Patent Publication Number: US-2021183028-A1

Title: Saturation control for high-dynamic range reconstruction

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to picture and video distribution using in high-dynamic range (HDR) and more generally for YUV Saturation control for HDR adaptation. 
     BACKGROUND 
     This section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present invention that are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     Standard-Dynamic-Range pictures (SDR pictures) are color pictures whose luminance values are represented with a limited dynamic usually measured in power of two or f-stops. SDR pictures have a dynamic around 10 fstops, i.e. a ratio 1000 between the brightest pixels and the darkest pixels in the linear domain, and are coded with a limited number of bits (most often 8 or 10 in HDTV (High Definition Television systems) and UHDTV (Ultra-High Definition Television systems) in a non-linear domain, for instance by using the ITU-R BT.709 OEFT (Optico-Electrical-Transfer-Function). This limited non-linear representation does not allow correct rendering of small signal variations, in particular in dark and bright luminance ranges. In High-Dynamic-Range pictures (HDR pictures), the signal dynamic is much higher (up to 20 f-stops, a ratio one million between the brightest pixels and the darkest pixels) and a new non-linear representation is needed in order to maintain a high accuracy of the signal over its entire range. In HDR pictures, raw data are usually represented in floating-point format (either 32-bit or 16-bit for each component, namely float or half-float), the most popular format being openEXR half-float format (16-bit per RGB component, i.e. 48 bits per pixel) or in integers with a long representation, typically at least 16 bits. 
     By contrast, High Dynamic Range pictures (HDR pictures) are color pictures whose luminance values are represented with a HDR dynamic that is higher than the dynamic of a SDR picture. The HDR dynamic is not yet defined by a standard but one may expect a dynamic range up to a few thousands nits. For instance, a HDR color volume is defined by a RGB BT.2020 color space and the values represented in said RGB color space belong to a dynamic range from 0 to 4000 nits. Another example of HDR color volume is defined by a RGB BT.2020 color space and the values represented in said RGB color space belong to a dynamic range from 0 to 1000 nits. 
     Tone mapping is a technique used in image processing and computer graphics to map one set of colors to another to approximate the appearance of high-dynamic-range images in a medium that has a more limited dynamic range. Tone mapping addresses the problem of strong contrast reduction from the scene radiance to the displayable range while preserving the image details and color appearance important to appreciate the original scene content. 
     One challenging problem is performing tone mapping in a way that true colors are represented during the distribution of an HDR picture (or video) while, at the same time, distributing an associated SDR picture (or video) representative of a color-graded version of said HDR picture (or video). Current prior art techniques are limited in solutions they present. Consequently, improved techniques are needed in the distribution of a video or HDR image that is to be processed by medium of a more limited dynamic range in a way that colors are reproduced correctly. 
     SUMMARY 
     In one embodiment, a method is provided for generating a tone mapping function to reduce dynamic range of a first image to produce a second image. A luma signal and a plurality of chroma components associated with the first and second image are then determined. A gamut color correction is then performed on the second image using an adaptive function. The adaptive function is generated by comparing said luma signal and at least one chroma component of said first and second image. 
     In a different embodiment, a system is provided having processing means configured to generate a tone mapping function to reduce dynamic range of a first image to produce a second image. A luma signal and a plurality of chroma components associated with the first and second image are then determined using the processing means. A gamut color correction is then performed using the processing means on the second image using an adaptive function. The adaptive function is generated by comparing said luma signal and at least one chroma component of said first and second image. 
     Additional features and advantages are realized through the techniques of the present disclosure. Other embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed invention. For a better understanding of the invention with advantages and features, refer to the description and to the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will be better understood and illustrated by means of the following embodiment and execution examples, in no way limitative, with reference to the appended figures on which: 
         FIG. 1  is an illustration of a schematic diagram for reconstructing an image I 3  representative of original image I 1  from a decoded image   in accordance with an embodiment of the present principles; 
         FIG. 2  is a schematic diagram showing an end-to-end workflow supporting content production and delivery to HDR and SDR enabled CE displays in accordance with an embodiment the present principles 
         FIG. 3  is an alternate embodiment of the diagram of  FIG. 2 ; 
         FIG. 4  is an alternate embodiment of the end-to-end workflow as show in  FIG. 2 ; 
         FIG. 5  is an example illustrating a perceptual transfer function; 
         FIG. 6  is an example illustrating a piece-wise curve used for mapping; 
         FIG. 7  is an example illustrating a curve used for converting back a signal to a linear light domain; 
         FIG. 8  is a flow diagram illustrating another example of reconstructing an image from a decoded image data and parameters obtained from a bitstream in accordance with an embodiment of the present principles; 
         FIG. 9  is a schematic diagram illustrating an architecture of a device in accordance with an embodiment of present principles; 
         FIG. 10  is a schematic diagram illustrating an exemplary HDR system in accordance with an embodiment of present principles; 
         FIG. 11  is a schematic diagram illustrating an exemplary synoptic of HDR-to-SDR decomposition process in accordance with an embodiment; 
         FIG. 12  is a schematic diagram illustrating a synoptic for LUT generation in accordance with an embodiment of present principles; 
         FIG. 13  is a block diagram showing a tone mapping algorithm in accordance with an embodiment of present principles; 
         FIG. 14  is a block diagram illustration of remote devices communicating over a communication network in accordance with an embodiment of present principles; 
         FIG. 15  is a flowchart depiction of a methodology in accordance to another embodiment of present principles. 
     
    
    
     Wherever possible, the same reference numerals will be used throughout the figures to refer to the same or like parts. 
     DESCRIPTION 
     It is to be understood that the figures and descriptions of the present invention have been simplified to illustrate elements that are relevant for a clear understanding of the present invention, while eliminating, for purposes of clarity, many other elements found in typical digital multimedia content delivery methods and systems. However, because such elements are well known in the art, a detailed discussion of such elements is not provided herein. The disclosure herein is directed to all such variations and modification. In addition, various inventive features are described below that can each be used independently of one another or in combination with other features. Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure. 
     In general, chromaticity is an objective specification of the quality of a color regardless of its luminance and is often represented by two independent parameters, namely hue (h) and colorfulness. The white point of an illuminant or of a display is a neutral reference characterized by a chromaticity and all other chromaticities may be defined in relation to this reference using polar coordinates. The hue is the angular component, and the purity is the radial component, normalized by the maximum radius for that hue. 
     A color picture also contains several arrays of samples (pixel values) in a specific picture/video format which specifies all information relative to the pixel values of a picture (or a video) and all information which may be used by a display and/or any other device to visualize and/or decode a picture (or video) for example. A color picture comprises at least one component, in the shape of a first array of samples, usually a luma (or luminance) component, and at least one another component, in the shape of at least one other array of samples. Or, equivalently, the same information may also be represented by a set of arrays of color samples (color component), such as the traditional tri-chromatic RGB representation. A pixel value is represented by a vector of C values, where c is the number of components. Each value of a vector is represented with a number of bits which defines a maximal dynamic range of the pixel values. 
       FIG. 1  is an illustration of a schematic diagram for reconstructing an image I 3  representative of original image I 1  from a decoded image   in accordance with an example of the present principles. 
     In step  10 , a set of parameters SP is obtained to reconstruct the image I 3 . These parameters are either parameters P obtained from the bitstream B, or recovered parameters P r  when at least one parameter P is lost, corrupted or not aligned with a decoded image   whose graphics or overlay is added to. In step  11 , a module M 1  obtains the decoded image   and in step  12 , a module M 2  reconstructs the image I 3  from the decoded image   by using the set of parameters SP. The decoded image data   is obtained from the bitstream (signal) B or any other bitstream and, possibly, said bitstreams may be stored on a local memory or any other storage medium. In sub-step  101  (of step  10 ), a module M 3  obtains the parameters P required to reconstruct the image I 3 . In sub-step  102  (of step  10 ), a module M 4  checks if at least one of the parameters P is lost, corrupted or not aligned with the decoded image   whose graphics or overlay is added to. When none of the parameter P is lost, corrupted, or not aligned with the decoded image   whose graphics or overlay is added to, the set of parameters SP only comprises the parameters P. 
     When at least one of the parameters P is either lost, corrupted or not aligned with the decoded image   whose graphics or overlay is added to, in sub-step  103  (of step  10 ), a module M 5  obtains an information data ID indicating how said parameters have been processed, in sub-step  104  (of step  10 ), a module M 6  selects a recovery mode RM i  according to said information data ID, and in sub-step  105  (of step  10 ), a module M 7  recovers said at least one lost, corrupted or not aligned parameter by applying the selected recovery mode RM i . The at least one recovered parameter P r  is added to the set of parameters SP. In step  12 , the image I 3  is then reconstructed taking also into account said at least one recovered parameter P r . The method is advantageous because it allows to obtain parameters for a single layer based distribution solution when multiple single layer based distribution solutions share a same set of syntax elements for carrying a common set of parameters and when said single layer based distribution solutions require different recovery modes (process) for recovering lost, corrupted or not aligned parameters, guaranteeing thus the success of the reconstruction of the image I 3  for each of said single layer based distribution solution. The method is also advantageous when a CE device, typically a set-top-box or a player, inserts graphics on top of a decoded imager  , because the method selects a specific recovery mode to replace the not aligned parameters by parameters adapted to the decoded image I 2  plus the graphics (or overlay) and reconstructs the image I 3  by using said recovered parameters from said decoded image   whose graphics or overlay is added to, avoiding thus some flickering artefacts or undesired effects impacting the reconstructed image quality. 
       FIG. 2  shows an end-to-end workflow supporting content production and delivery to HDR and SDR enabled CE displays in accordance with an example of the present principles. 
     This workflow involves a single layer based distribution solution with associated metadata and illustrates an example of the use of a method for reconstructing an image I 3  representative of original image data  1 , from a decoded image data   and a set of parameters SP obtained in accordance with an example of the present principles illustrated in  FIG. 1 . Basically, this single layer based distribution solution comprises a pre-processing part and a post-processing part. At the pre-processing part, a pre-processing stage  20  decomposes the original image I 1  in an output image I 12  and a set of parameters SP, and a switching step  24  determines if either the original image I 1  or the output image I 12  is encoded in the bitstream B (step  23 ). In step  23 , the image I 2  may be encoded with any legacy video codec and the bitstream B is carried throughout an existing legacy distribution network with accompanying associated metadata (set of parameters SP) conveyed on a specific channel or embedded in the bitstream B. In another embodiment, the bitstream B with accompanying metadata are stored on a storage medium such a Blu-ray disk or a memory or a register of a Set-Top-Box for example. 
     It should be noted that image data refer to one or several arrays of samples (pixel values) in a specific image/video format which specifies all information relative to the pixel values of an image (or a video) and all information which may be used by a display and/or any other device to visualize and/or decode a image (or video) for example. An image comprises a first component, in the shape of a first array of samples, usually representative of luminance (or luma) of the image, and a second and third component, in the shape of other arrays of samples, usually representative of the color (or chroma) of the image. Or, equivalently, the same information may also be represented by a set of arrays of color samples, such as the traditional tri-chromatic RGB representation. A pixel value is represented by a vector of C values, where C is the number of components. Each value of a vector is represented with a number of bits which defines a maximal dynamic range of the pixel values. 
     Standard-Dynamic-Range images (SDR images) are images whose luminance values are represented with a limited number of bits (typically 8). This limited representation does not allow correct rendering of small signal variations, in particular in dark and bright luminance ranges. In high-dynamic range images (HDR images), the signal representation is extended to maintain a high accuracy of the signal over its entire range. In HDR images, pixel values representing luminance levels are usually represented in floating-point format (typically at least 10 bits per component, namely float or half-float), the most popular format being openEXR half-float format (16-bit per RGB component, i.e. 48 bits per pixel) or in integers with a long representation, typically at least 16 bits. 
     The High Efficiency Video Coding (HEVC) standard (ITU-T H.265 Telecommunication standardization sector of ITU (10/2014), series H: audiovisual and multimedia systems, infrastructure of audiovisual services—coding of moving video, High efficiency video coding, Recommendation ITU-T H.265) enables the deployment of new video services with enhanced viewing experience, such as Ultra HD broadcast services. In addition to an increased spatial resolution, Ultra HD can bring a wider color gamut (WCG) and a higher dynamic range (HDR) than the Standard dynamic range (SDR) HD-TV currently deployed. Different solutions for the representation and coding of HDR/WCG video have been proposed (SMPTE 2014, “High Dynamic Range Electro-Optical Transfer Function of Mastering Reference Displays, or SMPTE ST 2084, 2014, or Diaz, R., Blinstein, S. and Qu, S. “Integrating HEVC Video Compression with a High Dynamic Range Video Pipeline”, SMPTE Motion Imaging Journal, Vol. 125, Issue 1. February 2016, pp 14-21). 
     SDR backward compatibility with decoding and rendering devices is an important feature in some video distribution systems, such as broadcasting or multicasting systems. This is because some applications may need a solution based on a single layer coding/decoding process may be backward compatible, e.g. SDR compatible, and may leverage legacy distribution networks and services already in place. Such a single layer based distribution solution enables both high quality HDR rendering on HDR-enabled Consumer Electronic (CE) devices, while also offering high quality SDR rendering on SDR-enabled CE devices. Such a single layer based distribution solution generates an encoded signal, e.g. SDR signal, and associated metadata (of a few bytes per video frame or scene) that can be used to reconstruct another signal, e.g. HDR signal, from a decoded signal, e.g. SDR signal. Metadata stored parameters values used for the reconstruction of the signal and may be static or dynamic. Static metadata means metadata that remains the same for a video (set of images) and/or a program. 
     Static metadata are valid for the whole video content (scene, movie, clip . . . ) and may not depend on the image content. They may define, for example, image format or color space, color gamut. For instance, SMPTE ST 2086:2014, “Mastering Display Color Volume Metadata Supporting High Luminance and Wide Color Gamut Images” is such a kind of static metadata for use in production environment. The Mastering Display Colour Volume (MDCV) SEI (Supplemental Enhanced Information) message is the distribution flavor of ST 2086 for both H.264/AVC (“Advanced video coding for generic audiovisual Services”, SERIES H: AUDIOVISUAL AND MULTIMEDIA SYSTEMS, Recommendation ITU-T H.264, Telecommunication Standardization Sector of ITU, January 2012) and HEVC video codecs. Dynamic metadata are content-dependent, that is metadata can change with the image/video content, e.g. for each image or when each group of images. As an example, SMPTE ST 2094:2016 standards families, “Dynamic Metadata for Color Volume Transform” are dynamic metadata for use in production environment. SMPTE ST 2094-30 can be distributed along HEVC coded video stream thanks to the Colour Remapping Information (CRI) SEI message. 
     Other single layer based distribution solutions exist on distribution networks for which display adaptation dynamic metadata are delivered along with a legacy video signal. These single layer based distribution solutions may produce HDR 10-bits image data (e.g. image data which signal is represented as an HLG10 or PQ10 signal as specified in Rec. ITU-R BT.2100-0 “Recommendation ITU-R BT.2100-0, Image parameter values for high dynamic range television for use in production and international program exchange”) and associated metadata from an input signal (typically 12 or 16 bits), encodes said HDR 10-bits image data using, for example an HEVC Main 10 profile encoding scheme, and reconstructs a video signal from a decoded video signal and said associated metadata. The dynamic range of the reconstructed signal being adapted according to the associated metadata that may depend on characteristics of a target display. 
     Dynamic metadata transmission in actual real-world production and distribution facilities were hard to guarantee and could be possibly lost or corrupted because of splicing, overlay layers insertion, professional equipment pruning bitstream, stream handling by affiliates and current lack of standardization for the carriage of metadata throughout the post-production/professional plant. The single layer based distribution solutions cannot work without the presence of different bunch of dynamic metadata with some of them being critical for guaranteeing the success of the reconstruction of the video signal. Similar issues may also occur when dynamic metadata are not aligned with an image whose graphics or overlay is added to. This occurs, for example, when graphics (overlays, OSD, . . . ) are inserted in (added to) an image outside the distribution chain because the metadata, computed for said image, is also applied once the graphics are inserted in (added to) the image. The metadata are then considered as being not aligned with the image whose graphics or overlay are added to because they may not be adapted to the part of said image which contains graphics or overlay. These issues might be characterized by image flickering on fixed portion of graphics when the decoded image is displayed over time or by undesirable effects (saturation, clipping . . . ) on portion of the image containing graphics or overlay processed with inappropriate metadata (e.g. bright OSD processed by metadata generated for a dark content). 
     Referring back to  FIG. 1 , the accompanying associated metadata is carried by another specific channel or store on a separate storage medium. Preferably, the video is coded with H.265/HEVC codec ( ITU - T H. 265  Telecommunication standardization sector of ITU  (10/2014),  series H: audiovisual and multimedia systems, infrastructure of audiovisual services—coding of moving video, High efficiency video coding, Recommendation ITU - T H. 265) or H.264/AVC (“ Advanced video coding for generic audiovisual Services ”, SERIES H: AUDIOVISUAL AND MULTIMEDIA SYSTEMS, Recommendation ITU-T H.264, Telecommunication Standardization Sector of ITU, January 2012). In the case the information data ID determines that the original image I 1  (possibly represented by the components (C1,U′, V′) or a Y′CbCr 4:2:0 PQ10 or HLG10 video signal) is encoded in step  23 , said original image I 1  may be encoded with the HEVC Main 10 profile. In the case the information data ID determines that the output image I 12  is encoded in step  23 , the output image I 12 , which can be represented as a Y′CbCr 4:2:0 gamma transfer characteristics (Standard Dynamic Range) signal may be encoded with any HEVC profile including Main 10 or Main profiles. The information data ID may be also conveyed as associated metadata (step  23 ). At the post-processing part, a decoded image   is obtained from the bitstream B (step  11 ), a set of parameters SP is obtained as explained in  FIG. 1 , step  10 , and a post-processing stage  12 , which is the functional inverse of the pre-processing stage  20 , reconstructs an image I 3  from the decoded image   and the set of parameters SP. This single layer based distribution solution may also comprise optional format adapting steps  21 ,  22 ,  25 ,  26 . For example, in step  21  (optional), the format of the original image I 1  may be adapted to a specific format (C1,U′,V′) of the input of the pre-processing stage  20 , and in step  22  (optional), the format (c, u′, v′) of the output image I 12  may also be adapted to a specific output format before encoding. In step  25 , the format of the decoded image   may be adapted to a specific format of the input of the post-processing stage  12 , and in step  26 , the image I 3  may be adapted to at least one characteristic of a targeted apparatus (e.g. a Set-Top-Box, a connected TV, HDR/SDR enabled CE device, a Blu-ray disc player) and/or an inverse gamut mapping may be used when the decoded image   and the image I 3  or the original image I 1  are represented in different color spaces and/or gamut. 
     The format adaptation of the above mentioned steps,  21 ,  22 ,  25 , and  26  may also include color space conversion and/or color gamut mapping. Usual format adapting processes may be used such as RGB-to-YUV or YUV-to-RGB conversion, BT.709-to-BT.2020 or BT.2020-to-BT.709, down-sampling or up-sampling chroma components, etc. Note that the well-known YUV color space refers also to the well-known YCbCr in the prior art. Annex E of the recommendation ETSI recommendation ETSI TS 103 433 V1.1.1, release 2016-8, provides an example of format adapting processes and inverse gamut mapping (Annex D). The input format adaptation step  21  may also include adapting the bit depth of the original image I 1  to specific bit depth such as 10 bits for example, by applying a transfer function on the original image I 1 . For example, a PQ or HLG transfer function may be used (Rec. ITU-R BT.2100-0). 
     In one embodiment, the pre-processing stage  20  comprises steps  200 - 202 . In step  200 , a first component c1 of the output image I 12  is obtained by mapping a first component C1 of the original image I 1 : 
         c   1   =TM ( C 1) 
     with TM being a mapping function. The mapping function TM may reduce or increase the dynamic range of the luminance of the original image I 1  and its inverse may increase or reduce the dynamic range of the luminance of an image. 
     In one embodiment, in step  201 , a second and third component u′, v′ of the output image I 12  are derived by correcting second and third components U′, V′ of the original image I 1  according to the first component c 1 . The correction of the chroma components may be maintained under control by tuning the parameters of the mapping. The color saturation and hue are thus under control. According to an embodiment of step  201 , the second and third components U′ and V′ are divided by a scaling function β 0 (c 1 ) whose value depends on the first component c 1 . Mathematically speaking, the second and third components u′, v′ are given by: 
     
       
         
           
             
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     Optionally, in step  202 , the first component c 1  may be adjusted to further control the perceived saturation, as follows: 
         c=c   1 −max(0, a.u′+b.v ′)
 
     where a and b are two parameters of the set of parameters SP. This step  202  allows to control the luminance of the output image I 12  to guarantee the perceived color matching between the colors of the output image I 12  and the colors of the original image I 1 . The set of parameters SP may comprise parameters relative to the mapping function TM or its inverse ITM, the scaling function β 0 (c 1 ). These parameters are associated with dynamic metadata and carried in a bitstream, for example the bitstream B. The parameters a and b may also be carried in a bitstream. 
     In one embodiment, at the post-processing part, in step  10 , a set of parameters SP is obtained as explained in  FIG. 1 . According to an embodiment of step  10 , the set of parameters SP is carried by static/dynamic metadata obtained from a specific channel or from a bitstream, including the bitstream B, possibly store on a storage medium. In step  11 , the module M 1  obtains a decoded image   by decoding the bitstream B and the decoded image   is then available for either an SDR or HDR enabled CE display. In more details, the post-processing stage  12  comprises steps  120 - 122 . In optional step  120 , the first component c of the decoded image   may be adjusted as follows: 
         c   1   =c +max(0, a.u′+b.v ′)
 
     where a and b are two parameters of the set of parameters SP. In step  121 , the first component C1 of the image I 3  is obtained by inverse-mapping the first component c 1 : 
         C   1   =ITM ( c   1 ) 
     In step  122 , the second and third component U′, V′ of the image I 3  are derived by inverse correcting the second and third components u′, v′ of the decoded image   according to the component c 1 . According to an embodiment, a second and third components u′ and v′ are multiplied by a scaling function β 0 (c 1 ) whose value depends on the first component c 1 . Mathematically speaking, the two first and second components U′, V′ are given by: 
     
       
         
           
             
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     According to a first embodiment of the method of  FIG. 2 , as illustrated in  FIG. 3 , at the pre-processing part, the first component C1 of the original image I 1  is a linear-light luminance component L obtained from the RGB component of the original image I 1  by: 
     
       
         
           
             
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     and the second and third component U′, V′ are derived by applying a pseudo-gammatization using square-root (close to BT.709 OETF) to the RGB components of the original image I 1 : 
     
       
         
           
             
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     In step  200 , the first component y 1  of the output image I 12  is obtained by mapping said linear-light luminance component L: 
         y   1   =TM ( L ) 
     In step  201 , the second and third component u′, v′ of the output image I 12  are derived by correcting the first and second components U′, V′ according to the first component y 1 . At the post-processing part, in step  121 , a linear-light luminance component L of the image I 3  is obtained by inverse-mapping the first component c 1 : 
         L=ITM ( y   1 ) 
     In step  122 , the second and third component U′, V′ of the image I 3  are derived by inverse correcting the second and third components u′, v′ of the output image I 12  according to the first component y 1 . According to an embodiment of step  122 , the second and third components u′ and v′ are multiplied by a scaling function β 0 (y 1 ) whose value depends on the first component y 1 . Mathematically speaking, the two first and second components U′, V′ are given by: 
     
       
         
           
             
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     According to a second embodiment of the method of  FIG. 2 , as illustrated in  FIG. 4 , at the pre-processing part, the first component C1 of the original image I 1  is a component Y′ obtained from the gamma-compressed RGB components of the original image I 1  by: 
     
       
         
           
             
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     and the second and third component U′, V′ by applying a gammatization to the RGB components of the original image I 1 : 
     
       
         
           
             
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               1024 
             
           
         
       
     
     where γ may be a gamma factor, preferably equal to 2.4. Note, the component Y′, which is a non-linear signal, is different of the linear-light luminance component L. 
     In step  200 , the first component y′ 1  of the output image I 12  is obtained by mapping said component Y′: 
         Y′   1   =TM ( Y ′)
 
     In step  121 , a reconstructed component   is obtained by inverse-mapping the first component y′ 1 : 
         = ITM ( y′   1 ) 
     where ITM is the inverse of the mapping function TM. The values of the reconstructed component   belong thus to the dynamic range of the values of the component Y′. 
     In step  201 , the second and third component u′, v′ of the output image I 12  are derived by correcting the first and second components U′, V′ according to the first component y′ 1  and the reconstructed component  . This step ( 201 ) allows to control the colors of the output image I 12  and guarantees their matching to the colors of the original image I 1 . The correction of the chroma components may be maintain under control by tuning the parameters of the mapping (inverse mapping). The color saturation and hue are thus under control. Such a control is not possible, usually, when a non-parametric perceptual transfer function is used. According to an embodiment of step  201 , the second and third components U′ and V′ are divided by a scaling function β 0 (y′ 1 ) whose value depends on the ratio of the reconstructed component   over the component y′ 1 : 
     
       
         
           
             
               
                 β 
                 0 
               
                
               
                 ( 
                 
                   y 
                   1 
                   ′ 
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     ITM 
                      
                     
                       ( 
                       
                         y 
                         1 
                         ′ 
                       
                       ) 
                     
                   
                   · 
                   Ω 
                 
                 
                   y 
                   1 
                   ′ 
                 
               
               = 
               
                 
                   · 
                   Ω 
                 
                 
                   y 
                   1 
                   ′ 
                 
               
             
           
         
       
     
     with Ω is constant value depending on the color primaries of the original image I 1  (equals to 1.3 for BT.2020 for example). At the post-processing part, in step  121 , a component   of the image I 3  is obtained by inverse-mapping the first component y′ 1 : 
     In step  122 , the second and third component U′, V′ of the image I 3  are derived by inverse correcting the second and third components u′, v′ of the decoded image   according to the first component y′ 1  and the component  . According to an embodiment of step  122 , a second and third components u′ and v′ are multiplied by the scaling function β 0 (y′ 1 ) Mathematically speaking, the two first and second components U′, V′ are given by: 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       U 
                       ′ 
                     
                   
                 
                 
                   
                     
                       V 
                       ′ 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 
                   β 
                   0 
                 
                  
                 
                   ( 
                   
                     y 
                     1 
                     ′ 
                   
                   ) 
                 
               
               · 
               
                 [ 
                 
                   
                     
                       
                         u 
                         ′ 
                       
                     
                   
                   
                     
                       
                         v 
                         ′ 
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
     The mapping function, TM, based on a perceptual transfer function, whose goal is to convert a component of an original image I 1  into a component of an output image I 12 , thus reducing (or increasing) the dynamic range of the values of their luminance. The values of a component of an output image I 12  belong thus to a lower (or greater) dynamic range than the values of the component of an original image I 1 . The perceptual transfer function uses a limited set of control parameters. 
       FIG. 5  is an illustration of a perceptual transfer function which may be used for mapping luminance components but a similar perceptual transfer function for mapping luma components may be used. The mapping is controlled by a mastering display peak luminance parameter (equal to 5000 cd/m 2  in  FIG. 5 ). To better control the black and white levels, a signal stretching between content-dependent black and white levels is applied. Then the converted signal is mapped using a piece-wise curve constructed out of three parts, as illustrated in  FIG. 6 . The lower and upper sections are linear, the steepness being determined by the shadowGain and highlightGain parameters respectively. The mid-section is a parabola providing a smooth bridge between the two linear sections. The width of the cross-over is determined by the midToneWidthAdjFactor parameter. All the parameters controlling the mapping may be conveyed as metadata for example by using a SEI message as defined in JCTVC-W0133 to carry the SMPTE ST 2094-20 metadata. 
       FIG. 7  provides an example of the inverse of the perceptual transfer function TM ( FIG. 5 ) to illustrate how a perceptual optimized video signal may be converted back to the linear light domain based on a targeted legacy display maximum luminance, for example 100 cd/m 2 . In step  10  ( FIG. 1 ), the set of parameters SP is obtained to reconstruct an image I 3  from a decoded image  . These parameters may be obtained from metadata obtained from a bitstream, for example the bitstream B. The recommendation ETSI TS 103 433 V1.1.1 clause 6, 2016-08 provides an example of syntax of said metadata. The syntax of the recommendation ETSI TS 103 433 v1.1.1 is described for reconstructing an HDR video from an SDR video but this syntax may extend to the reconstruction of any image I 3  from any decoded image  . The post-processing (step  12 ) operates on an inverse mapping function ITM and a scaling function β 0 (⋅) that are derived from dynamic metadata because they depend on the first component c 1 . 
     According one embodiment based on the recommendation ETSI TS 103 433 V1.1.1, the dynamic metadata may be conveyed according to either a so-called parameter-based mode or a table-based mode. The parameter-based mode may be of interest for distribution workflows which primary goal is to provide direct SDR backward compatible services with very low additional payload or bandwidth usage for carrying the dynamic metadata. The table-based mode may be of interest for workflows equipped with low-end terminals or when a higher level of adaptation is required for representing properly both HDR and SDR streams. 
     In the parameter-based mode, dynamic metadata to be conveyed are luminance mapping parameters representative of the inverse function ITM, i.e.
         tmInputSignalBlackLevelOffset;   tmInputSignalWhiteLevelOffset;   shadowGain;   highlightGain;   midToneWidthAdjFactor;   tmOutputFineTuning parameters;
 
Moreover, other dynamic metadata to be conveyed are color correction parameters (saturationGainNumVal, saturationGainX(i) and saturationGainY(i)) used to define the function β 0 (⋅) (ETSI recommendation ETSI TS 103 433 V1.1.1 clauses 6.3.5 and 6.3.6). The parameters a and b may be respectively carried/hidden in the saturationGain function parameters as explained above. These dynamic metadata may be conveyed using the HEVC Colour Volume Reconstruction Information (CVRI) user data registered SEI message whose syntax is based on the SMPTE ST 2094-20 specification (recommendation ETSI TS 103 433 V1.1.1 Annex A.3). Typical dynamic metadata payload is about 25 bytes per scene. In step  101 , the CVRI SEI message is parsed the SEI message to obtain mapping parameters and color-correction parameters. In step  12 , the inverse mapping function ITM (so-called lutMapY) is reconstructed (derived) from the obtained mapping parameters (see recommendation ETSI TS 103 433 V1.1.1 clause 7.2.3.1 for more details). In step  12 , the scaling function β 0 (⋅) (so-called lutCC) is also reconstructed (derived) from the obtained color-correction parameters (see recommendation ETSI TS 103 433 V1.1.1 clause 7.2.3.2 for more details).
       

     In the table-based mode, dynamic data to be conveyed are pivots points of a piece-wise linear curve representative of the inverse mapping function ITM. For example, the dynamic metadata are luminanceMappingNumVal that indicates the number of the pivot points, luminanceMappingX that indicates the x values of the pivot points, and luminanceMappingY that indicates they values of the pivot points (see recommendation ETSI TS 103 433 V1.1.1 clauses 6.2.7 and 6.3.7 for more details). Moreover, other dynamic metadata to be conveyed may be pivots points of a piece-wise linear curve representative of the scaling function β 0 (⋅). For example, the dynamic metadata are colorCorrectionNumVal that indicates the number of pivot points, colorCorrectionX that indicates the x values of pivot points, and colorCorrectionY that indicates the y values of the pivot points (see the recommendation ETSI TS 103 433 V1.1.1 clauses 6.2.8 and 6.3.8 for more details). These dynamic metadata may be conveyed using the HEVC Colour Remapping Information (CRI) SEI message whose syntax is based on the SMPTE ST 2094-30 specification (recommendation ETSI TS 103 433 V1.1.1 Annex A.4). Typical payload is about 160 bytes per scene. In step  102 , the CRI (Colour Remapping Information) SEI message (as specified in HEVC/H.265 version published in December 2016) is parsed to obtain the pivot points of a piece-wise linear curve representative of the inverse mapping function ITM and the pivot points of a piece-wise linear curve representative of the scaling function β 0 (⋅), and the chroma to luma injection parameters a and b. 
     In step  12 , the inverse mapping function ITM is derived from those of pivot points relative to a piece-wise linear curve representative of the inverse mapping function ITM (see recommendation ETSI TS 103 433 V1.1.1 clause 7.2.3.3 for more details). In step  12 , the scaling function β 0 (⋅), is also derived from those of said pivot points relative to a piece-wise linear curve representative of the scaling function β 0 (⋅), (see recommendation ETSI TS 103 433 V1.1.1 clause 7.2.3.4 for more details). Note that static metadata also used by the post-processing stage may be conveyed by SEI message. For example, the selection of either the parameter-based mode or table-based mode may be carried by the Information (TSI) user data registered SEI message (payloadMode) as defined by the recommendation ETSI TS 103 433 V1.1.1 (clause A.2.2). Static metadata such as, for example, the color primaries or the maximum display mastering display luminance are conveyed by a Mastering Display Colour Volume (MDCV) SEI message as defined in AVC, HEVC. 
     According an embodiment of step  103 , the information data ID is explicitly signaled by a syntax element in a bitstream and thus obtained by parsing the bitstream. For example, said syntax element is a part of an SEI message. According to an embodiment, said information data ID identifies what is the processing applied to the original image I 1  to process the set of parameters SP. According to this embodiment, the information data ID may then be used to deduce how to use the parameters to reconstruct the image I 3  (step  12 ). For example, when equal to 1, the information data ID indicates that the parameters SP have been obtained by applying the pre-processing stage (step  20 ) to an original HDR image I 1  and that the decoded image   is a SDR image. When equal to 2, the information data ID indicates that the parameters have been obtained by applying the pre-processing stage (step  20 ) to an HDR10 bits image (input of step  20 ), that the decoded image   is a HDR10 image, and the mapping function TM is a PQ transfer function. When equal to 3, the information data ID indicates that the parameters have been obtained by applying the pre-processing stage (step  20 ) to a HDR10 image (input of step  20 ), that the decoded image   is an HLG10 image, and the mapping function TM is a HLG transfer function to the original image I 1 . 
     According to an embodiment of step  103 , the information data ID is implicitly signaled. For example, the syntax element transfer-characteristics present in the VUI of HEVC (annex E) or AVC (annex E) usually identifies a transfer function (mapping function TM) to be used. Because different single layer distribution solutions use different transfer function (PQ, HLG, . . . ), the syntax element transfer-characteristics may be used to identify implicitly the recovery mode to be used. 
     The information data ID may also be signaled by a service defined at a higher transport or system layer. In accordance with another example, a peak luminance value and the color space of the image I 3  may be obtained by parsing the MDCV SEI message carried by the bitstream, and the information data ID may be deduced from specific combinations of peak luminance values and color spaces (color primaries). 
     According to an embodiment of step  102 , a parameter P is considered as being lost when it is not present in (not retrieved from) the bitstream. For example, when the parameters P are carried by SEI message such as the CVRI or CRI SEI messages as described above, a parameter P is considered as being lost (not present) when the SEI message is not transmitted in the bitstream or when the parsing of the SEI message fails. According to an embodiment of step  103 , a parameter P is considered as being corrupted when at least one of the following conditions is fulfilled:
         its value is out of a determined range of values (e.g. saturation_gain_num_val equal to 10 when the compliant range is 0 to 6);   said parameter does not have a coherent value according to other parameter values (e.g. saturation_gain_y[i] contains an outlier i.e. a value that is far from other saturation_gain_y[i] values; typically saturation_gain[0] until saturation_gain[4] are equal to value in the range of 0 to 16 and saturation_gain[1]=255).       

     According to an embodiment of the method, a recovery mode RM i  is to replace all the parameters P by recovered parameters P r  even if only some of the parameters P are not corrupted, lost or not aligned with the decoded image   (whose graphics or overlay is added to). According to an embodiment of the method, another recovery mode RM i  is to replace each lost, corrupted or not aligned parameter P by a recovered parameter P r . According to an embodiment of the method, a recovery mode RM i  is to replace a lost, corrupted or not aligned parameter P by a value of a set of pre-determined parameter values previously stored. For example, a set of pre-determined parameter values may gather a pre-determined value for at least one metadata carried by the CRI and/or CVRI SEI message. A specific set of pre-determined parameter values may be determined, for example, for each single layer based distribution solution identified by the information data ID. 
     Table 1 (below) provides for an illustration of a non-limitative example of specific set of predetermined values for 3 different single layer based distribution solutions. 
                         TABLE 1               Information data ID   ETSI TS 103 433 parameters                  0   Shadow gain: 1.16           Highlight gain: 2.0           MidTones Adjustment: 1.5           White stretch: 0           Black stretch: 0           Saturation Gain [ ]:{(0, 64); (24, 64);           (62, 59); (140, 61); (252, 64); (255, 64)}       1   Shadow gain: 1.033           Highlight gain: 2.0           MidTones Adjustment: 1.5           White stretch: 0           Black stretch: 0       2   Shadow gain: 1.115           Highlight gain: 2.0           MidTones Adjustment: 1.5           White stretch: 0                    
According to the Table 1, three different sets of predetermined values are defined according to the information data ID. These sets of predetermined values defined recovered values for some parameters used by the post-processing stage. The other parameters being set to fixed values that are common to the different single layer solutions.
 
     According to an embodiment of step  104 , a recovery mode RMi is selected according to either at least one characteristic of the original video (image I 1 ), typically the peak luminance of the original content, or of a mastering display used to grade the input image data or the image data to be reconstructed, or at least one characteristic of another video, typically the peak luminance of the reconstructed image I 3 , or of a target display. 
     According to an embodiment, a recovery mode RMi is to check if a characteristic of the original video ( 10  or of a mastering display used to grade the input image data or the image data to be reconstructed (e.g. a characteristic as defined in ST 2086) is present and to compute at least one recovered parameter from said characteristic. If said characteristic of the input video is not present and a characteristic of a mastering display is not present, one checks if a characteristic of the reconstructed image I 3  or of the target display is present (e.g. the peak luminance as defined in CTA-861.3) and computes at least one recovered parameter from said characteristic. If said characteristic of the reconstructed image I 3  is not present and said characteristic of the target display is not present, at least one recovered parameter is a fixed value (e.g. fixed by a video standardization committee or an industry forum such as, for example 1000 cd/m2). 
     In accordance with a non-limitative example, Table 2 provides examples of recovery values for some parameters used by the post-processing stage that depends on the presence of available information on the input/output content and mastering/target displays. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Syntax element 
                 Recovery value 
               
               
                   
                   
               
             
            
               
                   
                 matrix_coefficient_value[i] 
                 {889; 470; 366; 994}, if 
               
               
                   
                   
                 BT.2020 
               
               
                   
                   
                 {915; 464; 392; 987}, if 
               
               
                   
                   
                 BT.709 
               
               
                   
                 shadow_gain_control 
                 if MDCV SEI message is 
               
               
                   
                   
                 present, recovery mode 1 
               
               
                   
                   
                 otherwise 
               
               
                   
                   
                 recovery mode 2 
               
               
                   
                   
               
            
           
         
       
     
     The parameters matrix_coefficient_value[ i] may be set according to the input/output video color space, BT.709 or BT.2020 (characteristic of the input or output video) obtained by parsing a MDCV SEI/ST 2086 message if present. The recovery mode depends on said color spaces. The parameter shadow_gain_control may be computed according to a value obtained by parsing a MDCV SEI/ST 2086 message if present. For example, an information representative of the peak luminance of a mastering display is obtained from said MDCV SEI/ST 2086 message and the parameter shadow_gain_control is computed by (recovery mode 1): 
     
       
         
           
             
               shadow_gain 
                
               _control 
             
             = 
             
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                 ( 
                 
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                   ; 
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                               ( 
                               hdrDisplayMaxLuminance 
                               ) 
                             
                           
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                           0 
                         
                         , 
                         5 
                       
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               with 
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     It is likely that at a service level information or for a specific workflow the value of hdrDisplayMaxLuminance is known. This value may also be set to the peak luminance of a target (presentation) display when this characteristic is available. Otherwise (recovery mode 2), it is arbitrarily set to a default value, typically 1000 cd/m2. This default value corresponds to a currently observed reference maximum display mastering luminance in most of the current HDR markets. 
       FIG. 6  shows another example of the use of a method for reconstructing an image I 3  from a decoded image data   and a set of parameters SP obtained from a bitstream B in accordance with an example of the present principles. This example is intended to be implemented, at least partially, in any (mid-)device implementing an overlay inserting and mixing mechanism (e.g. Set-Top-Box or UltraHD Blu-ray player) and signaling/sending an event (typically an overlay_present_flag set to 1) to a decision module that an overlay has to be added to the decoded image  . When an overlay (graphics) has not to be added to a decoded image  , the set of parameters SP is obtained (step  10 ), the decoded image   is obtained (step  11 ) and the image I 3  is reconstructed (step  12 ) as described in  FIG. 1 . 
     When an overlay has to added to a decoded image  , the decoded image   is obtained (step  11 ) and, in step  60 , a composite image I′ 2  is obtained by adding graphics (overlay) to the decoded image  . The information data ID is then obtained (step  103 ), a recovery mode selected (step  104 ) and the selected recovery mode RMi applies (step  105 ) to obtain recovered parameters P r . The image I 3  is then reconstructed (step  12 ) from the recovered parameters P r  and the decoded image  . 
     According to an embodiment, the parameters Pr are obtained by training a large set of images of different aspects (bright, dark, with logos and other alternative embodiments). Optionally (not shown in  FIG. 8 ), the step  12  may be implemented in a remote device such a TV set. In that case, either the decoded image   plus the parameters P or the composite image I′ 2  plus the parameters Pr are transmitted to said TV set. In  FIGS. 1 through 6 , the modules are functional units, which may or not be in relation with distinguishable physical units. For example, these modules or some of them may be brought together in a unique component or circuit, or contribute to functionalities of a software. A contrario, some modules may potentially be composed of separate physical entities. The apparatus which are compatible with the present principles are implemented using either pure hardware, for example using dedicated hardware such ASIC or FPGA or VLSI, respectively «Application Specific Integrated Circuit», «Field-Programmable Gate Array», «Very Large Scale Integration», or from several integrated electronic components embedded in a device or from a blend of hardware and software components. 
       FIG. 9  represents an exemplary architecture of a device  70  which may be configured to implement a method described in relation with  FIGS. 1-8 . 
     Device  70  comprises following elements that are linked together by a data and address bus  71 :
         a microprocessor  72  (or CPU), which is, for example, a DSP (or Digital Signal Processor);   a ROM (or Read Only Memory)  73 ;   a RAM (or Random Access Memory)  74 ;   an I/O interface  75  for reception of data to transmit, from an application; and   a battery  76         

     In accordance with an example, the battery  76  is external to the device. In each of mentioned memory, the word «register» used in the specification can correspond to area of small capacity (some bits) or to very large area (e.g. a whole program or large amount of received or decoded data). The ROM  73  comprises at least a program and parameters. The ROM  73  may store algorithms and instructions to perform techniques in accordance with present principles. When switched on, the CPU  72  uploads the program in the RAM and executes the corresponding instructions. 
     RAM  64  comprises, in a register, the program executed by the CPU  72  and uploaded after switch on of the device  70 , input data in a register, intermediate data in different states of the method in a register, and other variables used for the execution of the method in a register. 
     The implementations described herein may be implemented in, for example, a method or a process, an apparatus, a software program, a data stream, or a signal. Even if only discussed in the context of a single form of implementation (for example, discussed only as a method or a device), the implementation of features discussed may also be implemented in other forms (for example a program). An apparatus may be implemented in, for example, appropriate hardware, software, and firmware. The methods may be implemented in, for example, an apparatus such as, for example, a processor, which refers to processing devices in general, including, for example, a computer, a microprocessor, an integrated circuit, or a programmable logic device. Processors also include communication devices, such as, for example, computers, cell phones, portable/personal digital assistants (“PDAs”), and other devices that facilitate communication of information between end-users. 
     In accordance with an example, the input video or an original image of an input video is obtained from a source. For example, the source belongs to a set comprising:
         a local memory ( 73  or  74 ), e.g. a video memory or a RAM (or Random Access Memory), a flash memory, a ROM (or Read Only Memory), a hard disk;   a storage interface ( 75 ), e.g. an interface with a mass storage, a RAM, a flash memory, a ROM, an optical disc or a magnetic support;   a communication interface ( 75 ), e.g. a wireline interface (for example a bus interface, a wide area network interface, a local area network interface) or a wireless interface (such as a IEEE 802.11 interface or a Bluetooth® interface); and   an image capturing circuit (e.g. a sensor such as, for example, a CCD (or Charge-Coupled Device) or CMOS (or Complementary Metal-Oxide-Semiconductor)).       

     In accordance with examples, the bitstreams carrying on the metadata are sent to a destination. As an example, one of these bitstream or both are stored in a local or remote memory, e.g. a video memory ( 74 ) or a RAM ( 74 ), a hard disk ( 73 ). In a variant, at least one of the bitstreams is sent to a storage interface ( 75 ), e.g. an interface with a mass storage, a flash memory, ROM, an optical disc or a magnetic support and/or transmitted over a communication interface ( 75 ), e.g. an interface to a point to point link, a communication bus, a point to multipoint link or a broadcast network. 
     In accordance with other examples, the bitstream carrying on the metadata is obtained from a source. Exemplarily, the bitstream is read from a local memory, e.g. a video memory ( 74 ), a RAM ( 74 ), a ROM ( 73 ), a flash memory ( 73 ) or a hard disk ( 73 ). In a variant, the bitstream is received from a storage interface ( 75 ), e.g. an interface with a mass storage, a RAM, a ROM, a flash memory, an optical disc or a magnetic support and/or received from a communication interface ( 75 ), e.g. an interface to a point to point link, a bus, a point to multipoint link or a broadcast network. 
     In accordance with examples, device  70  being configured to implement the method as described above, belongs to a set comprising:
         a mobile device;   a communication device;   a game device;   a tablet (or tablet computer);   a laptop;   a still image camera;   a video camera;   an encoding/decoding chip;   TV set;   a set-top-box;   a display;   a still image server; and   a video server (e.g. a broadcast server, a video-on-demand server or a web server).       

     Implementations of the various processes and features described herein may be embodied in a variety of different equipment or applications. Examples of such equipment include an encoder, a decoder, a post-processor processing output from a decoder, a pre-processor providing input to an encoder, a video coder, a video decoder, a video codec, a web server, a set-top box, a laptop, a personal computer, a cell phone, a PDA, and any other device for processing a image or a video or other communication devices. As should be clear, the equipment may be mobile and even installed in a mobile vehicle. 
     Additionally, the methods may be implemented by instructions being performed by a processor, and such instructions (and/or data values produced by an implementation) may be stored on a computer readable storage medium. A computer readable storage medium can take the form of a computer readable program product embodied in one or more computer readable medium(s) and having computer readable program code embodied thereon that is executable by a computer. A computer readable storage medium as used herein is considered a non-transitory storage medium given the inherent capability to store the information therein as well as the inherent capability to provide retrieval of the information therefrom. A computer readable storage medium can be, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. It is to be appreciated that the following, while providing more specific examples of computer readable storage mediums to which the present principles can be applied, is merely an illustrative and not exhaustive listing as is readily appreciated by one of ordinary skill in the art: a portable computer diskette; a hard disk; a read-only memory (ROM); an erasable programmable read-only memory (EPROM or Flash memory); a portable compact disc read-only memory (CD-ROM); an optical storage device; a magnetic storage device; or any suitable combination of the foregoing. 
     The instructions may form an application program tangibly embodied on a processor-readable medium. In addition, as provided in  FIG. 14 , this can be accomplished locally or through remote devices communicating over a communication network in accordance with an embodiment of present principles 
       FIG. 10  provides for a schematic block diagram of an HDR system architecture as per one embodiment. The block diagram in Error! Reference source not found. depicts the HDR decomposition and reconstruction processes. The center block (dashed box) corresponds to the distribution encoding and decoding stages (e.g. based on HEVC or AVC video coding specifications). The two extreme left and right grey-coloured boxes respectively enable format adaptation to the input video signal of the HDR system and to the targeted system (e.g. a STB, a connected TV, etc.) connected with the HDR system. The black solid line boxes are showing the HDR specific processing. The present invention relates to both the HDR signal reconstruction process and the HDR metadata. The core component of the HDR decomposition stage is the HDR-to-SDR decomposition that generates an SDR video from the HDR signal. Optionally, a block of gamut mapping may be used when the input HDR and output SDR signals are represented with different color gamut or color spaces. The decoder side implements the inverse processes, in particular the SDR-to-HDR reconstruction step that goes back to HDR from the SDR video provided by the decoder. 
     The HDR-to-SDR decomposition process aims at converting the input linear-light 4:4:4 HDR, to an SDR compatible version (also in 4:4:4 format). The process also uses side information such as the mastering display peak luminance, color primaries, and the color gamut of the container of the HDR and SDR pictures. The HDR-to-SDR decomposition process generates an SDR backward compatible version from the input HDR signal, using an invertible process that guarantees a high quality reconstructed HDR signal. 
     The process is summarized in Error! Reference source not found. First, from the input HDR picture and its characteristics, mapping variables are derived. Then the luminance signal is mapped to an SDR luma signal using the luminance mapping variables. Then a mapping of the color to derive the chroma components of the SDR signal is applied. This step results in a gamut shifting, which is corrected by a final step of color gamut correction. The successive steps of the process, applied to each pixel of the input HDR picture, are depicted in the steps shown. Once the mapping parameters have been derived (step  1  of Error! Reference source not found.), a luminance mapping function, noted LUT TM , is obtained. The next steps can be summarized as follows. First, the luma signal is derived from the HDR linear-light RGB signal and from the luminance mapping function (step  2  of Error! Reference source not found.). 
     A derivation of linear-light luminance L is then obtained from linear-light RGB signal is obtained then as follows: 
     
       
         
           
             
               
                 
                   L 
                   = 
                   
                     
                       A 
                       1 
                     
                      
                     
                       [ 
                       
                         
                           
                             R 
                           
                         
                         
                           
                             G 
                           
                         
                         
                           
                             B 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     Y 
                     tmp 
                   
                   = 
                   
                     
                       LUT 
                       TM 
                     
                      
                     
                       ( 
                       L 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .2 
                   
                   ) 
                 
               
             
           
         
       
     
     with A=[A 1  A 2  A 3 ] T  being the conventional 3×3 R′G′B′-to-Y′CbCr conversion matrix (e.g. BT.2020 or BT.709 depending on the colour space), A 1 , A 2 , A 3  being 1×3 matrices. 
     Then the linear-light luminance L is mapped to an SDR-like luma Y tmp , using the luminance mapping function: 
         Y   tmp =LUT TM ( L )  (eq. 3)
 
     In the next step, the chroma components are built as follows (step  3  of  FIG. 8 ), A pseudo-gammatization using square-root (close to BT.709 OETF) is applied 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             S 
                           
                         
                       
                       
                         
                           
                             G 
                             S 
                           
                         
                       
                       
                         
                           
                             B 
                             S 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             R 
                           
                         
                       
                       
                         
                           
                             G 
                           
                         
                       
                       
                         
                           
                             B 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .4 
                   
                   ) 
                 
               
             
           
         
       
     
     Then the U and V values are derived as follows: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             
                               pre 
                                
                               
                                   
                               
                                
                               0 
                             
                           
                         
                       
                       
                         
                           
                             V 
                             
                               pre 
                                
                               
                                   
                               
                                
                               0 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 A 
                                 2 
                               
                             
                           
                           
                             
                               
                                 A 
                                 3 
                               
                             
                           
                         
                         ] 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 R 
                                 S 
                               
                             
                           
                           
                             
                               
                                 G 
                                 S 
                               
                             
                           
                           
                             
                               
                                 B 
                                 S 
                               
                             
                           
                         
                         ] 
                       
                     
                     × 
                     1024 
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .5 
                   
                   ) 
                 
               
             
           
         
       
     
     In the final step, a colour correction (step  4 ) is applied
         The U and V values are corrected as follows:       

     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             U 
                             
                               pre 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       
                         
                           
                             V 
                             
                               pre 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       CLAMPUV 
                        
                       
                         ( 
                         
                           
                             1 
                             
                               
                                 β 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   Y 
                                   
                                     pre 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                           · 
                           
                             [ 
                             
                               
                                 
                                   
                                     U 
                                     
                                       pre 
                                        
                                       
                                           
                                       
                                        
                                       0 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     V 
                                     
                                       pre 
                                        
                                       
                                           
                                       
                                        
                                       0 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       CLAMPUV 
                        
                       
                         ( 
                         
                           
                             1024 
                             
                               
                                 β 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   Y 
                                   
                                     pre 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                           · 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       A 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     
                                       A 
                                       3 
                                     
                                   
                                 
                               
                               ] 
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       R 
                                     
                                   
                                 
                                 
                                   
                                     
                                       G 
                                     
                                   
                                 
                                 
                                   
                                     
                                       B 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .6 
                   
                   ) 
                 
               
             
           
         
       
     
     where A 2 , A 3  are made of the second and third lines of coefficients of the conversion matric from R′G′B′-to-Y′CbCr, and β 0  is the pre-processing colour correction LUT, and the CLAMP function is a clamping function defined by CLAMPUV(x)=min(max(x,−512),511) for a 10 bits YUV output. 
     The luma component is corrected as follows: 
         Y   pre1   =Y   pre0 −ν×max(0, a.U   pre1   +b.V   pre1 )  (eq. 7)
 
     Where a and b are two pre-defined parameters, and which results in the output SDR signal Y pre1 U pre1 V pre1 . 
     The luminance mapping variables used in the JHDR Tone mapping curve are defined in SMPTE ST 2094-20. 
     In one embodiment, the HDR reconstruction process is the inverse of the HDR-to-SDR decomposition process. It applies the following steps for each pixel of the SDR picture made of three components SDR y , SDR cb , SDR cr . First the values U post1  and V post1  are derived as follows: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             U 
                             
                               post 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           = 
                           
                             
                               
                                 
                                   SDR 
                                   cb 
                                 
                                  
                                 
                                   [ 
                                   x 
                                   ] 
                                 
                               
                                
                               
                                 [ 
                                 y 
                                 ] 
                               
                             
                             - 
                             midSampleVal 
                           
                         
                       
                     
                     
                       
                         
                           
                             V 
                             
                               post 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           = 
                           
                             
                               
                                 
                                   SDR 
                                   cr 
                                 
                                  
                                 
                                   [ 
                                   x 
                                   ] 
                                 
                               
                                
                               
                                 [ 
                                 y 
                                 ] 
                               
                             
                             - 
                             midSampleVal 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .8 
                   
                   ) 
                 
               
             
           
         
       
     
     The value Y post1  is derived as follows: 
         Y   post1   =SDR   y [ x ][ y ]ν×max(0, a×U   post1   +b×V   post1 )  (eq. 9)
 
     Possibly followed by a clipping to avoid to be out of the legacy signal range. 
     U post1  and V post1  are modified as follows: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             U 
                             
                               post 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           = 
                           
                             
                               
                                 β 
                                 p 
                               
                                
                               
                                 [ 
                                 
                                   Y 
                                   
                                     post 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 ] 
                               
                             
                             × 
                             
                               U 
                               
                                 post 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             V 
                             
                               post 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           = 
                           
                             
                               
                                 β 
                                 p 
                               
                                
                               
                                 [ 
                                 
                                   Y 
                                   
                                     post 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 ] 
                               
                             
                             × 
                             
                               V 
                               
                                 post 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .10 
                   
                   ) 
                 
               
             
           
         
       
     
     Where β p  is the post-processing colour correction LUT, that depends directly on the pre-processing colour correction LUT β 0 . 
     First a value T is derived as: 
         T=k 0× U   post1   ×V   post1   +k 1× U   post1   ×U   post1   +k 2× V   post1   ×V   post1   (eq. 11)
 
     where k0, k1, k2 are predefined values depending on the SDR colour gamut. The value S0 is then initialized to 0, and the following applies: 
       If( T≤ 1),  S 0 is set to Sqrt(1− T )
 
     Else, U post1  and V post1  are modified as follows: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             U 
                             
                               post 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           = 
                           
                             
                               U 
                               
                                 post 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             
                               T 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             V 
                             
                               post 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           = 
                           
                             
                               V 
                               
                                 post 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             
                               T 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .12 
                   
                   ) 
                 
               
             
           
         
       
     
     In a next step, the values R1, G1, B1 are derived as follows: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       
                         
                           
                             G 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       
                         
                           
                             B 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       M 
                       
                         
                           Y 
                           ′ 
                         
                          
                         CbCr 
                          
                         
                           - 
                         
                          
                         to 
                          
                         
                           - 
                         
                          
                         R 
                          
                         
                             
                         
                          
                         ′ 
                          
                         
                             
                         
                          
                         G 
                          
                         
                             
                         
                          
                         ′ 
                          
                         
                             
                         
                          
                         B 
                          
                         
                             
                         
                          
                         ′ 
                       
                     
                     × 
                     
                       [ 
                       
                         
                           
                             
                               
                                 S 
                                  
                                 
                                     
                                 
                                  
                                 0 
                               
                                
                               
                                   
                               
                             
                           
                         
                         
                           
                             
                               U 
                               
                                 post 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               V 
                               
                                 post 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .13 
                   
                   ) 
                 
               
             
           
         
       
     
     where M y′CbCr-to-R′G′B′  is the conventional conversion matrix from Y′CbCr to R′G′B′. The values R2, G2, 82 are derived from R1, G1, B1 as follows: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             R 
                              
                             
                                 
                             
                              
                             2 
                           
                           = 
                           
                             
                               lutMapY 
                                
                               
                                 [ 
                                 
                                   Y 
                                   
                                     post 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 ] 
                               
                             
                             × 
                             R 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                     
                       
                         
                           
                             G 
                              
                             
                                 
                             
                              
                             2 
                           
                           = 
                           
                             
                               lutMapY 
                                
                               
                                 [ 
                                 
                                   Y 
                                   
                                     post 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 ] 
                               
                             
                             × 
                             G 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                     
                       
                         
                           
                             B 
                              
                             
                                 
                             
                              
                             2 
                           
                           = 
                           
                             
                               lutMapY 
                                
                               
                                 [ 
                                 
                                   Y 
                                   
                                     post 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 ] 
                               
                             
                             × 
                             B 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .14 
                   
                   ) 
                 
               
             
           
         
       
     
     The output samples HDR R , HDR G , HDR B  are derived from R2, G2, B2 as follows: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             HDR 
                             R 
                           
                           = 
                           
                             R 
                              
                             
                                 
                             
                              
                             
                               2 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             HDR 
                             G 
                           
                           = 
                           
                             G 
                              
                             
                                 
                             
                              
                             
                               2 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             HDR 
                             B 
                           
                           = 
                           
                             B 
                              
                             
                                 
                             
                              
                             
                               2 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .15 
                   
                   ) 
                 
               
             
           
         
       
     
     A clipping may be applied to limit the range of the output HDR signal. 
         err  is initialized to 0. 
     A scanning of the RGB cube is performed, and each RGB sample is modified to reach a luminance of 1 cd/m 2 . Then the following applies 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           R 
                           = 
                           
                             L 
                             × 
                             
                               R 
                               SDR 
                             
                           
                         
                       
                     
                     
                       
                         
                           G 
                           = 
                           
                             L 
                             × 
                             
                               G 
                               SDR 
                             
                           
                         
                       
                     
                     
                       
                         
                           B 
                           = 
                           
                             L 
                             × 
                             
                               B 
                               SDR 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .15 
                   
                   ) 
                 
               
             
           
         
       
     
     The output sample YUVSDR as described in the HDR-to-SDR decomposition process is built, with β_0=β_test. Then an error in the Lab color space, errorab, between RGBsdr and RGBhdr is computed. This step is controlled by a parameter (saturation skew) that enables to control the color saturation of the derived SDR signal. And err is updated as follows: 
         err=err +error ab   (eq. 16)
 
     The final value β 0 [Y] corresponds to β test  giving the lowest cumulated err value among all the tested β test  values. 
     The LUTs β 0  and β test  are linked by the following equation 
     
       
         
           
             
               
                 
                   
                     
                       β 
                       P 
                     
                      
                     
                       ( 
                       Y 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         β 
                         O 
                       
                        
                       
                         ( 
                         Y 
                         ) 
                       
                     
                     
                       K 
                       × 
                       
                         
                           L 
                            
                           
                             ( 
                             Y 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                      
                     .17 
                   
                   ) 
                 
               
             
           
         
       
     
     Where K is a constant value. 
     For coding of the LUT □ P , as it can be seen, the derivation of these LUTs is not straightforward. In particular, it is not possible to apply this derivation process at the decoder to build the LUT □ P . Instead the following process is applied. 
     A set of pre-defined default LUTs □ P_default [k], k=1 to N, is used. For instance, one LUT is defined for each triple (container colour gamut, content colour gamut, peak luminance). At the pre-processing side, an adjustment function ƒ ad ; is built to map as much as possible the LUT □ P_default [k] to the real LUT □ P . that is such that 
       □ P_cod [ Y ]=ƒ adj [ Y ]×□ P_default [ k ][ Y ]  (eq. 18)
 
     is as close as possible to □ P_real [k][Y] for all Y values. 
     To limit the coding cost, the function ƒ adj  is modeled using pivot points of a piece-wise linear model. 
     Only these PWL pivot points are coded. The post-processing can then decode these points, build the function ƒ adj  and reconstruct the □ P_cod  LUT from the default LUT □ P_default  (identified thanks to the coded content characteristics parameters) and ƒ adj  by applying equation eq. 18. 
     From eq5 and eq8, it can be seen that if U pre1  and/or V pre1  are clamped, then it is not possible to achieve the equality Y pre1 =Y post1  necessary for good reconstruction. 
     As seen previously the β 0  computation results in finding the best color correction by minimizing an error criterion over the RGB samples. To be sure that no clamp occurs in eq5, we need to have for all RGB samples of the frame: 
     
       
         
           
             
               
                 
                   
                     - 
                     512 
                   
                   ≤ 
                   
                     
                       1024 
                       
                         
                           β 
                           0 
                         
                          
                         
                           ( 
                           
                             Y 
                             0 
                           
                           ) 
                         
                       
                     
                     · 
                     
                       
                         [ 
                         
                           
                             
                               
                                 A 
                                 2 
                               
                             
                           
                           
                             
                               
                                 A 
                                 3 
                               
                             
                           
                         
                         ] 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 R 
                               
                             
                           
                           
                             
                               
                                 G 
                               
                             
                           
                           
                             
                               
                                 B 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                   ≤ 
                   511 
                 
               
               
                 
                   ( 
                   
                     eq 
                     . 
                     
                         
                     
                      
                     19 
                   
                   ) 
                 
               
             
           
         
       
     
     To resolve this situation, avoiding UV saturation could be achieved by forcing the □ □ □Y 0 ) to be high enough but this would led to a loss of saturation in all SDR image which would be non-efficient for most content and is therefore not satisfactory. However, for some specific contents, it is necessary to decrease the SDR saturation in order to allow a correct HDR reconstruction. 
     The process for deriving the LUT □ 0  is independent is independent from the content can be performed in the following manner. It applies in the container color gamut and takes into account the content color gamut. The synoptic of this process is summarized herein. 
     The process can be summarized as follows. For each luma value Y, the following steps are applied. The luminance is generated using the inverse function of LUT TM : L=invLUT TM [Y]. Then the best β 0 [Y] for luminance L (and therefore for luma Y) is identified as follows. Values β test  in a given pre-defined range are evaluated as follows. The cumulative error err associated to β test  is computed as follows. 
     In order to prevent the UV saturation, the function ƒ adj  is adapted for each frame in the following way: 
     A graphical depiction of the result is provided in  FIG. 15 . In this example, an algorithm can be used, that has the following characteristics:
         Build the Beta0 color correction with the initial tone mapping curve in the same way that described previously   Iterate on the current sub sampled frame pixels and compute the RGB       

     
       
         
           
             
               [ 
               
                 
                   
                     
                       U 
                       
                         pre 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                 
                 
                   
                     
                       V 
                       
                         pre 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                 
               
               ] 
             
             = 
             
               
                 
                   1 
                   
                     
                       β 
                       0 
                     
                      
                     
                       ( 
                       
                         Y 
                         
                           pre 
                            
                           
                               
                           
                            
                           0 
                         
                       
                       ) 
                     
                   
                 
                 · 
                 
                   [ 
                   
                     
                       
                         
                           U 
                           
                             pre 
                              
                             
                                 
                             
                              
                             0 
                           
                         
                       
                     
                     
                       
                         
                           V 
                           
                             pre 
                              
                             
                                 
                             
                              
                             0 
                           
                         
                       
                     
                   
                   ] 
                 
               
               = 
               
                 
                   1024 
                   
                     
                       β 
                       0 
                     
                      
                     
                       ( 
                       
                         Y 
                         
                           pre 
                            
                           
                               
                           
                            
                           0 
                         
                       
                       ) 
                     
                   
                 
                 · 
                 
                   
                     [ 
                     
                       
                         
                           
                             A 
                             2 
                           
                         
                       
                       
                         
                           
                             A 
                             3 
                           
                         
                       
                     
                     ] 
                   
                    
                   
                     [ 
                     
                       
                         
                           
                             R 
                           
                         
                       
                       
                         
                           
                             G 
                           
                         
                       
                       
                         
                           
                             B 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
         
         
           
             1. Detect the eventual UV saturation. We note UV either U pre1  or V pre1    
             2.
           if(UV&gt;511)   ƒ adj_corrected [Y]=511.f/UV;   if(UV&lt;−512)   ƒ adj_corrected [Y]=512.f/UV;
 
values that are potentially saturated (eq. 5, without the clamping)
   
         
             3. Recompute the new Beta0 with the ƒ adj_corrected  function that prevents UV saturation 
             4. Process the frame with the new color correction. 
           
         
       
    
     This algorithm needs a temporal stabilization which can be done, for instance, by: 
       ƒ adj_corrected ( t )=0.25*ƒ adj_corrected +0.75*ƒ adj_corrected ( t− 1)
 
     According to an embodiment illustrated in  FIG. 14 , in a transmission context between two remote devices A and B over a communication network NET, the device A comprises means which are configured to implement a method for encoding an picture as described in relation with the  FIGS. 2-7  and the device B comprises means which are configured to implement a method for decoding as described in relation with  FIG. 8-12 . 
     According to an embodiment of the disclosure, the network is a broadcast network, adapted to broadcast still pictures or video pictures from device A to decoding devices including the device B. 
     In addition, this same process can be applied to both HDR codecs that have a Constant Luminance mode (already discussed) and one that has a Non Constant Luminance mode. The latter computes HDR luma Y′ instead of a linear-light luminance L from linear-light RGB signal while maintaining the compatibility with SLHDR1 post-processing. In one embodiment, this luma Y′ component is a weighted sum of gamma-compressed R′G′B′ components of a color video depending of the input color gamut. In this way, the HDR chrominance (U′ HDR , V′ HDR ) components are corrected to produce SDR chroma components. 
     Implementations of the various processes and features described herein may be embodied in a variety of different equipment or applications. Examples of such equipment include an encoder, a decoder, a post-processor processing output from a decoder, a pre-processor providing input to an encoder, a video coder, a video decoder, a video codec, a web server, a set-top box, a laptop, a personal computer, a cell phone, a PDA, and any other device for processing a picture or a video or other communication devices. As should be clear, the equipment may be mobile and even installed in a mobile vehicle. 
     Additionally, the methods may be implemented by instructions being performed by a processor, and such instructions (and/or data values produced by an implementation) may be stored on a computer readable storage medium. A computer readable storage medium can take the form of a computer readable program product embodied in one or more computer readable medium(s) and having computer readable program code embodied thereon that is executable by a computer. A computer readable storage medium as used herein is considered a non-transitory storage medium given the inherent capability to store the information therein as well as the inherent capability to provide retrieval of the information therefrom. A computer readable storage medium can be, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. It is to be appreciated that the following, while providing more specific examples of computer readable storage mediums to which the present principles can be applied, is merely an illustrative and not exhaustive listing as is readily appreciated by one of ordinary skill in the art: a portable computer diskette; a hard disk; a read-only memory (ROM); an erasable programmable read-only memory (EPROM or Flash memory); a portable compact disc read-only memory (CD-ROM); an optical storage device; a magnetic storage device; or any suitable combination of the foregoing. 
     The instructions may form an application program tangibly embodied on a processor-readable medium. 
     Instructions may be, for example, in hardware, firmware, software, or a combination. Instructions may be found in, for example, an operating system, a separate application, or a combination of the two. A processor may be characterized, therefore, as, for example, both a device configured to carry out a process and a device that includes a processor-readable medium (such as a storage device) having instructions for carrying out a process. Further, a processor-readable medium may store, in addition to or in lieu of instructions, data values produced by an implementation. 
       FIG. 15  provides for a flow chart illustration of a methodology that can provide matching colors between images of different dynamic ranges. In the example of  FIG. 15 , an image or series of images such as in a video or image stream with HDR can be provided to an output device having a limited range such as an SDR. In step  1510 , a tone mapping function is generated to reduce dynamic range of a first image to produce a second image. In step  1520 , a luma signal and a plurality of chroma components associated with the first and second image are determined such as by a processing means. In step  1530  a gamut color correction is performed on the second image using an adaptive function. In one embodiment, the adaptive function is generated by comparing said luma signal and at least one chroma component of said first and second image. 
     In this way, as provided in flowchart depictions of  FIGS. 16   19  and as discussed specifically in conjunction with  FIGS. 8-14 , the distribution of a compressed HDR video can be distributed to a device with a more limited dynamic range. For this purpose, a codec has been proposed with a color correction function, β′, that is used to control the colors of the derived SDR pictures. Consequently, for example, in this way color correction is achieved through the use of an adaptive function. In this way the color correction necessary will allow a correct HDR image or video reconstruction by avoiding lower range frequencies (i.e SDR) saturation though the use of the adaptive function. 
     As will be evident to one of skill in the art, implementations may produce a variety of signals formatted to carry information that may be, for example, stored or transmitted. The information may include, for example, instructions for performing a method, or data produced by one of the described implementations. For example, a signal may be formatted to carry as data the rules for writing or reading the syntax of a described embodiment, or to carry as data the actual syntax-values written by a described embodiment. Such a signal may be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The formatting may include, for example, encoding a data stream and modulating a carrier with the encoded data stream. The information that the signal carries may be, for example, analog or digital information. The signal may be transmitted over a variety of different wired or wireless links, as is known. The signal may be stored on a processor-readable medium. 
     A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made. For example, elements of different implementations may be combined, supplemented, modified, or removed to produce other implementations. Additionally, one of ordinary skill will understand that other structures and processes may be substituted for those disclosed and the resulting implementations will perform at least substantially the same function(s), in at least substantially the same way(s), to achieve at least substantially the same result(s) as the implementations disclosed. Accordingly, these and other implementations are contemplated by this application.