HK1221544B - Image processing for hdr images - Google Patents

Description

Image processing method, device and storage medium for high dynamic range images

This application is a divisional application of the Chinese invention patent application with application number 201380003328.2, application date July 31, 2013, and titled “Image processing for high dynamic range images”.

A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all other copyright rights whatsoever.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent Application No. 61/681,061, filed August 8, 2012, the entire contents of which are incorporated herein by reference.

Technical Field

The present invention relates generally to image processing. More particularly, embodiments of the present invention relate to image processing for images with high dynamic range (HDR).

Background Art

Some contemporary or older digital images follow a 24-bit format. These images include up to 24 bits storing both color and brightness information (such as luminance and chrominance data) for each pixel in the image. This format retains enough image information to allow the image to be drawn or reproduced by older electronic displays and is therefore considered an output reference standard. Older displays typically have a dynamic range (DR) of three orders of magnitude. However, because normal human vision can distinguish contrast ratios of up to 1:10,000 or higher, images with significantly higher dynamic ranges can be perceived.

The development of modern electronic display technology has made it possible to draw and reproduce images with a higher dynamic range that significantly exceeds the DR of older displays. High dynamic range (HDR) images represent real-world scenes more faithfully than image formats that follow output-referenced standards. Therefore, HDR images can be considered to be reference scenes. In the context of HDR images and displays capable of rendering them, older or other images and displays with more limited DR may be referred to herein as low dynamic range (LDR) images/displays.

The approaches described in this section are approaches that could be pursued, but are not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any approach described in this section qualifies as prior art simply because it is included in this section. Similarly, it should not be assumed based on this section that the problems identified for one or more approaches have been recognized in any prior art, unless otherwise indicated.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by way of limitation, in the accompanying figures and in which like references refer to similar elements and in which:

FIG1A depicts an exemplary local multiscale tone mapping system according to one embodiment of the present invention;

FIG1B depicts an exemplary image encoding process according to an embodiment of the present invention;

FIG2 depicts an exemplary local multi-scale image processing method according to an embodiment of the present invention;

3A and 3B respectively depict an exemplary HCTN block and corresponding multi-scale filtering according to an embodiment of the present invention;

4A , 4B , and 4C , respectively, depict an exemplary multiscale filter block and a corresponding exemplary multiscale filtering implementation and exemplary processing according to an embodiment of the present invention;

FIG5 depicts an exemplary ratio image processor according to an embodiment of the present invention;

6A and 6B depict an exemplary encoding process data flow for an HDR image according to an embodiment of the present invention;

FIG. 7 depicts a fusion-merging exposure process for displaying an HDR image according to an embodiment of the present invention; and

8A and 8B depict an exemplary JPEG-HDR encoding and decoding process supporting a wide color gamut and multiple color spaces according to an embodiment of the present invention.

DETAILED DESCRIPTION

Exemplary embodiments of image processing involving HDR images are described herein. In the following description, for illustrative purposes, numerous specific details are set forth to provide a thorough understanding of the present invention. However, it will be apparent that the present invention can be practiced without these specific details. In other instances, well-known structures and devices are not described in detail to avoid unnecessarily obscuring, obscuring, or confusing aspects of the present invention.

Overview—HDR Images

This overview presents a basic description of some aspects of exemplary embodiments of the present invention. It should be noted that this overview is not an extensive or exhaustive summary of all aspects of possible embodiments. Furthermore, it should be noted that this overview is not intended to be understood as identifying any particularly important aspects or elements of possible embodiments, nor is it intended to be understood as specifically reciting any range of possible embodiments, nor is it intended to be understood as generally reciting any range of the present invention. This overview merely presents some concepts related to possible exemplary embodiments in a concise, simplified format, and should be understood as merely a conceptual prelude to the more detailed description of exemplary embodiments that follows below.

Example embodiments of the present invention relate to encoding an HDR image. Logarithmic (log) luminance in an HDR input image is histogrammed to produce a tone map, and a log overall tone map luminance image is calculated. The log overall tone map luminance image is downscaled. The log luminance and the log overall tone map luminance image produce a log ratio image. The log ratio image is subjected to multi-scale resolution filtering to produce a log multi-scale ratio image. The log multi-scale ratio image and the log luminance produce a second log tone map image, which is normalized to output a tone map image based on the downscaled log overall tone map luminance image and the normalized image. The HDR input image and the output tone map image produce a quantized second ratio image.

An array of active devices (e.g., transistors) is disposed within a semiconductor die. The active devices are configured to function as, or are operatively interconnected to function as, an image encoder. The encoder includes a first tone mapper for histizing a plurality of logarithmic luminance values derived from each pixel of a high dynamic range (HDR) input image. The first tone mapper plots a first ratio image using the histogrammed values. A multiscale filter-decimator recursively downscales the first ratio image and low-pass filters each pixel thereof horizontally and vertically. Depending on the size of the first ratio image, the first ratio image is decimated and filtered at one, two, or three levels. A corresponding ratio image is plotted at each of these levels. Each of the corresponding ratio images is written to a storage device (e.g., a memory) independent of (i.e., external to) the IC device. An amplifier at each of these levels weights each filtered pixel of each of the corresponding ratio images using a scaling factor corresponding to each level acted upon by the decimator. A bilinear interpolator upscales each of the weighted ratio images to the next level after each of the previous levels. An adder at each of these levels sums each of the weighted ratio images with the weighted ratio image from the previous level. A second tone mapper tone maps the base image and its tone-mapped ratio image, both of which correspond to the input HDR image but with a lower dynamic range. The base image and its base ratio image are quantized. The quantized base image and base ratio image can be output to, for example, a JPEG encoder for compression in the JPEG format.

Some modern electronic displays essentially render HDR images of a reference scene that exceed the DR capabilities of older displays. In the context of display DR capabilities, the terms "render," "restore," "render," "generate," "restore," and "produce" may be used synonymously and/or interchangeably herein. Embodiments of the present invention operate effectively with modern displays as well as older displays. Embodiments enable capable modern displays to render HDR images at substantially their full contrast ratio, and backward compatibility enables older display devices and LDR display devices to render images within their own more limited DR rendering capabilities. Embodiments support such backward compatibility for LDR displays as well as newer HDR display technologies.

An embodiment essentially represents an HDR image using a tone-mapped base image (such as an instance of an image having a lower DR than a corresponding HDR instance of the image) together with encoded metadata that provides additional information about the image. The additional information includes image intensity-related (e.g., brightness, luma) data and/or color-related (e.g., chroma) data. The additional data is related to the DR difference between the HDR image instance and the corresponding base image instance. Thus, a first (e.g., older) display with relatively limited DR reproduction capabilities can use the tone-mapped image to render a normal DR image, for example, according to an existing, established, or popular image compression/decompression (codec) standard.

Exemplary embodiments enable processing of normal DR images in accordance with the JPEG standard of the Joint Photographic Experts Group of the International Telecommunication Union and the International Electrotechnical Commission, JPEG ISO/IEC 10918-1 ITU-T Rec. T.81, the entire contents of which are incorporated herein by reference for all purposes as if fully set forth herein. Furthermore, a second (e.g., modern) HDR-capable display can process the tone-mapped image along with the image metadata to effectively render the HDR image. In one aspect, the tone-mapped image is used to render a normal dynamic range image on an older display. In another aspect, the additional metadata can be used with the tone-mapped image to generate, restore, or render an HDR image (e.g., by an HDR display). Embodiments use a tone mapping operator (TMO) to create a tone-mapped image instance based on the HDR image.

Various TMOs, such as Reinhardt's global capture operator, can be used to generate tone-mapped images relatively efficiently. Where computational cost is irrelevant, available, or otherwise negligible, bilateral filtering can be used to generate relatively high-quality tone-mapped images. Bilateral filtering helps preserve image detail, such as in bright areas, that the typically more computationally efficient Reinhardt operator may lose. Additionally or alternatively, a histogram adjustment operator (TMO) and/or a gradient domain operator (TMO) can be used.

In embodiments, the image format is capable of efficiently rendering both HDR and non-HDR images. Embodiments may operate with the JPEG format and/or various other image formats. For example, embodiments may operate with one or more of MPEG, AVI, TIFF, BMP, GIF, or other suitable formats familiar to those skilled in the art of image processing. Embodiments operate according to the JPEG-HDR format, which is described in Ward, Greg, and Simmons, Maryanne, “Subband Encoding of High Dynamic Range Imagery,” in First ACM Symposium on Applied Perception in Graphics and Visualization (APGV) , pp. 83-90 (2004); Ward, Greg, and Simmons, Maryanne, “JPEG-HDR: Backwards-Compatible, High Dynamic Range Extension to JPEG,” in Proceedings of the Thirteenth Color Imaging Conference, pp. 283-290 (2005), and E. Reinhard, G. Ward, et al. , High Dynamic Range Imaging–Acquisition, Display and Image- based Lighting , Elsevier, MA (2010), pp. 105-108, the entire contents of which are incorporated herein by reference for all purposes as if fully set forth herein.

To display images on a variety of image rendering devices, a tone mapping operator (TMO) processes the input HDR image into a tone-mapped (TM) base image. The TM base image can include color variations relative to the input image (e.g., chroma variations, color clipping, artistic appearance, etc.). According to some techniques, the TM base image is provided to a downstream image decoder along with the luminance ratio to reconstruct an HDR image comparable to the input HDR image. However, the downstream image decoder will not be able to remove the color variations in the reconstructed HDR image, relying on the TM base image and the grayscale luminance ratio. As a result, the color variations will still be noticeable in the reconstructed HDR image.

The HDR image encoder of the embodiment described herein not only creates a brightness ratio, but also creates a color residual value based on the input HDR image and the TM base image. The brightness ratio and the color residual value can be jointly represented as HDR reconstruction data. Optionally and/or additionally, the brightness ratio is transformed into a logarithmic domain to support a relatively wide range of brightness values. Optionally and/or additionally, the resulting logarithmic brightness ratio and the color residual value are quantized. Optionally and/or additionally, the quantized logarithmic ratio and the color residual value are stored in a residual image. In some embodiments, the quantized logarithmic ratio and the color residual value, or the residual image, are provided to a downstream image decoder together with the TM base image. Optionally and/or additionally, together with the TM base image, parameters related to the quantized logarithmic ratio and the color residual value (e.g., range limits, etc.) are also provided.

The TMO of the embodiments described herein can freely perform color clipping in the color channel for individual pixels with low (black) or high (white) brightness levels. In addition, the TMO described herein is not required to maintain the chromaticity at every pixel. According to the technology described herein, the user is free to select the TMO based on the image content (e.g., human figures, indoor images, outdoor scenes, night scenes, sunsets, etc.) or application (e.g., applications used in movies, posters, wedding photos, magazines, etc.). Color clipping or modification can be used intentionally and freely to create an artistic look for the image. The HDR image encoder and decoder herein support TMOs implemented by different types of editing software and camera manufacturers, which can introduce a wide range of possible color changes. According to the technology described herein, the HDR encoder provides color residual values to the HDR decoder. The HDR decoder then uses these color residual values to prevent (or minimize) color changes from being present in the reconstructed HDR image.

Embodiments may use bitstreams and/or image files to store TM base images and their respective corresponding HDR reconstruction data, and provide these images and data to downstream image viewers or decoders for decoding and/or rendering. In exemplary embodiments, the image format supports TMO, which may be implemented by various editing software applications and/or camera manufacturers. Exemplary embodiments may operate with various image formats, including, for example, the standard JPEG image format, as well as extended, enhanced, augmented, or improved JPEG-related formats, such as JPEG-HDR. Additionally, alternatively, or optionally, exemplary embodiments may use image formats based on or used with codecs/standards that differ in one or more significant aspects, attributes, objects, coding specifications, or performance parameters relative to those codecs and/or standards that may be used with JPEG-related image formats. Exemplary embodiments use the JPEG-HDR image format to support storage of TM base images along with luminance ratios and color residual values. Additionally, alternatively, or optionally, one or both of the TM base image and the residual image stored in the image file may be compressed. In exemplary embodiments, image data compression is performed in accordance with the JPEG standard. Additionally, alternatively, or optionally, exemplary embodiments may perform compression according to standards that vary in one or more significant aspects, attributes, objects, encoding specifications, or performance parameters relative to those standards that may be used with JPEG-related image formats.

Because the JPEG format is limited to LDR images, JPEG-HDR essentially comprises a backward-compatible HDR extension of the JPEG format. JPEG-HDR supports both rendering of HDR images on modern HDR displays and rendering of non-HDR (e.g., LDR) images on both HDR and non-HDR displays. JPEG-HDR stores the tone-mapped image in a standard location as defined in JPEG (e.g., in the bitstream, on disk, etc.) and stores additional metadata in a new location that can be ignored by non-HDR displays. The additional metadata can be used together with the tone-mapped image to generate and/or restore an HDR version of the original HDR image.

In an embodiment, the JPEG HDR encoder is implemented using, or provided in, an integrated circuit (IC) device. In an embodiment, the apparatus, circuits, and/or mechanisms as described herein comprise components in a camera or other image recording and rendering or display system, a cellular radiotelephone, a personal digital assistant (PDA), or a personal portable or consumer electronic device (e.g., for pictures, computing, movies, music, information, entertainment, calculations, voice).

Embodiments may perform one or more functions as described in patent application No. PCT/US2012/033795, entitled “ENCODING, DECODING, AND REPRESENTING HIGH DYNAMIC RANGE IMAGE,” filed by Wenhui Jia et al. on April 16, 2012 under the Patent Cooperation Treaty (PCT), or in Dolby Laboratories’ standardization document “JPEG-HDR Encoder and Decoder Algorithm Specification,” which is incorporated herein for all purposes, a copy of which is attached as Appendix “A” to this specification (at the time of filing).

Embodiments may perform one or more functions as described in PCT/US2012/027267, filed by Gregory John Ward on March 1, 2012, entitled “LOCAL MULTI-SCALE TONE MAPPING OPERATOR,” the entire contents of which are incorporated herein by reference for all purposes.

Various modifications to the preferred embodiments and overall principles and features described herein will be readily apparent to those skilled in the art. Therefore, the present disclosure is not intended to be limited to the embodiments shown, but is to be accorded the broadest scope consistent with the principles and features described herein.

Example JPEG HDR encoder

In an embodiment, the JPEG HDR encoder is implemented using an integrated circuit (IC) device, which is often referred to as a chip. For example, the encoder may be provided within the IC device. The IC device may be implemented as an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), and/or a graphics processor. The IC device may be implemented as a system-on-chip (SOC) using an ASIC or one or more configurable or programmable devices, such as a microprocessor, a programmable logic device (PLD), a field-programmable gate array (FPGA), or a microcontroller.

The IC device includes an array of active device components (such as transistors) disposed within a semiconductor die. The active device components are arranged, configured, and/or programmed to function as modules, registers, caches, logic gates, logic and computational (e.g., arithmetic/floating point) units, or to perform other such operations consistent with JPEG HDR encoding. The active components of the array are interconnected with at least partially conductive routing structures (such as a network of traces/vias, a grid of address/word lines, etc.) disposed within the die to enable electrical/electronic exchange of signals and data between the active device components and various functional modules formed therewith. The active components are operatively addressable via at least partially conductive interfaces, which enable electrical, electronic, and/or communicative coupling with signals, data, and power external to the IC device.

An exemplary JPEG HDR encoder embodiment is described herein as being implemented using an ASIC. For clarity, brevity, and consistency, the exemplary ASIC implementation described herein also represents a configurable and programmable IC implementation. FIG1A depicts an exemplary JPEG HDR encoder 10 according to an embodiment of the present invention.

The example encoder 10 is implemented using an ASIC. The encoder 10 receives an input image via an Advanced High-Performance Bus (AHB) interface. A pre-tone mapper (Pre_TM) converts the input image data into a format useful for tone mapping. Pre_TM performs chroma upsampling, for example, from a 4:2:2 chroma sampling format to a 4:4:4 format. Pre_TM converts the color space of the image input (e.g., YCbCr) to a three-color color space, such as RGB. Pre_TM performs inverse gamma (γ) correction on the RGB converted image.

The encoder 10 performs a tone mapping function to generate a tone-mapped base image from an input HDR image. The encoder 10 can be implemented to process HDR images input in various formats, such as the example input formats shown in Table 1 below.

Table 1

The tone mapping function includes a Histogram Adjusted Multi-Scale Tone Mapping Operator (HAMS-TMO), which uses Contrast Limited Adaptive Histogram Equalization (CLAHE) to perform a tone mapping normalization function on the input HDR image. This normalization function can be implemented on the input image using Histogram CLAHE Tone Mapping Normalization (HCTN). The HAMS-TMO HCTN outputs a normalized tone mapped base image in 12-bit linear RGB format. An example HAMS-TMO HCTN embodiment is described below (Figures 2 and 3A). A ratio image processor RI_Proc can calculate one or more ratio images from the normalized tone mapped base image and process these ratio images.

When performing HAMS-TMO HCTN processing, the post-tone mapping Post_TM restores the gamma correction of the normalized 12-bit RGB image and produces an 8-bit RGB image therewith. Post_TM is responsible for sending the tone mapped base image to the JPEG encoder for compression. Post_TM converts the RGB color space of the re-gamma-corrected 8-bit image into a YCbCr image with a JPEG compatible color format (e.g., 4:2:2 or 4:2:0). For example, the post-TMO may include the following operations: gamma encoding (wherein the 12-bit RGB input is typically converted to 8-bit input via a user-defined lookup table), RGB to YCbCr color conversion (e.g., via a 3×3 color matrix conversion), and 4:4:4 to 4:2:2 or 4:2:0 conversion via appropriate subsampling of the chroma color planes. The encoder 10 may include more than one post-tone mapping module Post_TM sub-block. For example, the encoder 10 may be implemented with three (3) Post_TM sub-blocks.

FIG1B depicts an exemplary image encoding process 100 according to an embodiment of the present invention. In an embodiment, encoder 10 operates as described in connection with process 100 upon receiving or accessing an input HDR image. In step 101, a histogram is calculated based on the logarithmic luminance values of pixels in the HDR input image. In step 102, a tone mapping curve is generated based on the calculated histogram. In step 103, a logarithmic overall tone-mapped luminance image is calculated based on the logarithmic luminance pixel values of the input HDR image and the tone mapping curve.

In step 104, the logarithmic global tone-mapped luminance image is downsampled (e.g., decimated vertically and horizontally) to calculate a downscaled logarithmic global tone-mapped luminance image. In step 105, a logarithmic ratio image is calculated based on the downscaled logarithmic global tone-mapped luminance image and the logarithmic luminance pixel values of the HDR input image. In step 106, multiscale filtering is performed on the logarithmic ratio image to generate a logarithmic multiscale ratio image. In step 107, a second logarithmic tone-mapped image is generated based on the logarithmic multiscale ratio image and the logarithmic luminance pixel values of the HDR input image.

In step 108, the second logarithmic tone-mapped image is normalized to change the range of pixel intensity values and achieve contrast stretching, and an output tone-mapped image is generated based on this and the downscaled logarithmic overall tone-mapped luminance image. In step 109, a second ratio image is generated based on the output tone-mapped image and the input HDR image. In step 110, the second ratio image is quantized. In step 111, the output tone-mapped image and the quantized second ratio image are output to a JPEG encoder. At each step of the example process 100, the generated overall tone-mapped image and ratio image can be written to and/or read from an external memory, for example, via an interface of the example encoder 10.

FIG2 depicts an exemplary histogram-adjusted multi-scale tone mapper 200 according to an embodiment of the present invention. In an embodiment, the histogram-adjusted multi-scale tone mapper 200 implements the HAMS-TMO HCTN functionality described above ( FIG1A ). The HAMS-TMO 200 receives an HDR image in a three-color (e.g., RGB) or other (e.g., YCbCr) color space. The luminance module (201) calculates a 16-bit luminance value Y for the input HDR RGB image. The logarithmic luminance module LOG (202) transforms the luminance value Y from a linear domain to a logarithmic domain. The LOG 202 module implements a transformation of the luminance value Y to its base-2 logarithm "logY."

When converting 16-bit linear luminance values, the LOG module stores the resulting base-2 logarithm (log ₂ ) value, logY, as Q4.12 data (e.g., 4 bits before the nominal binary point and 12 bits after it). For example, the logarithm includes an integer component and a fractional component. Therefore, embodiments separate the integer logY component and the fractional logY component to implement the base-2 logarithm, log ₂ Y. For example, as shown in the example pseudocode of Table 2 below, the integer portion is calculated based on the number of left shifts in normalization, and the fractional 8 bits are indexed into the lookup table LUT.

Table 2

A histogram HIST (203) comprising 512 bins is constructed from the fractional logY components. The fractional logarithmic luminance values are processed as 16-bit integer values. Therefore, the interval between bins comprises 65536/512=128. The HAMS-TMO 200 then performs a CLAHE adjustment on the histogram. The dynamic range is calculated from the histogram, for example, according to the example pseudocode shown in Table 3A below.

Table 3A

The output dynamic range (ODR) is configurable in the natural (base e) logarithmic domain with a default value of 3.5, which is converted to a base 2 value of five (5). For example, the histogram cutoff factor "cf" is calculated as follows:

cf=((odr*(bmax-bmin+1))<<12)/(drin);

And along with it the histogram may be adjusted by, for example, multiple iterations according to the pseudo code shown in Table 3B below.

Table 3B

For example, according to the pseudo code shown in Table 3C below, a cumulative histogram is calculated from the adjusted histogram and mapped to the 12-bit logarithmic domain of the Q4.12 data format.

Table 3C

Such CLAHE histogram equalization produces a mapping curve that is implemented as an overall tone mapping operator for the logY image. When the mapping curve includes 512 bins, a linear interpolation is calculated for the luminance values in each of the 512 bins, for example, according to the pseudo code shown in Table 3D below.

Table 3D

The CLAHE mapping output comprises a logY image (204) in Q4.12 format. In an embodiment, the HAMS-TMO 200 is implemented with a block that performs a histogram CLAHE (Contrast Limited Adaptive Histogram Equalization) tone mapping normalization function.

FIG3A and FIG3B respectively depict the flow of an exemplary histogram CLAHE tone mapping normalization (HCTN) block 30 and a corresponding exemplary HCTN process 300, according to an embodiment of the present invention. The HCTN block 30 can be implemented to support images of 25 million pixels or more. Upon receiving an input image in a three-color (e.g., RGB) or other (e.g., YCbCr) color space, the HCTN 30 calculates its luminance value, Y (processing step 301). In step 302, the Y value is exported to shared logic for calculating its corresponding logarithmic value, "logY," which is returned to the HCTN block 30. In step 303, a histogram is calculated based on these logY values and stored in a table, "ht0." Once all input image pixels are counted, contrast limited adaptive histogram equalization (CLAHE) is calculated in step 304 to normalize the ht0 histogram values.

Once all input image pixels are counted, contrast-limited adaptive histogram equalization (CLAHE) is calculated in step 304 to normalize the ht0 histogram values. In step 305, the buffered logY values are interpolated, generating a logarithmic tone-mapped image, "logYtm." For example, a tone-mapped curve is implemented across the 512 bins of the histogram. Therefore, linear interpolation is calculated for the luminance values in each of these 512 bins to implement logYtm. In step 306, a log-ratio image, "logRI," is calculated from the logY values and the logYtm image using the subtraction function performed in the logarithmic domain: logRI = logYtm - logY. In step 307, the logY histogram is then clipped. In step 308, after multi-scale filtering, the tone-mapped logY values are normalized to linear luminance values, Y'. In step 309, an optional curve function can be applied to the linear tone-mapped Y' values to output the final tone-mapped image.

4A , 4B and 4C depict an exemplary multiscale filter (MSF) block 400, and a corresponding exemplary multiscale filtering implementation and example process 400, respectively, according to an embodiment of the present invention. As with the HCTN block 30 ( FIG. 3A ), the MSF 4000 can be implemented to support images of 25 million pixels or more. The MSF 4000 decimates the input log-ratio image IBI by a pre-calculated factor (e.g., 8) in its horizontal dimension and in its vertical dimension. The MSF 4000 low-pass filters each pixel that constitutes the decimated image through a plurality of (e.g., seven (7)) taps. The low-pass downscaled image can then be upscaled using, for example, the same pre-calculated factor by which it was previously downscaled.

MSF 4000 calculates in advance the number of levels "msn" at which to scale the input image based on its original size at input, for example, according to the following exemplary implementation equation: msn = floor(log ₈ min(width, height)) + 1 = floor(log ₂ min(width, height)/3 + 1). MSF 4000 may be implemented to decimate the input log-ratio image IBI by a factor of up to eight (8) in the horizontal dimension and in the vertical dimension at each of four (4) levels, for a total of 64 in each dimension.

Thus, in an embodiment, as depicted in FIG4B , the filtering implementation includes four (4) stages 40, 41, 42, and 43. Each of the stages 40-43 decimates the image in both the vertical and horizontal dimensions by a factor of eight, such that the image size is reduced by a factor of 8 ² =64, so that the MSF 4000 decimates the image by a total factor of 64. Thus, at each stage, the log-ratio image is downscaled by a factor of eight. This downscaling by a factor of 8 is repeated at each of the msn levels (e.g., stages), for example, according to the pseudo-code shown in Table 4 below.

Table 4

/＊dimenslon for next stage＊/

width＝(width+6)/8+1；

height = (height + 6) / 8 + 1;

At each stage, a 7-tap low-pass filter can be performed on each pixel of the decimated image. An embodiment is implemented in which the decimated image is first filtered in a horizontal direction corresponding to a first spatial orientation of each of the decimated images, and then filtered in a vertical direction spatially orthogonal to the first orientation. At the boundaries of the respective scaled images, the scaled images are aligned, for example, by padding (such as mirroring).

At each stage, the amplifier applies a weighting factor "Alpha" to the ratio image. For each of the stages "k," where k comprises an integer ranging from zero to msn minus one (k=0, ..., msn-1), an embodiment calculates the weighting factor Alpha (A) according to _Ak = 2*(k+1)/(msn(msn+1)). The weights sum to 1. Embodiments may also be implemented in which the weighting factor is calculated as 2*(msn-(k-1)+1)/msn*(msn+1) or 1/msn.

Upscaling is performed (msn-1) times on the downscaled filtered ratio image. At each level, the weighted log-ratio image is added to the upscaled image. An embodiment achieves upscaling by interpolation (e.g., bilinear interpolation) of the lower resolution image of the previous level (e.g., using four (4) points at the spatial corners of the image and interpolation in its horizontal and vertical dimensions to reconstruct the upsampled block).

Stage 401 downscales and filters the input image _R0 and passes the first ratio image _R1 to stage 402. Similarly, stage 402 and each of stages 403-407 (inclusive) pass downscaled low-pass filtered ratio images to their respective next stages, which are sequentially followed by the ratio images passed to them by each of their respective previous stages. The weighted ratio images from each stage are summed with the upscaled image from the next stage.

The MSF 4000 generates tone-mapped luma, luminance, or other intensity-related tone-mapped values that are written to off-board memory using configuration registers via a register interface.

In an embodiment, the MSF 4000 and/or implementation 400 operates according to one or more steps of an exemplary multi-scale resolution filtering process 400. The exemplary process 400 is described below with reference to the flowcharts depicted in FIG4B and FIG4C. The process 400 begins by processing a log-ratio image _R0 (e.g., generated in step 105 at FIG1B) by progressively downscaling the image at each of levels 41, 42, and 43. At each level of downscaling, the image is progressively decimated vertically and horizontally.

In step 401, the log-ratio image R ₀ is downscaled vertically and horizontally by a factor "N", where N comprises a positive integer, such as eight (8). This produces a first-level downscaled log-ratio image R ₁ . Then, in step 402, the first-level downscaled log-ratio image R ₁ is decimated by a factor N to produce a second-level downscaled log-ratio image R ₂ . Then, in step 403, the second-level downscaled log-ratio image R ₂ is decimated by a factor N to produce a third-level downscaled log-ratio image R ₃ . In an exemplary embodiment, the downscaled image output of each level is low-pass filtered. In an exemplary embodiment, not all levels need be used.

In step 404, the pixel values of the third layer downscaled log-ratio image R ₃ are scaled by a third layer scaling factor (e.g., Alpha[3]) to produce a third layer weighted ratio image R' _3. In step 405, the pixel values of the second layer downscaled log-ratio image R ₂ are scaled by a second layer scaling factor (e.g., Alpha[2]) to produce a second layer weighted ratio image R' _2. In step 406, the third layer weighted ratio image R' ₃ is upscaled by a factor N and summed with the second layer scaled weighted ratio image R' ₂ to produce a second layer upscaled log-ratio image

In step 407, the first layer downscaled ratio image _R'1 is scaled by a first layer scaling factor (e.g., Alpha[1]) to produce a first layer weighted ratio image _R'1 . In step 408, the second layer upscaled log-ratio image is upscaled by a factor N to produce a first layer upscaled log-ratio image. In step 409, the log-ratio image _R0 is scaled by a zero layer scaling factor (e.g., Alpha[0]) to produce a zero layer weighted log-ratio image _R'0 . In step 410, the first layer upscaled log-ratio image is upscaled by a factor N and summed with the zero layer scaled weighted ratio image _R'0 to produce a logarithmic multi-scale ratio image. The steps of the example process 400 may be optional.

FIG5 depicts an exemplary ratio image processor 500 according to an embodiment of the present invention. The embodiment implements RI_Proc ( FIG1A ) using ratio image processor 500. Ratio image processor 500 receives an input image from TMO 200 ( FIG2 ). It calculates a luminance ratio from the luminance value Y from the original HDR input image and the luminance value from the tone-mapped image. It calculates the maximum and minimum values across the entire image, which are used to quantize the logarithmic luminance values logY and the CbCr chrominance values DiffCbCr for the different images.

For example, logY and DiffCbCr are saved to/written to external memory via an Advanced eXtensible Interface (AXI) interface or a similarly capable interface. The externally saved/stored values are read/loaded back via AXI for timely quantization. A linear feedback shift register (LFSR) generates random values for dithering the logY channel during quantization. RI_Proc 500 outputs the quantized DiffCbCr and logY values to a JPEG encoder, which can output a JPEG-formatted image corresponding to the input image.

6A and 6B depict an exemplary encoding process 60 and an example data flow timeline 600, respectively, according to an embodiment of the present invention. Upon receiving an HDR input picture (61), a histogram and a downscaled LogY image LogY1 are generated in step 62. The histogram is normalized. In process 600, a JPEG-HDR encoder (e.g., encoder 100; FIG. 1B ) core reads the entire HDR input image. The encoder generates a histogram based on the LogY values of the input image pixels, equalizes the histogram, and writes LogY1 to a downscaled image buffer Buff_Log1. In an embodiment, the histogram is equalized using CLAHE.

In step 63, multiscale filtering is performed, which produces the actual per-pixel scaling factors used in tone mapping. In step 64, the per-pixel scaling factors are applied to each pixel. The tone-mapped base image is converted to 8-bit gamma-encoded YCbCr 4:2:2/4:2:0/4:4:4 and can be sent to a JPEG encoder, which writes the compressed base image to external memory. The original and tone-mapped RGB data are processed to produce the original pre-quantization ratio image, which is also written to external memory. In step 65, the unprocessed ratio image is read back from external memory and the ratio image is quantized. The quantized ratio image can be output to a JPEG encoder (66) and compressed using a JPEG encoder.

Example weighted multi-zone based exposure for HDR images

Traditional low-end consumer display devices (such as smartphones, computer monitors, etc.) may not be able to display the full dynamic range of a JPEG-HDR image. In such cases, the display will typically output a tone-mapped, low dynamic range (LDR) version of the corresponding HDR image. This tone-mapped image is typically generated automatically by the camera without user input, so it may not capture the photographer's intent.

In some embodiments, a user can use a user interface of the device (such as a touch screen, a computer mouse, a scroll bar, etc.) to scroll through the entire HDR picture. In this case, the user may be able to observe a portion of the image over the entire dynamic range, but the rest of the image may be displayed too darkly or too brightly. However, the user may want to view details in multiple portions of the image. Therefore, it would be beneficial to allow the user to adjust the exposure of the HDR image based on the region of interest.

In one embodiment, the exposure of the final HDR image can take into account two or more regions of interest selected by the user. These regions can be selected before (e.g., with a camera or other capture device) capturing the image, or after (e.g., when displaying the corresponding LDR image). In some embodiments with a touch screen interface (e.g., iPhone or iPad), these regions can represent pixels of relatively equal brightness around one or more pixels touched by the user. In other embodiments, the user can use an alternative interface (such as a computer mouse, trackball, keyboard, etc.) to select these regions. In other embodiments, these regions can be automatically selected based on pre-selected user preferences (e.g., faces, animals, text, etc.).

In one embodiment, the area around the first touch point can be set to a first optimal exposure gamma (e.g., 18% grayscale). Then, for the second touch point, a second optimal exposure gamma is calculated. The final image can be displayed using a final exposure gamma weighted by the first exposure gamma and the second exposure gamma. This allows both the first touch point and the second touch point to be within the dynamic range of the display while blending in with the rest of the resulting image. Any number of touch points can be recognized, such as 3, 4, or N. The weighting factor can be an equal average, mean, median, proportional weight, linear, nonlinear, and/or limited (maximum/minimum). In certain embodiments, the technique can be undone by a user command (e.g., an undo button).

As depicted in FIG7 , in another embodiment, a fusion-merging process may be used to produce the resulting image. In this process, for each selected point of interest (710), the process produces a corresponding exposed LDR image (720). Given N such exposures (or LDR images) created from the original HDR image, an embodiment may create a fused image (730) by appropriately fusing all N exposures into a single output image. An example of such a fusion process may be implemented using the techniques described in “Exposure Fusion” by T. Mertens et al., ¹⁵ Pacific Conference on Computer Graphics and Applications (Pacific Graphics, 2007), pp. 382-390, the entire contents of which are incorporated herein by reference as if fully set forth herein.

Exemplary Adaptive Ratio Image Quantization

Given the luminance HDR image (Y _h ) and its tone-mapped representation (Y _t ) as described above, the ratio image Y _R can be expressed as:

The dynamic range of the ratio image can be compressed by applying a reversible function (such as a logarithmic function or a root mean square function) to the ratio image. Therefore, in one embodiment, a logarithmic function is applied:

The logarithmic ratio image (log(Y _R )) can be further quantized to obtain an 8-bit ratio image:

Since the original ratio image includes pixel values represented with high precision or dynamic range (e.g., using floating point numbers), quantizing the ratio image to 8-bit pixel values will produce rounding errors that cannot be recovered when the inverse quantization function is applied. This error can affect the accuracy of the image encoding and can limit the dynamic range of images that can be encoded using the JPEG-HDR format.

In an embodiment, the above logarithmic function is therefore replaced by an arbitrary reversible function "F". Given F, the quantized 8-bit ratio image can be expressed as:

This allows the decoder to recover the original ratio image according to the following formula:

wherein Y _R ′ denotes the recovered ratio image. In an embodiment, the minimum and maximum F(Y _R ) values are included in the JPEG-HDR image as metadata accessible to a JPEG decoder.

In an embodiment, the function F may be selected so that it minimizes M(Y _R ′, Y _R ), where M represents a metric that measures the difference between Y _R ′ and Y _R according to some quality criterion, such as mean square error, signal-to-noise ratio (SNR), or peak signal-to-noise ratio (PSMR). M (e.g., the MSE between the two images) represents the objective function for the optimization process of F. F may be a parameterized function or may be defined via a (LUT). Given M, well-known optimization techniques may be applied to determine F, such as the Nelder-Mead method described by J.A. Nelder, John, and R. Mead in “A simplex method for function minimization,” Computer Journal, vol. 7, pp. 308-313, 1965.

In an embodiment, the JPEG-HDR header may include a decoding LUT representing the inverse encoding function F ^{- 1.} An adapted JPEG-HDR decoder may use this LUT to convert the received ratio image from 8-bit data to higher precision (e.g., floating point) Y channel data. The LUT may have 256 entries that directly map 8-bit data to floating point values.

Exemplary histogram equalization-based method

Embodiments also relate to computational efficiency, as histogram equalization or contrast-limited histogram equalization provides a process for deriving an F function. The histogram equalization process converts source luminance with an arbitrary distribution into luminance with a uniform histogram, allowing for more efficient encoding of contrast images. In embodiments using histogram equalization, F can be calculated as follows.

a) Compute the histogram histogram of Y _R. The histogram simply represents the number of instances where pixel value i is encountered in the ratio image (e.g., hist _i );

b) Calculate the cumulative histogram c_hist of hist. For example, the cumulative histogram can be calculated as:

as well as

c) Determine F by normalizing and scaling c_hist. For example:

F _i =((c_hist _i -min(c_hist))/(max(c_hist)-min(c_hist))*scale

The variable scale determines the maximum value of F, for example, 255.

The encoding function F calculated as above may have regions with infinite derivatives or slopes, and therefore, F may not provide a unique mapping, and the inverse function F ⁻¹ does not exist. Limiting the slope or derivative of F allows embodiments to confirm the uniqueness of the mapping provided by F and the existence of F ⁻¹ .

The histogram equalization method makes the coding accuracy proportional to the frequency of occurrence of the luminance value. Therefore, less frequently occurring luminance values can be quantized with a higher error, while frequently occurring luminance values can be quantized with a lower error.

Example custom color gamut support in JPEG-HDR

The file format of a typical single image can use an ICC (International Color Consortium) or WCS (Windows Color Management System) profile to transmit color information to a rendering device (e.g., a display). ICC and WCS profiles require that images be rendered into a specific color space. As part of rendering, all colors that are not representable in the target color space should be gamut-mapped to representable colors. As a result of this gamut mapping, some color information may be lost in the rendered image.

For example, an image can be captured with a high-end camera with a wide color gamut, or an image can be created using computer graphics (CG) software. The resulting image can then be mapped to the sRGB color space. The sRGB color space is the most common color space and is supported by most operating systems and display devices. However, because sRGB has a relatively small color gamut, all image colors that are not covered by sRGB need to be mapped to sRGB colors. If the sRGB image is then sent to an imaging device with a much wider color gamut, there is no reliable way to restore the original, wider color gamut mapped colors. Therefore, color gamut mapping can cause irreversible information loss and can result in suboptimal color reproduction.

Another aspect of image rendering involves specifying viewing conditions. For example, viewing conditions at home and in the office are often different from those used in a color grading or color matching environment. The ICC workflow specifies precise viewing conditions (VC), making the workflow inflexible. WCS allows some VC flexibility, but once an image is rendered, it is virtually impossible to reverse the changes.

Both gamut mapping and VC define a set of rendering decisions that content creators should make based on assumptions about how the image will be viewed. In real life, it is impossible to make the best rendering decisions for all possible situations and target imaging devices and all possible purposes.

In an embodiment, the JPEG-HDR file format takes into account two different sets of color gamut-related metadata: one set related to the capture device or original HDR data, and the other set related to the target legacy workflow using color images. Therefore, legacy imaging devices with standard color gamut and dynamic range can still display default rendering images based on conventional ICC and WCS workflows to deliver color-accurate image content. At the same time, devices that support wider color gamut, higher dynamic range and/or real-time rendering may also be able to restore the original image data for dynamic rendering that takes into account both viewing conditions and device properties. For example, an application can restore the original scene data and render it based on the current viewing conditions and the characteristics of the target display device. Therefore, the base image can provide backward compatibility with existing color management workflows, while the JPEG-HDR metadata enables more accurate and flexible real-time rendering.

A JPEG-HDR image contains a base image (e.g., a baseline JPEG image) and HDR metadata (e.g., a ratio image and color residual data). The base image is a tone-mapped and gamut-mapped rendered image, typically rendered in the sRGB color space. The JPEG container can indicate the color space of the base image, or it can include an ICC/WCS color profile that enables consistent color reproduction on various imaging devices.

HDR metadata may also include color space information in a device-independent space (such as XYZ primitives), or in an additional second ICC/WCS color profile. The HDR metadata color space may be different from the color space of the base image. The color gamut of the metadata is typically larger than the color gamut of the base image. For example, the metadata color space for a camera typically matches the color space of the camera sensor. For CG images, the metadata color space may include all colors present in the original image. Therefore, an embodiment uses two or more color space descriptors (e.g., profiles) to provide enhanced support for wide color gamuts in JPEG-HDR. One profile defines the encoding color space of the base image, and a second profile defines the encoding color space of the HDR metadata.

FIG8A depicts an encoding process supporting dual color spaces according to an exemplary embodiment. As depicted in FIG8A , an input HDR image 805 captured in color space B can be tone mapped by a TMO process 810 to produce a tone-mapped image 815 in color space B. A gamut transform process 820 can further process image 815 to produce a base image 825 in color space A. Using information about the two color spaces, a color transform T _AB can be created to transform the image from color space A to color space B. Transform T _AB can be applied in a color transform step 840 to create a base image 845 in color space B.

Using the original HDR image 805 and the base image 845, process 830 can generate HDR metadata 835 according to the methods previously described herein. Finally, the image 825 (in color space A) and the HDR metadata 835 (in color space B) can be encoded and combined to produce a JPEG-HDR image (855). The file format of the JPEG-HDR image 855 can include appropriate color descriptors for both color spaces. In some embodiments, processing steps 810 and 820 can be combined into a single step, where, given the HDR image (805) in color space B, it outputs a tone-mapped image (825) in color space A. Using an additive color space, such as a matrix TRC (tone reproduction curve), allows steps 810 and 820 to be combined during encoding, as both gamut mapping and tone mapping can be performed in the original color space (e.g., B). In addition, color conversion between color spaces becomes more accurate and computationally efficient.

FIG8B depicts a dual-color gamut decoding process according to an exemplary embodiment. As depicted in FIG8B , given an input JPEG-HDR image that defines data in two color spaces (a base image in color space A and HDR metadata in color space B), the base decoder extracts a base image 865 in color space A (i.e., sRGB). Image 865 can be used to display the base image on older display devices with standard dynamic range.

By using information about these two color spaces, a color transform T _AB can be created to transform the image from color space A to color space B. Transform T _AB can be applied in a color transform step 870 to create a base image 875 in color space B. Given input 855, a metadata decoding process 890 extracts HDR metadata 895 in color space B. Finally, an HDR decoder 880 can combine the base image 875 and the metadata 895 to produce an HDR image 885 in color space B.

If the HDR metadata resides in a wide color space that encapsulates all possible colors of the image, the encoded image values will always be positive. Positive values allow the image to be validated during the encoding and decoding stages. That is, if negative values are detected, they can be zeroed and/or an error message can be issued. The methods described herein can also be applied to encoded input standard dynamic range (SDR) images that have a wider color gamut than conventional SDR images. For input SDR images (e.g., 805), the TMO processing step (810) can be omitted.

The image 885 can then be rendered to a target imaging device for the specific current viewing conditions. A standard display, an HDR display, a wide color gamut display, and a printer are examples of target imaging devices. A dimly lit, neutral-painted room and a brightly lit, yellow-painted room are examples of different viewing conditions.

An exemplary embodiment of the present invention is thus described in relation to encoding an HDR image. Log luminance in an HDR input image is histogrammed to produce a tone map, and a log overall tone mapped luminance image is calculated together with the tone map. The log overall tone mapped luminance image is downscaled. The log luminance and the log overall tone mapped luminance image produce a log ratio image. The log ratio image is multi-scale resolution filtered to produce a log multi-scale ratio image. The log multi-scale ratio image and the log luminance produce a second log tone mapped image, which is normalized to output a tone mapped image based on the downscaled log overall tone mapped luminance image and the normalized image. The HDR input image and the output tone mapped image produce a quantized second ratio image. The quantized base image and the base ratio image can be output to, for example, a JPEG encoder for compression in JPEG format.

Exemplary JPEG-HDR encoding with multi-scale ratio image formation

In an embodiment, the additional image metadata includes a local multi-scale grayscale ratio image derived from the original HDR image. An embodiment uses a color gamut (such as the extended YCC color gamut published with the image format herein) to enable full restoration at each pixel in an HDR version of the original HDR image, which is generated/restored from the tone mapped image and the local multi-scale grayscale ratio image. In an embodiment, the techniques as described herein minimize the number of full black tone map values in the tone mapped image that are below a threshold (e.g., 0.01%, 0.1%, 1%, 2%, etc. of the total number of pixels in the tone mapped image) to enable full restoration at each pixel in the HDR version of the original HDR image.

According to the techniques herein, rather than using a global tone mapping (TM) operator (which compresses global contrast to fit within a desired luminance value output range and loses local contrast that is important for human visual perception), a local multi-scale tone mapping process can be used to produce a tone-mapped image that improves local contrast that would be lost in a global TM operator, while preserving the global mapping intact. In an embodiment, the local multi-scale TM process uses a global curve (e.g., a histogram-adjusted TM curve) to map luminance values without loss of detail. In an embodiment, the local multi-scale TM process is performed efficiently without generating/introducing new artifacts (such as halos) in the process. In a specific embodiment, a highly efficient recursive process is implemented to perform the local multi-scale process as described herein with high computational efficiency. In a specific possible embodiment, the local multi-scale process takes only 30% longer than the TM process of the global TM operator.

According to the techniques herein, rather than using a global tone mapping (TM) operator (which compresses global contrast to fit within a desired luminance value output range and loses local contrast that is important for human visual perception), a local multi-scale tone mapping process can be used to produce a tone-mapped image that improves local contrast that would be lost in a global TM operator, while preserving the global mapping intact. In an embodiment, the local multi-scale TM process uses a global curve (e.g., a histogram-adjusted TM curve) to map luminance values without loss of detail. In an embodiment, the local multi-scale TM process is performed efficiently without generating/introducing new artifacts (such as halos) in the process. In a specific embodiment, a highly efficient recursive process is implemented to perform the local multi-scale process as described herein with high computational efficiency. In a specific possible embodiment, the local multi-scale process takes only 30% longer than the TM process of the global TM operator.

In an embodiment, an input HDR image is loaded and its luminance values are converted to a logarithmic domain. A histogram adjustment TM curve is calculated and applied to the luminance values to determine an overall ratio grayscale image. As used herein, a ratio image generally refers to an image comprising the ratio between the luminance values in a pre-tone mapped image (e.g., the input HDR image or its logarithmic equivalent) and the luminance values in a post-tone mapped image (e.g., the tone mapped image or its logarithmic equivalent). In an embodiment, the ratio image is logically represented at each pixel position in a non-logarithmic domain as the pre-tone mapped image divided by the post-tone mapped image, or equivalently represented at each pixel position in a logarithmic domain as the pre-tone mapped image minus the post-tone mapped image. In certain other embodiments, the ratio image is logically represented at each pixel position in a non-logarithmic domain as the post-tone mapped image divided by the pre-tone mapped image, or equivalently represented at each pixel position in a logarithmic domain as the post-tone mapped image minus the pre-tone mapped image. In all of these embodiments, it should be noted that if the ratio image (e.g., the local multi-scale TM image) and the pre-tone mapping image (e.g., the input HDR image) are known, the pre-tone mapping image (e.g., the local multi-scale TM image) can be obtained via simple algebraic operations (e.g., multiplication/division in the non-logarithmic domain; addition and subtraction in the logarithmic domain).

In an embodiment, an overall ratio image used to generate other ratio images to be incorporated into the local multi-scale ratio is efficiently computed in the logarithmic domain using subtraction of 16-bit integer quantities. In an embodiment, a reference maximum value on the tone-mapped image can be computed, and the tone-mapped image can be modified so that no more than a small percentage of pixels lie outside a supported color gamut (e.g., an extended YCC color gamut).

In an embodiment, an overall ratio image used to generate other ratio images to be incorporated into the local multi-scale ratio is efficiently computed in the logarithmic domain using subtraction of 16-bit integer quantities. In an embodiment, a reference maximum value on the tone-mapped image can be computed, and the tone-mapped image can be modified so that no more than a small percentage of pixels lie outside a supported color gamut (e.g., an extended YCC color gamut).

Equivalents, extensions, replacements and others

In the foregoing specification, embodiments of the invention have been described with reference to numerous specific details that may vary in different implementations. Thus, the sole and exclusive indicator of what is the invention, and what the applicants intend to be the invention, is the set of claims issuing from this application, in the specific form in which such claims issue, including any subsequent amendments. Any definitions expressly set forth herein for terms contained in such claims shall govern the meaning of such terms as used in the claims. Therefore, no limitation, element, property, feature, advantage, or attribute that is not expressly recited in a claim should in any way limit the scope of such claim. The specification and drawings are, therefore, to be regarded in an illustrative and not restrictive sense.

Claims (13)

1. A method for encoding a high dynamic range (HDR) image using a processor, the method comprising: Receive an input image having a first dynamic range; Generate a tone-mapped image based on the input image, wherein the tone-mapped image has a dynamic range lower than a first dynamic range; Generate a ratio image ( _YR ) that includes the following luminance pixel values of the input image, which have been divided pixel by pixel by the corresponding luminance pixel values in the tone map image; Apply an invertible function (F) to the ratio image to generate a modified ratio image (F(Y _R )); Generate a lookup table representing the inverse function ( ^F⁻¹ ) of an invertible function, wherein the lookup table ( ^F⁻¹ ) is applied to the modified ratio graph to generate an approximate graph of the ratio graph; and Generate coded HDR images based on tone-mapped images and modified ratio images. The invertible function is chosen such that when the inverse of the invertible function is applied to the modified ratio image, the distance between the ratio image and its approximate image is minimized according to a predetermined metric. The method further includes: Calculate a histogram of pixel values in the ratio image; Calculate the cumulative histogram based on the histogram; and Generate invertible functions based on cumulative histograms. 2. The method of claim 1, wherein the distance between the ratio image and an approximate image of the ratio image is minimized according to the mean square error criterion. 3. The method of claim 1, wherein the predetermined metric includes the signal-to-noise ratio between the ratio image and an approximate image of the ratio image. 4. The method of claim 1, wherein the predetermined metric includes the peak signal-to-noise ratio of an approximate image of the ratio image. 5. The method of claim 1, wherein the file format for encoding the HDR image includes an encoded tone map image, an encoded version of the modified ratio image, and a lookup table representing the inverse function of the inverse function. 6. The method of claim 5, wherein decoding the encoded HDR image in the decoder comprises: Receive encoded HDR images; Extract tone-mapped images, modified ratio images, and lookup tables from coded HDR images; Apply a lookup table to the modified ratio image to generate an approximate image of the ratio image; and An HDR image is generated from an approximate image based on a tone-mapped image and a ratio image. 7. The method according to claim 1 further includes quantizing the modified ratio image to generate a quantized ratio image. 8. The method of claim 7, wherein quantizing the modified ratio image includes calculating... Where _YQ refers to the quantized ratio image, _YR refers to the ratio image, F( _YR ) refers to the modified ratio image, scale refers to the scaling factor, and min(F( _YR )) and max(F( _YR )) refer to the minimum and maximum values of the modified ratio image. 9. The method of claim 8, wherein scale = ^2B - 1, where B refers to the number of bits used to represent the pixels of the quantized ratio image. 10. The method of claim 1, wherein generating the invertible function comprises calculating F _i =((c_hist _i -min(c_hist))/(max(c_hist)-min(c_hist))*scale Where c_hist _i refers to the cumulative histogram value of the i-th pixel in the ratio image, min(c_hist) and max(c_hist) refer to the minimum and maximum values of the cumulative histogram, and scale refers to the scaling factor. 11. The method of claim 10, wherein scale = ^2B - 1, where B refers to the number of bits used to represent the pixels of the modified ratio image. 12. A non-transitory computer-readable storage medium storing computer-executable instructions for executing the method according to any one of claims 1-11 by a processor. 13. An apparatus for decoding encoded high dynamic range (HDR) images, the apparatus comprising: Processor; and A non-transitory computer-readable storage medium storing computer-executable instructions for executing the method according to any one of claims 1-11 by a processor.