs(R _n -K _n )<Thl)?l: 0)

 «=0

 Among them, abs (A-B) is the absolute value operation of A-B. For the horizontal boundary, the same method is adopted, and the three sets of points in the horizontal direction are summed to obtain num. The symbol "?" indicates that the front value is greater than 0, and the A value in A: B is taken, otherwise the B value is taken. .

Where Thl and Th2 are flatness thresholds, and the index of the table index can be calculated according to the QP average QP _{av of the} two blocks.

The QP average QP _av of the two blocks is: QP _av = (QP _p + QP _q + 1 )» 1, the index Index is

According to the correspondence between the index Index and the flatness thresholds 13⁄4 and ₂ , the values obtained from the following table -

步骤 22: 根据统计的相似点的个数确定待滤波编码块的块效应值， 具体 为- 图像为高清或标清图像（水平方向的像素宽度大于等于 500个像素），贝 IJ: 1、 若 num<4， strength =0；

Step 22: Determine the block effect value of the code block to be filtered according to the number of statistical similarities, specifically - the image is a high definition or standard definition image (the pixel width in the horizontal direction is greater than or equal to 500 pixels), and IJ: 1. If num<4, strength =0;

 2. If num>=4 and num<12, strength= l ;

 3. If num>= 12, strength= 2 o

 The image is a non-HD or non-standard definition image (such as the horizontal width of the pixel is less than 500 pixels), then -

1. If num<4, strength=0;

 2. If num>=4 and num<16, strength = 1;

 3. If num>=16, strength =2.

 Here, 4, 12, and 16 are only specific judgment thresholds exemplified in the specific embodiment of the present invention, and of course, other values may be selected.

 Of course, the corresponding block effect value may also be determined according to the number of similar points and other threshold values; Step 23: Determine whether there is an intra block, and if yes, perform step 24; otherwise, directly execute step 25:

 Determining whether there is an intra block is specifically as follows: If at least one of the blocks on both sides of the edge of the coding block is in intra coding, it is determined that there is an intra block.

 Step 24: If there is a code block that is an intra block, add 1 to the corresponding strength, and then go to step 25.

 Secondly, it is necessary to perform filtering processing in accordance with the block effect value determined above.

 Since the filtering is a smoothing operation, it is possible to smooth the real edges. In order to effectively prevent such operations, it is necessary to make a true and false discrimination for the current edge before filtering.

 Step 25: Determine whether the current edge is a real edge. If not, go to step 26, otherwise, the process ends.

 Specifically, the pixel difference between the pixels on both sides of the edge of the coding block and the pixel difference of the pixel inside the coding block are calculated, and it is determined whether the difference is greater than the corresponding threshold. If it is greater than, the true edge of the image is not required. Filtering, otherwise, determining the edge that needs to be filtered;

In order to determine whether it is a true edge, it is first necessary to calculate the pixel difference value, and specifically, a preset one-dimensional linear operator can be used. Its operation object is a preset one-dimensional window. For example, set a pair of points on both sides of the code block edge, R0 and L0 as shown in Figure 4, and two pairs of points L0 and L1, R0 and Ri o inside the code block. In addition, it is also necessary to preset corresponding threshold values, and the specific threshold values are respectively stored in two threshold values, which are assumed to be α, β tables, respectively, and the α table records two pixels on both sides of the code block edge. The threshold of the pixel difference value, the β table records the threshold of the pixel difference of two pixels inside the coding block, and two one-dimensional arrays are recorded in the two tables.

 Moreover, the specific values of the threshold values in the two tables are determined according to the quantization step size QP of the coding block quantization. At the same time, in order to adjust the intensity of the filter execution, it is also possible to manually set the offset of the two adjustment filters. At this time, the array index value of the threshold table is the quantized value plus the offset. In the default state, the values of the two offsets are all 0. When looking up the table, we use the sum of QP and the offset to get two values, and then make a constraint to get two index values indexA and indexB. According to these two values, the corresponding α, β values are found in the α, β table as the threshold value for discrimination;

 The α and β tables can be displayed in array form and list form as follows:

 (1) The α table is:

 Byte ALPHA_TABLE[64]=

 {

 0, 0, 0, 0, 0, 0, 1, 1,

 1, 1, 1, 2, 2, 2, 3, 3,

 4, 4, 5, 5, 6, 7, 8, 9,

 10,11,12,13,15,16,18,20,

 22,24,26,28,30,33,33,35,

 35,36,37,37,39,39,42,44,

 46,48,50,52,53,54,55,56,

 57,58,59,60,61,62,63,64

 };

 (2) The β table is:

 Byte BETA- TABLE[64] =

 {

 0, 0, 0, 0, 0, 0, 1, 1,

 1, 1, 1, 1, 1, 2, 2, 2,

2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6,

 6, 7, 7, 7, 8, 8, 8, 9,

 9,10,10,11,11,12,13,14

 15,16,17,18,19,20,21,22:

 23,23,24,24,25,25,26,27

 As shown in Fig. 4, it is illustrated in the horizontal direction: subtracting R0 and L0 to obtain a difference C1; subtracting R1 from R0 to obtain a difference C2; subtracting L1 from L0 to obtain a difference C3; If C1 is smaller than α, C2 is smaller than β, and C3 is smaller than β, it is considered that the characteristic edge of the image is not a real edge, and filtering can be performed; otherwise, no filtering is performed.

When it is determined that the filtering process needs to be performed, the corresponding filtering process is performed according to the block effect value determined in step 22 or step 24, and the following processing is specifically implemented: Step 26: Perform filtering processing according to the block effect value by using a corresponding filtering manner, where: determining whether the block effect value is 0, and if yes, the process ends, because no filtering is needed when the block effect value is 0. Processing, otherwise continue to judge;

 Determining whether the block effect value is 1, if yes, filtering processing is performed by using a filtering processing mode when the block effect value is 1, that is, filtering processing is performed by using a difference filtering method; otherwise, judging is continued; determining the block effect Whether the value is 2, if yes, the filtering processing is performed when the block effect value is 2, otherwise the filtering processing is performed when the block effect value is 3.

 Here, the block value is 2 and the block value is 3, which is the mean filtering mode, but the number of pairs of pixels processed by the two is different, which will be described in detail below.

 The mean filtering method used in the present invention is to re-assign a plurality of pairs of pixels at a coding block boundary, and adjust the pixel value by using a window filtering formula, and the corresponding output value is jointly determined by 8 points in FIG. 4; Filtering is an adjustment of four points, which adds or subtracts a difference from the original pixel value, thereby narrowing the gap between the two pixel values, so that the visual block effect is eliminated.

 The specific filtering process corresponding to each block effect value will be exemplified below.

 The filter operators used in the present invention have three levels, corresponding to three different non-zero block effect values strengt. Since it is an 8X 8 block, the filter window can be extended to an 8-tap filter. As shown in FIG. 4, the corresponding specific operators are described as follows, where L0, L1, L2, L3 and R0, Rl, R2, R3 represent the original reconstructed pixel values of the unfiltered operation, 10, 11, 12, 13 and R0, rl, r2, r3 represent the pixel values after the filtering operation:

 (1) When strength = l, 差值 filter with difference filtering:

 The difference Δ1 = IClip(-C0, CO, ( (R0-L0) * 3 + (LI - Rl) + 4) » 3 ); Then after filtering, 10 = L0 + A1, r0 = R0 - Al ;

Δ2= IClip(-C0 ₅ CO, ( (10—Ll) * 3 + (L2~r0) + 4) » 3 ), then after filtering, 11-L1+A2;

 Δ3 = IClip(-C0, CO, ( (Rl - rO) * 3 + (10-R2) + 4) » 3 ), then after filtering, rl = Rl - Δ3.

 (2) When strength=2, filter by means of mean filtering:

R0 = aq ? ( Rl + (R0 « 1)+L0 +2 ) »2: ((Rl « 1) + R0 + L0 +2 ) » 2 ; 10 = ap? ((L0 « 1)+ L1 + R0 +2 ) »2: ((LI « 1) + L0 + R0 +2 ) » 2; Rl = aq? ( R2+ Rl + rO + 10 + 2 ) » 2 : Rl;

 11 = ap ? ( L2 + LI + 10 + rO + 2 ) » 2 : LI;

 In the above filtering method:

 Use (1, 2, 1) and (1, 1, 2) weight coefficient pairs for RO;

 The (1, 2, 1) and (1, 1, 1) weight coefficient pairs are used for L0;

 A (1, 1, 1, 1) weight coefficient pair is used for R1 and L1.

 At the same time, in the specific implementation process, R1 and L1 can also be filtered as follows to obtain AVS Part 2 compatible filter design, which reduces the implementation complexity of the system:

 Rl = aq? (R2 + Rl + R0 + L0 + 2) » 2 : R1;

 11 = ap?(L2 + Ll + L0 + R0 + 2)»2 :L1;

 Where "d=a? b:c" means that when a is greater than 0, d=b, otherwise d=c.

(3) When _S trength=3, the mean filtering method is still used for filtering:

 R0= aq? ((Rl«l) + R2 + ((R0+L0)«1) + LI +4 ) »3 : ( Rl + (R0«l)+L0 + 2)»2 ;

 10 = ap ? ( L2 + (Ll«l) + ((R0+L0)«1) + Rl +4 ) »3: ((L0«1) + LI + R0+2)»2;

 Rl = aq?(R0 + (Rl«l)+ L0 + 2)»2: R1;

Ll=ap? ((Ll«l) + L0 + R0 + 2)»2: L1 _;

 R2= aq? (RO + R1 + (R2«2) + (R3«l) +4)»3: R2;

12 = ap ? (LO + L1 + (L2«2) + (L3«l) +4)»3: L2 _;

 In the above filtering method:

 For the RO and LO, the (1, 2, 2, 2, 1) and (1, 2, 1) weight coefficient pairs are used; for R1 and L1, (1, 1, 2) and (2, 1, 1 are used respectively. Weight coefficient pairs; (1, 1, 4, 2) and (2, 4, 1, 1) weight coefficient pairs are used for R2 and L2, respectively. Where aq = (abs(R0- R2)<p); ap = (abs(L0 - L2) < β) .

 The calculation formula of the above filtering process is obtained by querying a filter cut parameter table CLIP-TAB table, first with QP as the index, and the value found in CLIPJTAB is C0, the

CLIP—TAB tables can be represented in array and table form as:

Byte CLIP_TAB[64] = 0, 0, 0, 0, 0, 0, 0, 0,

 o, o, 0, 0, 0, 0, 0, 0,

 ι,ι,ι, 1, 1, 1,1,1,

 1,1,1, 1, 1, 1,2, 2,

 2, 2, 2, 2, 2, 2, 3, 3,

 3 3 3 3, 3, 4, 4, 4,

 5, 5, 5, 6, 6, 6, 7, 7,

 7, 7, 8, 8, 8, 9, 9,9

In the foregoing description, the filtering process of the vertical boundary is taken as an example. For the horizontal boundary, the filtering window is in the vertical state, but the corresponding filtering operator and the filtering calculation on the vertical boundary. The sub-consistent, the corresponding filtering process is the same, so it will not be detailed.

 In summary, the loop filtering implementation method adopted by the present invention can improve the objective performance.

With a signal-to-noise ratio of around 0.08 db, the code rate drops by about 1.5%.

 Moreover, the loop filtering algorithm of the present invention uses the number of similar point pairs to determine the block effect value, and the flatness region has high sensitivity to the above-described block effect value determining method, thereby achieving high intensity smoothing of the flat region. Filtering, with better deblocking effect.

 The filter series is extended to make the filter operator more detailed and more suitable for different deblocking occasions.

 For the texture region, since the true edge is checked before filtering, there is no phenomenon that the real edge is smoothed.

 Parallel processing at the macroblock level can be realized, that is, the filtering processing of multiple edges is simultaneously processed in parallel within the same macroblock.

 The above is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of changes or within the technical scope disclosed by the present invention. Alternatives are intended to be covered by the scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

Claim A loop filtering method in an image encoding process, comprising:  a block effect value determining step of counting the number of similar points in the boundary region of the coded block to be filtered, and determining a block effect value of the coded block according to the number of similar points;  The image real edge judging step determines whether the edge of the encoding block is the real edge of the image according to the pixel difference value of the pixel points on both sides of the encoding block edge and the pixel difference value of the pixel point inside the encoding block;  In the filtering step, when the coding block edge is not the real edge of the image, the coding block is filtered by using a filtering method corresponding to the block effect value of the coding block.  The loop filtering method in the image encoding process according to claim 1, wherein in the block effect value determining step, when the number of similar points is smaller than the first predetermined value, the block effect value is determined to be 0. When the number of similar points is greater than or equal to the first predetermined value and less than the second predetermined value, the block effect value is determined to be 1, and when the number of similar points is greater than or equal to the second predetermined value, the block effect value is determined to be 2.  The loop filtering method in the image encoding process according to claim 1 or 2, wherein, in the block effect value determining step, when the coded block is an intra-coded block, The determined blockiness value is increased by one.  The loop filtering method in the image encoding process according to claim 3, wherein in the filtering step, when the blockiness value is 0, no filtering process is performed;  The filtering processing method corresponding to the block effect value of 3 is to filter the pixel values by the corresponding filtering window to generate three pairs of new pixel values;  The filtering processing method corresponding to the block effect value of 2 is to filter the pixel values by the corresponding filtering window to generate two pairs of new pixel values;  The filter processing method corresponding to the block effect value is differential filtering, which generates 2 pairs of new pixel values.  The loop filtering method in image encoding processing according to claim 1, 2 or 4, wherein the similarity point refers to a point in the boundary region where the pixel difference value is smaller than a flatness threshold.  The loop filtering method in the image encoding process according to claim 5, wherein the number of similar points is the sum of the number of similar points on the same side and the two sides of the coded block edge. The loop filtering method in image encoding processing according to claim 6, wherein the flatness threshold value is obtained by calculating a lookup table index based on a QP average value of two blocks. The loop filtering method in the image encoding process according to claim 1, 2 or 4, wherein in the image real edge determining step, the difference of the pixel pairs at the boundary of the encoding block is smaller than a predetermined one. At the threshold value, it is determined that the coded block is not the true edge of the image.  The loop filtering method in the image encoding process according to claim 8, wherein the predetermined threshold value is obtained according to a table lookup method, and the specific threshold values are respectively stored in two thresholds. The value table is assumed to be the α and β tables, respectively. The α table records the threshold of the pixel difference between the pixels on both sides of the code block, and the β table records the threshold of the pixel difference of the pixel inside the code block. Two one-dimensional arrays whose length are the number of quantized values, and the lookup table index is the quantization step size plus an offset.  10. The loop filtering method in image encoding processing according to claim 9, wherein the threshold value table is -

Or, the alpha and beta tables are represented as an array, which are:  The α table is:  Byte ALPHA_TABLE[64]=  {  0, 0, 0, 0, 0, 0, 1, 1,  1, 1, 1, 2, 2, 2, 3, 3,  4, 4, 5, 5, 6, 7, 8, 9, 10,11,12,13,15,16,18,20, 22,24,26,28,30,33,33,35: 35,36,37,37,39,39,42,44 46,48,50,52,53,54,55,56: 57,58 ,59,60,61,62,63,64 The β table is: Byte BETA_TABLE[64] = {  o, 0, 0, 0, o, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3 _? 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9,10,10,11,11,12,13,14 15,16,17,18,19,20,21,22:23,23,24,24,25,25,26,27