CORRECTING SDR DATA DURING INVERSE TONE MAPPING TO IMPROVE HDR DATA IN SL-HDR1 POST-PROCESSING

Abstract

The invention relates to a method comprising: obtaining (40) image data in the first dynamic range; determining (41) a first function that allows mapping image data from the first dynamic range to the second dynamic range; signaling (42) metadata that allows obtaining a second function corresponding to an approximate version of the first function in the video data; determining (43) a third function from the first and second functions such that applying the second function to the intermediate data obtained from applying the third function to image data in the first dynamic range is equivalent to applying the first function to image data in the first dynamic range; and signaling (44) data representing the intermediate data in the video data.

Description

[0001]CORRECTION OF SDR DATA IN INVERSE TONE MAPPING TO IMPROVE HDR DATA IN SL-HDR1 POSTPROC 1. TECHNICAL FIELD At least one of the present embodiments generally relates to the field of production of video and more particularly to a method, a device and a system for improving HDR data in a SL-HDR1 system. 2. BACKGROUND Recent advancements in display technologies are beginning to allow for an extended dynamic range of color, luminance and contrast in images to be displayed. The term image refers here to an image content that can be for example a video or a still picture or image. High-dynamic-range video (HDR video) describes video having a dynamic range greater than that of standard-dynamic-range video (SDR video). HDR video involves capture, production, content / encoding, and display. HDR capture and display devices are capable of brighter whites and deeper blacks. To accommodate this, HDR encoding standards allow for a higher maximum luminance and use at least a 10-bit dynamic range (compared to 8-bit for non-professional and 10-bit for professional SDR video) in order to maintain precision across this extended range. HDR production is a new domain and there will be a transition phase during which both HDR contents and SDR contents will coexist. During this coexistence phase, a same content will be produced simultaneously in a HDR and a SDR version. A user can then display the HDR or the SDR version of the content depending on his preferences or capabilities. One solution proposed by the standard SL-HDR1 (ETSI TS 103433-1 V1.4.1) consists in producing a content in the form of a SDR video along with metadata. The metadata are representative of inverse tone mapping curves allowing transforming the SDR video in a HDR video. The standard SL-HDR1 proposes therefore a single layer approach avoiding transmitting an SDR and an HDR version of a same content to users. In some cases, the inverse tone mapping curves are designed on a sender device to obtain a desired quality of rendering of the HDR video. The metadata are then used to re-generate the inverse tone mapping curves on a receiver side used to generate the HDR video from the SDR video. However, due to some quantization applied to parameters representative of the inverse tone mapping curves, the HDR video generated on the receiver side may be slightly different from the desired HDR video. It is desirable to overcome the above drawbacks. It is particularly desirable to propose a system that allows obtaining a HDR video as close as possible to the desired HDR video from the metadata and the SDR video. 3. BRIEF SUMMARY In a first aspect, one or more of the present embodiments provide a method comprising: obtaining picture data in a first dynamic range; determining a first function allowing mapping the picture data from the first dynamic range to a second dynamic range; signaling metadata allowing obtaining a second function corresponding to an approximated version of the first function in video data; determining a third function from the first function and the second function such that an application of the second function to intermediate data resulting from an application of the third function to the picture data in the first dynamic range is equivalent to an application of the first function to the picture data in the first dynamic range; and signaling data representative of the intermediate data in the video data. In an embodiment, the dynamic range of the first dynamic range is lower than the dynamic range of the second dynamic range. In an embodiment, the metadata are representative of an inverse of the first function. In an embodiment, the second function is an inverse of an intermediate function derived from the metadata. In an embodiment, the intermediate function is a tone mapping function represented by a first look-up table derived from the metadata and the second function is an inverse tone mapping function represented by a second look-up table derived by inverting the intermediate function from the first look-up table. In an embodiment, the third function is derived from the intermediate function or from the second function. In an embodiment, the method further comprises: obtaining chroma components from a current sample of the intermediate data using a color correction function; estimating a clipping factor based on the obtained chroma components and on a precision value; representing each obtained chroma component as a multiplication of a first sub- part depending on a luma component of the sample of the intermediate data and a second sub-part depending on a corresponding chroma component of the sample of the intermediate data and obtaining a first ratio of a correction factor to be applied to the first sub-part and a second ratio of the correction factor to be applied to the second sub- part, the correction factor being based on the clipping factor; obtaining a luma value of a sample of a corrected intermediate data corresponding to the sample of the intermediate data using a division of the first sub- part by the correction factor to a power equal to the first ratio; and for each chroma component, obtaining a chroma value for the sample of the corrected intermediate data corresponding to the sample of the intermediate data by dividing the second sub-part of the chroma component by the correction factor to a power equal to the second ratio; wherein the data representative of the intermediate data are the corrected intermediate data. In a second aspect, one or more of the present embodiments provide a device comprising an electronic circuitry configured for: obtaining picture data in a first dynamic range; determining a first function allowing mapping the picture data from the first dynamic range to a second dynamic range; signaling metadata allowing obtaining a second function corresponding to an approximated version of the first function in video data; determining a third function from the first function and the second function such that an application of the second function to intermediate data resulting from an application of the third function to the picture data in the first dynamic range is equivalent to an application of the first function to the picture data in the first dynamic range; and signaling data representative of the intermediate data in the video data. In an embodiment, the dynamic range of the first dynamic range is lower than the dynamic range of the second dynamic range. In an embodiment, the metadata are representative of an inverse of the first function. In an embodiment, the second function is an inverse of an intermediate function derived from the metadata. In an embodiment, the intermediate function is a tone mapping function represented by a first look-up table derived from the metadata and the second function is an inverse tone mapping function represented by a second look-up table derived by inverting the intermediate function from the first look-up table. In an embodiment, the third function is derived from the intermediate function or from the second function. In an embodiment, the electronic circuitry is further configured for: obtaining chroma components from a current sample of the intermediate data using a color correction function; estimating a clipping factor based on the obtained chroma components and on a precision value; representing each obtained chroma component as a multiplication of a first sub- part depending on a luma component of the sample of the intermediate data and a second sub-part depending on a corresponding chroma component of the sample of the intermediate data and obtaining a first ratio of a correction factor to be applied to the first sub-part and a second ratio of the correction factor to be applied to the second sub- part, the correction factor being based on the clipping factor; obtaining a luma value of a sample of a corrected intermediate data corresponding to the sample of the intermediate data using a division of the first sub- part by the correction factor to a power equal to the first ratio; and for each chroma component, obtaining a chroma value for the sample of the corrected intermediate data corresponding to the sample of the intermediate data by dividing the second sub-part of the chroma component by the correction factor to a power equal to the second ratio; wherein the data representative of the intermediate data are the corrected intermediate data. In a third aspect, one or more of the present embodiments provide a non- transitory information storage medium storing program code instructions for implementing the method according to the first aspect. In a fourth aspect, one or more of the present embodiments provide a computer program comprising program code instructions for implementing the method according to the first aspect. In a fifth aspect, one or more of the present embodiments provide a signal generated by the method of the first aspect or by the device of the second aspect. 4. BRIEF SUMMARY OF THE DRAWINGS Fig.1 illustrates schematically a context in which embodiments are implemented; Fig. 2 illustrates schematically a system adapted to a reversible inverse tone mapping scheme; Fig. 3A illustrates schematically an example of hardware architecture of a processing module able to implement various aspects and embodiments; Fig. 3B illustrates a block diagram of an example of a first system in which various aspects and embodiments are implemented; Fig.3C illustrates a block diagram of an example of a second system in which various aspects and embodiments are implemented; Fig.4 provides a high-level representation of various embodiments; Fig. 5 illustrates a post-processing process allowing generating a HDR picture from a SDR picture; Fig.6 illustrates a SDR to HDR reconstruction process; Fig.7 illustrates a correction process applied to a SDR picture; Fig.8 illustrates a detail of the correction process; Fig.9A illustrates a process for deriving an inverse tone mapping look-up table; Fig.9B illustrates a process for deriving a tone mapping look-up table; Fig. 10A illustrates schematically a process for obtaining the luma LUT allowing modifying a SDR picture according to a first embodiment; and, Fig. 10B illustrates schematically a process for obtaining the luma LUT allowing modifying a SDR picture according to a second embodiment. 5. DETAILED DESCRIPTION Fig. 1 illustrates schematically a context in which embodiments are implemented. In Fig. 1, a system 11, that could be a camera, a storage device, a computer, a server or any device capable of delivering video data, transmits video data to a system 13 using a communication channel 12. The video data are either encoded and transmitted by the system 11 or received and / or stored by the system 11 and then transmitted. The communication channel 12 is a wired (for example Internet or Ethernet) or a wireless (for example WiFi, 3G, 4G or 5G) network link. The system 13, that could be for example a set top box, receives and decodes the video stream to generate a sequence of decoded pictures. A post-processing is applied to the decoded pictures. The obtained sequence of decoded pictures is then transmitted to a display system 15 using a communication channel 14, that could be a wired or wireless network. The display system 15 then displays said pictures. In an embodiment, the system 13 is comprised in the display system 15. In that case, the system 13 and display system 15 are comprised in a TV, a computer, a tablet, a smartphone, a head-mounted display, etc. In an embodiment, the post-processing is executed by a post-processing compliant with the standard SL-HDR1 (ETSI TS 103433-1 V1.4.1). As represented in Fig. 2, the system 11 comprise a RITM (Reversible Inverse Tone Mapping) module 110 and a SL-HDR pre-processor 111. Fig.2 illustrates schematically a system 11 adapted to a reversible inverse tone mapping scheme. In a RITM (Reversible Inverse Tone Mapping) scheme, a RITM module (for example, the RITM module 110 of Fig.2) obtains inverse tone mapping curves that are then converted in metadata and inverse tone map an original SDR (Standard Dynamic Range) picture into an HDR (High Dynamic Range) picture, called original HDR picture, using the inverse tone mapping curves. The original HDR picture is then sent to a SL-HDR Pre-Processor (for example the SL-HDR pre-processor 111) along with the metadata. In this mode, instead of estimating tone mapping parameters, the SL- HDR Pre-Processor uses the metadata to generate a pre-processed SDR picture from the original HDR picture. One effect of the RITM scheme, called round-trip effect, is to provide to an SL-HDR1 post-processor (for example, the SL-HDR1 post-processor comprised in the system 13) a pre-processed SDR picture close to the original SDR picture and then to allow the SL-HDR1 Post-Processor to produce a post-processed HDR picture close to the original HDR picture by inverse tone mapping the pre- processed SDR picture using the metadata. One can note that the combination of the system 11 of Fig.2 and the system 13 comprising a SL-HDR1 post-processor implements a RITM scheme. The inverse tone mapping curves obtained by the RITM module allows defining a luminance LUT (look-up table) for a luminance component of the picture and a chrominance LUT for a chrominance component of the picture. These look-up tables are then represented by the metadata. An example of process for generating the metadata for the luminance component comprise the following steps: ^ a luma LUT called itmedLUT which enables to transform the luminance component of the original SDR picture into a luminance component of the HDR picture is computed; ^ The luma LUT itmedLUT is inversed to produce a luma LUT called L_LUT which enables to transform the luminance component of the HDR picture back to the luminance component of the original SDR picture. ^ Metadata allowing approximating the luma LUT L_LUT by a luma LUT called meta_L_LUT are then computed. These metadata are defined in the standard SL-HDR1 (ETSI TS 103 433-1 V1.4.1) and comprise tmInputSignalBlackLevelOffset, tmInputSignalWhiteLevelOffset (denoted WS, White Stretch or WhiteLevelOffset below), shadowGain, highlightGain, midToneWidthAdjFactor and a number tmOutputFineTuningNumVal of pairs (tmOutputFineTuningX, tmOutputFineTuningY) pairs (denoted (FTFX,FTFY)) below) defining a piece-wise linear tone mapping output fine tuning function. These metadata are then transmitted to the SL-HDR pre-processor and then to the SL-HDR1 post-processor. ^ The luma LUT meta_L_LUT is inverted and provides a SDR to HDR LUT called meta_itmedLUT which is finally applied to the luminance component of the original SDR picture to get the luminance component of the original HDR picture inputted to the SL-HDR1 pre-processor. Similarly, the chrominance LUT is represented by other metadata described in section 6.3.6 of standard SL-HDR1 (ETSI TS 103433-1 V1.4.1) such as parameters saturationGainX and saturationGainY called parameters SGF in the following representing a saturation gain function. In some implementations of the RITM scheme, metadata are first estimated using floating point estimation but then quantized (signaled) on a limited number of bits. For example, WS and FTFY are signaled using “12” bits while FTFX is signaled using “8” bits. These metadata are sent to the SL-HDR pre-processor which uses them to produce a pre-processed SDR picture which is closer to the original SDR picture. The SL-HDR pre-processor reduces then the precision of WS and FTFY down to “8” bits before sending them to the SL-HDR1 post-processor. In some cases, the SL-HDR pre-processor is not used (The SL-HDR pre- processor 111 is bypassed in Fig.2). Such situation occurs for instance, when a whole video production is done in SDR which means that no HDR data is used and consequently, that the SL-HDR pre-processor is useless. In this situation, another scheme can be used where the RITM module delivers SDR pictures associated with metadata (i.e. with picture dependent (FTFX, FTFY), SGF and WS parameters, the other parameters being fixed). The SDR pictures and the metadata enable a SL-HDR1 post- processor to produce HDR pictures which are close to the HDR pictures which would have been produced by the RITM using the ITM LUTs, such as the luma LUT itmedLUT for the luminance. The standard HDR output of the RITM is (or can be) disabled. This is called the SL-ITM mode (or Single Layer ITM mode). Additionally, a correction module may be added. The correction module applies a correction process to a SDR signal outputted by a SL-HDR pre-processing module in order to limit risks of clipping. The correction process is applied to each sample of the SDR picture. This process consists first in determining for each sample, if the sample needs to be corrected, i.e. if a sample risks to provoke a clipping. The determination of the risk of clipping is based on an emulation of the implementation of the SL-HDR1 post-processing module. This emulation allows determining a clipping factor that is used to determine a correction factor to be used to correct the luma and the chroma components of the sample. A corrected SDR picture is generated by the correction module. The corrected SDR picture replaces the pre-processed SDR picture. The optional correction module is represented by reference 112 in Fig.2. In Summary, the RITM module 110 in SL-ITM mode receives an original SDR picture, produces ITM LUTs which can transform the original SDR picture into an HDR picture, computes SL-HDR metadata from these LUTs, outputs the produced metadata together with the original SDR picture. Optionally, A color correction could be applied to the original SDR picture using the color correction module. The SL-HDR1 post-processor receives the SDR (original or corrected) picture and the associated metadata, reconstructs LUTs called itm_meta_LUTs from the metadata (the LUT itm_meta_LUTs comprise the luma LUT meta_itmedLUT for the luminance) and outputs a HDR picture from the SDR picture using the LUTs itm_meta_LUTs. It has been observed that some noticeable differences may appear between the HDR image reconstructed by the SL-HDR1 post-processor using the luma LUT meta_itmedLUT and the original HDR image produced by the RITM module using the luma LUT itmedLUT. These differences are due to the small number of (FTFX,FTFY) parameters (i.e. the small number of points) defining the piece-wise linear tone mapping output fine tuning function (tmOutputFineTuningNumVal is limited to a maximum of “10”) and their precision (8 bits), as well as the number of bits (8 bits) of the WS parameter. The effect of the lack of accuracy of the luma LUT meta_itmedLUT is that an application of the luma LUT meta_itmedLUT to the Y component of the original SDR picture may provide a result different from an application of the luma LUT itmedLUT to the Y component of the original SDR: meta_itmedLUT[Y] ≠ itmedLUT[Y] It is generally considered that modifying the SL-HDR1 post-processor, the number of (FTFX,FTFY) parameters and the precision of the (FTFX,FTFY) and WS parameters is difficult. Other solutions are expected for solving the problem of noticeable differences between the reconstructed HDR picture and the original HDR picture. In the following, various embodiments propose to bias the SDR picture sent by the RITM tool to the SL-HDR1 post-processor while keeping the metadata the same, knowing that the biasing of the SDR picture shall not be noticeable. The biasing is obtained by applying a biasing function called slitmLUT in the following such that: meta_itmedLUT[slitmLUT[Y]] = itmedLUT[Y] (Eq.1) Equation Eq.1 can be re-written as follows: slitmLUT [Y] = meta_itmedLUT-1[itmedLUT[Y]] (Eq.2) which is equivalent mathematically to: slitmLUT [Y] = meta_L_LUT [itmedLUT[Y]] (Eq.3) One can note that in the standard SL-HDR1, the luma LUT meta_L_LUT and the luma LUT meta_itmedLUT are constructed using the parameters tmOutputFineTuningNumVal and the pairs of parameters (tmOutputFineTuningX, tmOutputFineTuningY) (i.e., (FTFX,FTFY)). However, while the LUT meta_L_LUT is constructed using a curve representing FTFY in function of FTFX (FTFY in ordinates and FTFX in abscissa), the LUT meta_itmedLUT is constructed using a curve representing FTFX in function of FTFY (FTFX in ordinates and FTFY in abscissa). In some implementations, the luma LUT meta_itmedLUT is implemented by a N values LUT (N being a number equal for example to “65”, “129” or “257”). This means that addressing this using the luma LUT meta_itmedLUT with luminance values defined on more than “6” bits (2^ൌ 64) implies interpolating undefined values between the 64 points of the luma LUT meta_itmedLUT. For example, if the luma component is coded using “10” bits and N=65, then resulting luminance mapping function derived from the luma LUT meta_itmedLUT is a piecewise linear function made of “64” segments of “16” values (16 * 64 = 1024), values in segments being interpolated. It is preferable to take into account this aspect in the construction of the luma LUT slitmLUT to minimize an error between the luma LUT meta_itmedLUT and the luma LUT itmedLUT. One can note in particular that deriving the luma LUT slitmLUT from meta_itmedLUT and deriving the luma LUT slitmLUT from meta_L_LUT may provide a different result due, in part, to these interpolations. It's also worth mentioning that the whole set of luma LUTs (i.e. itmedLUT, L_LUT, meta_itmedLUT and meta_L_LUT) are defined in the gamma domain and that FTF(X,Y) are defined in the perceptual domain Fig. 3A illustrates schematically an example of hardware architecture of a processing module 300 comprised at least in the system 11 or in the system 13. The processing module 300 comprises, connected by a communication bus 305: a processor or CPU (central processing unit) 306 encompassing one or more microprocessors, general purpose computers, special purpose computers, and processors based on a multi-core architecture, as non-limiting examples; a random access memory (RAM) 301; a read only memory (ROM) 302; a storage unit 303, which can include non-volatile memory and / or volatile memory, including, but not limited to, Electrically Erasable Programmable Read-Only Memory (EEPROM), Read-Only Memory (ROM), Programmable Read-Only Memory (PROM), Random Access Memory (RAM), Dynamic Random Access Memory (DRAM), Static Random Access Memory (SRAM), flash, magnetic disk drive, and / or optical disk drive, or a storage medium reader, such as a SD (secure digital) card reader and / or a hard disc drive (HDD) and / or a network accessible storage device; at least one communication interface 304 for exchanging data with other modules, devices, systems or equipment. The communication interface 304 can include, but is not limited to, a transceiver configured to transmit and to receive data over a communication network 61 (not represented in Fig.3A). The communication interface 304 can include, but is not limited to, a modem or a network card. For example, the communication interface 304 enables the processing module 300 to receive an SDR video and to output a SDR video with SL-HDR1 metadata. The processor 306 is capable of executing instructions loaded into the RAM 301 from the ROM 302, from an external memory (not shown), from a storage medium, or from a communication network. When the processing module 300 is powered up, the processor 306 is capable of reading instructions from the RAM 301 and executing them. These instructions form a computer program causing, for example, the implementation by the processor 306 of a method described in relation to Figs. 4, 5, 6, 7, 8, 9A, 9B, 10A and 10B. All or some of the algorithms and steps of executed in the various embodiments described below may be implemented in software form by the execution of a set of instructions by a programmable machine such as a DSP (digital signal processor) or a microcontroller, or be implemented in hardware form by a machine or a dedicated component such as a FPGA (field-programmable gate array) or an ASIC (application- specific integrated circuit). The processor 306, a DSP, a microcontroller, a FPGA and an ASIC are therefore examples of electronic circuitry adapted or configured to implement the method described in relation to Figs.4, 5, 6, 7, 8, 9A, 9B, 10A and 10B. Fig. 3C illustrates a block diagram of an example of the system 13 in which various aspects and embodiments are implemented. System 13 can be embodied as a device including various components or modules and is configured to receive a video content in a first range and to generate a video content in a second range. Examples of such system include, but are not limited to, various electronic systems such as a personal computer, a laptop computer, a smartphone, a tablet or a set top box. Components of the system 13, singly or in combination, can be embodied in a single integrated circuit (IC), multiple ICs, and / or discrete components. For example, in at least one embodiment, the system 13 comprises one processing module 300 that implements a SL-HDR1 post-processor. In various embodiments, the system 13 is communicatively coupled to one or more other systems, or other electronic devices, via, for example, a communications bus or through dedicated input and / or output ports. The input to the processing module 300 can be provided through various input modules as indicated in block 320. Such input modules include, but are not limited to, (i) a radio frequency (RF) module that receives an RF signal transmitted, for example, over the air by a broadcaster, (ii) a component (COMP) input module (or a set of COMP input modules), (iii) a Universal Serial Bus (USB) input module, and / or (iv) a High Definition Multimedia Interface (HDMI) input module. Other examples, not shown in Fig.3C, include composite video. In various embodiments, the input modules of block 320 have associated respective input processing elements as known in the art. For example, the RF module can be associated with elements suitable for (i) selecting a desired frequency (also referred to as selecting a signal, or band-limiting a signal to a band of frequencies), (ii) down-converting the selected signal, (iii) band-limiting again to a narrower band of frequencies to select (for example) a signal frequency band which can be referred to as a channel in certain embodiments, (iv) demodulating the down-converted and band- limited signal, (v) performing error correction, and (vi) demultiplexing to select the desired stream of data packets. The RF module of various embodiments includes one or more elements to perform these functions, for example, frequency selectors, signal selectors, band-limiters, channel selectors, filters, downconverters, demodulators, error correctors, and demultiplexers. The RF portion can include a tuner that performs various of these functions, including, for example, down-converting the received signal to a lower frequency (for example, an intermediate frequency or a near-baseband frequency) or to baseband. Various embodiments rearrange the order of the above- described (and other) elements, remove some of these elements, and / or add other elements performing similar or different functions. Adding elements can include inserting elements in between existing elements, such as, for example, inserting amplifiers and an analog-to-digital converter. In various embodiments, the RF module includes an antenna. Additionally, the USB and / or HDMI modules can include respective interface processors for connecting the system 13 to other electronic devices across USB and / or HDMI connections. It is to be understood that various aspects of input processing, for example, Reed-Solomon error correction, can be implemented, for example, within a separate input processing IC or within the processing module 300 as necessary. Similarly, aspects of USB or HDMI interface processing can be implemented within separate interface ICs or within the processing module 300 as necessary. The demodulated, error corrected, and demultiplexed stream is provided to the processing module 300. Various elements of the system 13 can be provided within an integrated housing. Within the integrated housing, the various elements can be interconnected and transmit data therebetween using suitable connection arrangements, for example, an internal bus as known in the art, including the Inter-IC (I2C) bus, wiring, and printed circuit boards. For example, in the system 13, the processing module 300 is interconnected to other elements of the system 13 by the bus 305. The communication interface 304 of the processing module 300 allows the system 13 to communicate on the communication network 310. The communication network 310 can be implemented, for example, within a wired and / or a wireless medium. Data is streamed, or otherwise provided, to the system 13, in various embodiments, using a wireless network such as a Wi-Fi network, for example IEEE 802.11 (IEEE refers to the Institute of Electrical and Electronics Engineers). The Wi- Fi signal of these embodiments is received over the communications network 310 and the communications interface 304 which are adapted for Wi-Fi communications. The communications network 310 of these embodiments is typically connected to an access point or router that provides access to external networks including the Internet for allowing streaming applications and other over-the-top communications. Still other embodiments provide streamed data to the system 13 using the RF connection of the input block 320. As indicated above, various embodiments provide data in a non- streaming manner, for example, when the system 13 is a smartphone or a tablet. Additionally, various embodiments use wireless networks other than Wi-Fi, for example a cellular network or a Bluetooth network. The system 13 can provide an output signal to various output devices using the communication network 310 or the bus 305. For example, the system 13 can provide a post-processed reconstructed video content to the display system 15. The system 13 can provide an output signal to various output devices, including the display system 15, speakers 360, and other peripheral devices 370. The display system 15 can include one or more of, for example, a touchscreen display, an organic light-emitting diode (OLED) display, a curved display, and / or a foldable display. The display system 15 can be for a television, a tablet, a laptop, a smartphone (mobile phone), or other devices. The display system 15 can also be integrated with other components (for example, as in a smartphone or a tablet), or separate (for example, an external monitor for a laptop). The other peripheral devices 370 include, in various examples of embodiments, one or more of a stand-alone digital video disc (or digital versatile disc) (DVR, for both terms), a disk player, a stereo system, and / or a lighting system. Various embodiments use one or more peripheral devices 370 that provide a function based on the output of the system 13. For example, a disk player performs the function of playing the output of the system 13. In various embodiments, control signals are communicated between the system 13 and the display system 15, speakers 360, or other peripheral devices 370 using signaling such as AV.Link, Consumer Electronics Control (CEC), or other communications protocols that enable device-to-device control with or without user intervention. The output devices can be communicatively coupled to the display system 15 via dedicated connections through respective interfaces (330, 340 and 350). Alternatively, the output devices can be connected to the system 13 using the communication network 310 via the communication interface 304. The display system 15 and speakers 360 can be integrated in a single unit with the other components of the system 13 in an electronic device such as, for example, a television. In various embodiments, the display interface includes a display driver, such as, for example, a timing controller (T Con) chip. The display system 15 and speakers 360 can alternatively be separate from one or more of the other components, for example, if the RF module of input block 320 is part of a separate set-top box. In various embodiments in which the display system 15 and speakers 360 are external components, the output signal can be provided via dedicated output connections, including, for example, HDMI ports, USB ports, or COMP outputs. Fig. 3B illustrates a block diagram of an example of the system 11 adapted to provide SDR video data and metadata to the system 13. System 11 can be embodied as a device including the various components and modules described above and is configured to perform one or more of the aspects and embodiments described in this document. Examples of such devices include, but are not limited to, various electronic devices such as personal computers, laptop computers, a camera, a smartphone and a server. Elements or modules of the system 11, singly or in combination, can be embodied in a single integrated circuit (IC), multiple ICs, and / or discrete components. In various embodiments, the system 11 is communicatively coupled to one or more other systems, or other electronic devices, via, for example, a communications bus or through dedicated input and / or output ports. The input to the processing module 300 can be provided through various input modules as indicated in block 320 already described in relation to Fig.3C. Various elements of the system 13 can be provided within an integrated housing. Within the integrated housing, the various elements can be interconnected and transmit data therebetween using suitable connection arrangements, for example, an internal bus as known in the art, including the Inter-IC (I2C) bus, wiring, and printed circuit boards. For example, in the system 13, the processing module 300 is interconnected to other elements of the system 13 by the bus 305. The communication interface 304 of the processing module 300 allows the system 11 to communicate on the communication network 310. The communication network 310 can be implemented, for example, within a wired and / or a wireless medium. Data is streamed, or otherwise provided, to the system 11, in various embodiments, using a wireless network such as a Wi-Fi network, for example IEEE 802.11 (IEEE refers to the Institute of Electrical and Electronics Engineers). The Wi- Fi signal of these embodiments is received over the communications network 310 and the communications interface 304 which are adapted for Wi-Fi communications. The communications network 310 of these embodiments is typically connected to an access point or router that provides access to external networks including the Internet for allowing streaming applications and other over-the-top communications. Still other embodiments provide streamed data to the system 11 using the RF connection of the input block 320. As indicated above, various embodiments provide data in a non- streaming manner. When a figure is presented as a flow diagram, it should be understood that it also provides a block diagram of a corresponding apparatus. Similarly, when a figure is presented as a block diagram, it should be understood that it also provides a flow diagram of a corresponding method / process. The implementations and aspects described herein can 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), the implementation of features discussed can also be implemented in other forms (for example, an apparatus or program). An apparatus can be implemented in, for example, appropriate hardware, software, and firmware. The methods can be implemented, for example, in 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, smartphones (cell phones), portable / personal digital assistants ("PDAs"), tablets, and other devices that facilitate communication of information between end-users. Reference to “one embodiment” or “an embodiment” or “one implementation” or “an implementation”, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment” or “in one implementation” or “in an implementation”, as well any other variations, appearing in various places throughout this application are not necessarily all referring to the same embodiment. Additionally, this application may refer to “determining” various pieces of information. Determining the information can include one or more of, for example, estimating the information, calculating the information, predicting the information, retrieving the information from memory or obtaining the information for example from another device, module or from user. Further, this application may refer to “accessing” various pieces of information. Accessing the information can include one or more of, for example, receiving the information, retrieving the information (for example, from memory), storing the information, moving the information, copying the information, calculating the information, determining the information, predicting the information, or estimating the information. Additionally, this application may refer to “receiving” various pieces of information. Receiving is, as with “accessing”, intended to be a broad term. Receiving the information can include one or more of, for example, accessing the information, or retrieving the information (for example, from memory). Further, “receiving” is typically involved, in one way or another, during operations such as, for example, storing the information, processing the information, transmitting the information, moving the information, copying the information, erasing the information, calculating the information, determining the information, predicting the information, or estimating the information. It is to be appreciated that the use of any of the following “ / ”, “and / or”, and “at least one of”, “one or more of” for example, in the cases of “A and / or B” and “at least one of A and B”, “one or more of A and B” is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and / or C” and “at least one of A, B, and C”, “one or more of A, B and C” such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as is clear to one of ordinary skill in this and related arts, for as many items as are listed. As will be evident to one of ordinary skill in the art, implementations or embodiments can produce a variety of signals formatted to carry information that can be, for example, stored or transmitted. The information can include, for example, instructions for performing a method, or data produced by one of the described implementations or embodiments. For example, a signal can be formatted to carry a post-processed reconstructed video content. Such a signal can be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The information that the signal carries can be, for example, analog or digital information. The signal can be transmitted over a variety of different wired or wireless links, as is known. The signal can be stored on a processor- readable medium. Fig.4 provides a high-level representation of various embodiments. The process of Fig. 4 is executed by the processing module 300 of the system 11 before the SL-HDR pre-processor 111. For instance, the process of Fig.4 is executed by the RITM module 110. In the following, we describe an application of the process of Fig. 4 on the luminance component of pictures. However, a similar process could be applied to other components. In a step 40, the processing module 300 obtains picture data in a first dynamic range. The first dynamic range is for example a standard dynamic range and the picture data represent an original SDR picture. In a step 41, the processing module 300 determines a first function allowing mapping the picture data from the first dynamic range to a second dynamic range. The second dynamic range is for example a high dynamic range. The first function is the luma LUT itmedLUT for the luminance component. In a step 42, the processing module 300 obtains metadata allowing obtaining a second function corresponding to an approximated version of the first function. For example, regarding the luminance component, an example of process for obtaining the metadata comprises inverting the luma LUT itmedLUT to produce the luma LUT L_LUT which enables to transform the luminance component of a HDR picture back to the luminance component of the original SDR picture and deriving the metadata from the luma LUT L_LUT as specified in the standard SL-HDR1 (ETSI TS 103 433-1 V1.4.1). These metadata are then signaled in video data. These metadata allow approximating the luma LUT L_LUT by the luma LUT meta_L_LUT. The luma LUT meta_L_LUT is then inverted and provides the SDR to HDR LUT luma meta_itmedLUT. The second function is represented by the luma LUT meta_itmedLUT. In a step 43, the processing module 300 determines a third function from the first function and the second function such that an application of the second function to intermediate data resulting from an application of the third function to the picture data in the first dynamic range is equivalent to an application of the first function to the picture data in the first dynamic range. In other words, applying the luma LUT meta_itmedLUT on slitmLUT[Y] allows obtaining a HDR picture closer to the original HDR picture obtained by applying itmedLUT to the luminance component Y. In addition, from the LUTs meta_itmedLUT and itmedLUT, the processing module 300 computes a new LUT slitmLUT, which, when applied to the original SDR picture produces a new SDR picture, called slitmSDR picture, close to the original SDR picture. In a step 44, the processing module 300 applies the third function to the original SDR picture to obtain the slitmSDR picture and signals the slitmSDR picture in the video data along with the metadata. The obtained picture data are intended to be transmitted to the system 13 and in particular to the SL-HDR1 post-processor comprised in the system 13. Then, the SL- HDR1 post-processor reconstructs a HDR picture from the slitmSDR picture and the metadata which is closer to the HDR picture that would have been produced by the RITM module. When the system 11 comprises a correction module 112, the correction module 112 receives the slitmSDR picture and applies the correction process to the slitmSDR picture. As indicated earlier, the correction module 112 emulates the SL-HDR1 post- processing process allowing generating a HDR picture from a SDR picture. Fig. 5 illustrates a post-processing process allowing generating a HDR picture from a SDR picture. The post-processing process described in Fig. 5 is a summary of the post- processing process described in section 7.2.4 of the standard SL-HDR1 (ETSI TS 103 433-1 V1.4.1). The post-processing process of Fig.5 is for instance executed by the processing module 300. In a step 50, the processing module 300 obtains a SDR picture and metadata (here SL-HDR1 metadata). In a step 52, the processing module 300 derives an ITM function to be applied to a luma (i.e. luminance) component of the SDR picture from the SL-HDR1 metadata. During step 52, the process described in section 7.2.3.1 of the SL-HDR1 specification is applied. In a step 53, the processing module 300 derives a color correction function to be applied to chroma (i.e., chrominance) components of the SDR picture from the SL- HDR1 metadata. During step 53, the process described in section 7.2.3.2 of the SL- HDR1 specification is applied. In a step 54, the processing module 300 reconstructs a HDR picture from the SDR picture and the SL-HDR1 metadata. During step 54, the process described in section 7.2.4 of the SL-HDR1 specification is applied. An example of implementation of step 54 is detailed in relation to Fig.6. Fig.6 illustrates a SDR to HDR reconstruction process. In general, the SDR picture is represented in YUV 420 format with a limited range while the internal calculations in the post-processor are performed in YUV 444 format with a full range. A limited range means that a range of possible values defined by the bit-depth (8 bits, 10 bits, 12 bits, etc) is not fully occupied. An example of a typical limited range for a bit-depth of 10 bits for a Y (respectively for a U or V) component is [64;940] (respectively [64; 960]) while the full range allowed by the 10 bits is [0; 1023]. In a step 541, the processing module 300 converts the SDR picture in a converted picture in YUV 444 format with a full range. To do so, the processing module 300 starts by up-sampling the chroma components of the input SDR picture to obtain a SDR picture in YUV 444 format. Then, each component of each sample of the picture in YUV 444 format is converted from the limited range to the full range, for example, by applying the following process: ^^^^ൌ ^ ^^^^_^^െ 64^ / 876 ൈ 1023 ^^^^ൌ ^ ^^^^_^^െ 512^ / 896 ൈ 1023 ^ 512 ^^^^ൌ ^ ^^^^_^^െ 512^ / 896 ൈ 1023 ^ 512 where ^^^^_^^, ^^^^_^^and ^^^^_^^are the three components of a sample of the SDR picture in YUV 444 format and ^^^^, ^^^^and ^^^^are three components of a corresponding sample of the converted picture. In other words, the processing module 300 converts the values representative of the samples (i.e. the Y, U and V components) of the SDR picture in YUV 444 format from a first range (i.e. the limited range) to a second range (i.e. the full range), the second range being larger than the first range. During step 541, the processing module 300 centers the obtained chroma components ^^^^and ^^^^using equation (25) of section 7.2.4 of the SL-HDR1 specification to obtain centered components ^^^^^௧^and ^^^^^௧^: ^^^^^^௧^ ൌ ^^^^ െ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^^^^^௧^ ൌ ^^^^ െ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^where the value midSampleVal is defined in the SL-HDR1 specification (“512” for “10” bits components). One can note that the SDR picture could be in another format such as the format YUV 444. In that last case, no up-sampling of the chroma components is required. In a step 542, the processing module 300 determines if all samples of the converted picture have been processed. If at least one sample of the converted picture remains to be processed, step 542 is followed by steps 543 to 547. Steps 543 to 547 are applied to one sample of the converted picture, called current sample in the following. In step 543, the processing module 300 computes a luma component ^^^^^௧ଶ. To do so, the processing module first applies a re-saturation to the luma component ^^^^of the current sample using equation (26) specified in section 7.2.4 of the SL-HDR1 specification to obtain a re-saturated luma component ^^^^^௧^: ^^^^^௧^ൌ ^^^^^ ^^ ^^ ^^^0; ^^ ^^^ൈ ^^^^^௧^^ ^^ ^^^ൈ ^^^^^௧^^ The [0; 1023] using equation (27) of section 7.2.4 of the SL-HDR1 specification to obtain the luma component value ^^^^^௧ଶ: ^^^^^௧ଶൌ ^^ ^^ ^^ ^^3^0; ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ െ 1; ^^^^^௧^^ In a step 544, the processing module 300 computes a color correction function using SL-HDR1 metadata. The computation of the color correction function amounts in constructing a color correction look-up table lutCC[]. The construction of the look- up table lutCC[] use equation (21) and (22) of section 7.2.3.2 of the SL-HDR1 specification as follows: ^^ ^^ ^^ ^^ ^^^0^ൌ 0,125ö ÷ ø HDR1 In a step 545, the processing module 300 applies an inverse color correction to the chroma components values ^^^^^௧^and ^^^^^௧^using the look-up table lutCC[]. To do so, the processing module 300 applies equation (28) of section 7.2.4: ^^^^^^௧ଶ ൌ ^^ ^^ ^^ ^^ ^^^ ^^^^^௧ଶ^ ൈ ^^^^^௧^^^ ^^ ^^ ^^ ^^^ In a step 546, the processing module 300 computes components ^^^, ^^^^^௧ଷ, ^^^^^௧ଷ. Components ^^^, ^^^^^௧ଷand ^^^^^௧ଷare computed using equations (29) and (30) specified in section 7.2.4 of the SL-HDR1 specification as follows: ^^^is initialized to zero. ^^ ൌ ^^^ൈ ^^^^^௧ଶൈ ^^^^^௧ଶ^ ^^^ൈ ^^^^^௧ଶൈ ^^^^^௧ଶ^ ^^ଶൈ ^^^^^௧ଶൈ ^^^^^௧ଶ Otherwise ( ^^ ^ 1^, ^^^^^௧ଷand ^^^^^௧ଷare derived from ^^^^^௧ଶand ^^^^^௧ଶas follows:ì^^ ï^^^^௧ଷൌ^^^௧ଶ^^^ The most used implementation of SL-HDR1, called non-constant luminance (NCL) mode, specifies that k0 = k1 = k2 = 0. Therefore, in the NCL mode, ^^^, ^^^^^௧ଷ, ^^^^^௧ଷare defined as follows: ^^^ൌ 1 ^^^^^௧ଷൌ ^^^^^௧ଶ^^^^^௧ଷൌ ^^^^^௧ଶIn most of the cases, these equations are sufficient to render accurately HDR video in the NCL mode. However, some errors may occur in some particular cases. As an example, an integer implementation of a post-processor module in NCL mode could use a precision of “14” bits + “1” bit for sign for an internal representation of chroma values ^^^^^௧ଶand ^^^^^௧ଶwhile a precision of “9” bits + “1” bit for sign is used for a representation of the chroma values ^^^^^௧ଷand ^^^^^௧ଷ. In this integer implementation and for some very saturated red and blue colors in the SDR video (provided, for instance, by the pre-processor 11), ^^^^^௧ଶand / or ^^^^^௧ଶcould have an absolute value higher than 9 bits. In that case, the conversion from ^^^^^௧ଶ / ^^^^^௧ଶon “14” bits + “1” bit for sign to ^^^^^௧ଷ / ^^^^^௧ଷon “9” bits + “1” bit for sign implies clipping when ^^^^^௧ଶ / ^^^^^௧ଶhas an absolute than “9” bits. Such clipping is at the origin of errors in the reconstructed HDR image. In a step 547, the processing module 300 derives RGB values of a sample of a HDR picture corresponding to the current sample from the values ^^^, ^^^^^௧ଷand ^^^^^௧ଷusing equations (31), (32) and (33) of section 7.2.4 of the SL-HDR1 specification. When all samples of the converted picture have been processed, the processing module stops the computation of the HDR picture in a step 548. Fig.7 illustrates a correction process applied to a SDR picture implemented by the correction module 112. The purpose of the process of Fig. 7 is to prevent any clipping of the chroma components values ^^^^^௧ଶand ^^^^^௧ଶ. The process of Fig.7 is applied to SDR pictures outputted by the SL-HDR pre-processor 111. In SL-ITM mode, when the RITM module 110 outputs a slitmSDR picture, then the correction process is applied to the slitmSDR picture. In a step 1121, the processing module 300 converts a SDR picture in a converted picture in YUV 444 format with a full range applying the same process than in step 541. In a step 1122, the processing module 300 determines if all samples of the converted picture have been processed. If at least one sample of the converted picture remains to be processed, step 1122 is followed by steps 1123. Step 1123 is applied to one sample of the converted picture, called current sample in the following. During step 1123, the processing module 300 corrects the current sample, if necessary, i.e. if the current sample risk to provoke a clipping during the post- processing. Step 1123 is detailed in relation to Fig.8. If all samples of the converted picture have been processed, the processing module converts the corrected converted picture (in YUV 444 format with full range) back to a SDR picture in YUV 420 format and limited range. This conversion is typically done as follow: ^^୧୬_ୡ୭୰୰_୪୰= (INT)( ^^୧୬_ୡ୭୰୰ / 1023 * 876 + 64.5) = * sample of the corrected of the U and V components components a converted picture in YUV 420 format and limited range . Fig.8 illustrates a detail of the correction process of step 1123. Fig.8 illustrates a correction process applied to a current sample of a converted picture, the same process being applied to each sample of the converted picture. In a step 11231, the processing module 300 computes chroma components of a sample from the chroma components of the current sample using a color correction function. In an embodiment, during step 11231, the processing module 300 executes steps 543 to 546 described in relation to Fig.6. In other words, the processing module 300 computes the chroma components ^^^^^௧ଷand ^^^^^௧ଷfrom the components of the current sample using the color correction function represented by the look-up table lutCC[]. In a step 11232 the processing module 300 estimates a clipping factor div_UV based on the computed chroma components ^^^^^௧ଷand ^^^^^௧ଷand on a precision of the components ^^^^^௧ଷand ^^^^^௧ଷcomputed in step 546. The purpose of step 11232 is to estimate when the values ^^^^^௧ଷand ^^^^^௧ଷrisk to be clipped. Taking again the example of the integer implementation of a post-processor module in NCL mode using a precision of “14” bits + “1” bit for sign for an internal representation of chroma values ^^^^^௧ଶand ^^^^^௧ଶand a precision of “9” bits + “1” bit for sign for a representation of the chroma values ^^^^^௧ଷand ^^^^^௧ଷ, a maximum absolute value that can be taken by ^^^^^௧ଷ(respectively ^^^^^௧ଷ) is Umax (respectively Vmax) equal to “2ଽൌ511”. All absolute values of ^^^^^௧ଶ(respectively ^^^^^௧ଶ) greater than “511” are clipped to “511” when converted to “9” bits + “1” bit for sign to compute ^^^^^௧ଷand ^^^^^௧ଷ. The following process is applied during step 11232 to determine the clipping factor div_UV (all computations being performed in floating points): if ( ^^^^^௧ଶ> Umax) ; In a step 11233, each computed chroma component ^^^^^௧ଷand ^^^^^௧ଷas a multiplication of a first sub-part depending on a luma component of the current sample and a second sub-part depending on a corresponding chroma component of the current sample and obtains a first ratio partY of a correction factor based on the clipping factor to be applied to the first sub-part and a second ratio (1-partY) of the correction factor to be applied to the second sub-part. As detailed in equation (29) of the SL-HDR1 specification: ^^^^^௧ଷൌ ^^ ^^ ^^ ^^ ^^^ ^^୮୭^^ଶ൧. ^^୮୭^^^^^ ^^ ^^ ^^ ^^^ When the clipping sample is greater than “1”, this means that the chroma need to be modified follow: ^^^^ ൌ ^^^௧ଷ ^^ ^^ ^^ ^^ ^^^ ^^୮୭^^ଶ൧ . ^^୮୭^^^ ^^ ^^ ^^ ^^ ^^^ ^^୮୭^^ଶ൧ ^^୮୭^^div_UVൌdiv_UVൌdiv_UV. ^^^^௧ଷ^ೌ^^^^ ୮ୟ୰^ଢ଼ div_UV^^ି୮ୟ୰^ଢ଼^^^^^^ ^^ ^^ ^^ ^^ ^^^ ^^ ൧ . ^^ ^^ ^^ ^^ ^^ ^^^ ^^ ൧ ^^^^ ௧ଷ ୮୭^^ଶ ୮୭^^^ ୮୭^^ଶ ୮୭^^^^^^௧ଷ^ೌ^^^^ൌdiv_UVൌdiv_UVൌdiv_UV୮ୟ୰^ଢ଼.div_UV^^ି୮ୟ୰^ଢ଼^^^ ^^ ^^ ^^ ^^^^^୮୭^^ଶ൧corresponds to the first sub-part and ^^୮୭^^^corresponds to the second sub-part. As can be seen, one part of the correction applies to the first sub-part lutCC^ ^^^^^௧ଶ൧ that depends on the Luma component Ypost2that depends directly on the luma component Yin of the converted picture. A second part of the correction applies to the chroma components Upost1and Vpost1that depend directly on the chroma components Uin and Vin of the converted picture. The first ratio partY defines what correction needs to be applied to the luma component of the converted picture and, via the second ratio (1-partY), what correction needs to be applied to the chroma components of the converted picture to avoid any clipping by the post-processor comprised in the system 13. The ratio partY has a direct influence on the SDR picture. If the correction is applied only on the luma component Yin of the current sample, i.e. partY = 1, the corrected sample is appearing much brighter when compared to the corresponding sample in the input SDR picture. If the correction is applied only on the chroma components Uinand Vinof the current sample, i.e. partY = 0, the corrected sample is appearing much darker when compared to the corresponding sample of the input SDR picture. In an embodiment, the first ratio partY is a pre-determined fixed value defined for all samples. This fixed value can be selected by finding the best compromise for a set of selected SDR pictures that originally make the post-processor module clip, the best compromise being the ratio partY minimizing a visual difference between the input SDR picture and the corrected SDR picture. In an embodiment, the ratio partY value is fixed to “0.75” for all samples, therefore (1 – partY) = 0.25. It has a limited impact on the perception of the corrected picture and it has the advantage of being efficiently implemented on CPU based platforms. Indeed, in CPU based platforms, the square root function is very efficient and very fast, while the power function is a lot slower and less efficient. Using partY =0.75 leads to the following computations:div_UV^^ି୮ୟ୰^ଢ଼^ ൌ div_UV^.ଶହ ൌ div_UV^.ହ^^.ହ ൌ sqrt^div_UV^. sqrt^div_UV^୮ୟ୰^ଢ଼ ^ div_UVdiv_UV ൌ div_UV .^ହ ൌ div_UV^ି^.ଶହ ൌdiv_UV^.ଶହdiv_UVൌsqrt^div_UV^. sqrt^div_UV^In a step 11234, the processing module 300 computes a corrected luma value ^^^^_^^^^of a sample of a corrected SDR picture corresponding to the current sample using a division of the first sub-part by the correction factor to a power equal to the first ratio as follows: ^^ ^^ ^^ ^^ ^^^ ^^ ^ ൌ^^ ^^ ^^ ^^ ^^^ ^^post2൧In a first function represented by the look-up table lutCC[] is always a monotonic decreasing function, this can be done by increasing a value ^^^^_^^^^progressively with small increment values Δ (forexample Δ =1) until finding a value of ^^ such that ^^ ^^ ^^ ^௨௧^^^^౦^౩౪మ൧^^_^^^^^^ ^^^^^^^ ^^_ ^^ ^^ ^^ ^^^<^୧^_^^౦^౨౪ౕ.The final value of ^^^^_^^^^respecting the condition ^^ ^^ ^^ ^^ ^^ ^ ^^^^ ^^_ ^^ ^^ ^^ corresponds to the searched value ^^^^_^^^^. In a second embodiment of step 11234, the corrected luma value ^^^^_^^^^is computed by dichotomy. In a step 11235, for each chroma component ( ^^୧୬^^ ^^ ^^ ^^୧୬^, the processing module 300 computes a chroma value ( ^^୧୬_ୡ୭୰୰or ^^୧୬_ୡ୭୰୰^ for the sample of the corrected SDR picture corresponding to the current sample by using a division of the second sub- part of the chroma component by the correction factor to a power equal to the second ratio as follows: ^^^^ ൌ ୮୭^^^^^_^^^^At the end of the module 300 obtains a corrected sample with components ^^୧୬_ୡ୭୰୰, ^^^^_^^^^and ^^^^_^^^^. In the following, various embodiments are proposed for determining the third function represented by the luma LUT slitmLUT. In a first embodiment, the luma LUT slitmLUT is determined using the luma LUT meta_itmedLUT. As already described above, the luma LUT slitmLUT can be derived either from from the luma LUT meta_itmedLUT (equation Eq. 2) or from the luma LUT meta_L_LUT (equation Eq.3). Fig. 9A remind a process for deriving the luma LUT meta_itmedLUT. The process of Fig.9A is for example executed by the processing module 300. In a step 901, the processing module 300 initialize a variable i to zero. The variable i represents an entry of the luma LUT meta_itmedLUT in the [0 to N] range (N being a number equal for example to “65”, “129” or “257”). In a step 902, the processing module 300 normalizes i in the [0.0 to 1.0] range in a value inorm. In a step 903, the processing module 300 linearizes inorm in a value inormLin (inormLin = ^^ ^^ ^^ ^^ ^^ଶ.ସ^. In a step 904, the processing module 300 applies a perceptual OETF (opto- electronic transfer function) in the SDR domain to the value inormLin to obtain a value puInp. puInp is in the perceptual SDR domain. In a step 905, the processing module 300 identifies an index p for which FTFY[p] ≤ puInp < FTFY[p+1]. The index p necessarily exists as FTFY[0] = 0 and FTFY[tmOutputFineTuningNumVal -1] = 1. In a step 906, the processing module 300 obtains a corrected value corVal corresponding to puInp by interpolation, knowing puInp, p, FTFY[p], FTFY[p+1], FTFX[p], FTFX[p+1] (f =FTFX[p+1] - FTFX[p]) / (FTFY[p+1] - FTFY[p] and corVal = FTFX[p] + f * (puInp - FTFY[p])). In a step 907, following the clause 7.2.3.1.5 of the standard SL-HDR1 (ETSI TS 103433-1 V1.4.1), the processing module 300 applies an inverse tone mapping to the corrected value corVal, to obtain a value puHdr. In a step 908, the processing module 300 applies an inverse of the WS to the value puHdr to obtain a value puHdrWs: puHdrWs = puHdr * (1 – WS). In a step 909, the processing module 300 applies a perceptual EOTF (Electro- Optical Transfer Function) in the HDR domain to the value puHdrWs to obtain a value YhdrNormLin in the linear domain. In a step 910, the processing module 300 converts back the value YhdrNormLin in the gamma domain to obtain YhdrNorm in the [0 to 1] range (YhdrNorm= ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^ / ଶ.ସ^. In a step 911, the processing module 300 increments the variable i of one unit. In a step 912, the processing module 300 determines if i ≤ N. Responsive to i ≤ N, step 912 is followed by step 902. Otherwise, the process ends in a step 913. The set of obtained pair (i, YhdrNorm) for i in [0;N] forms the luma LUT meta_itmedLUT. Fig.9B remind a process for deriving the luma LUT meta_L_LUT. The process of Fig.9B is for example executed by the processing module 300. In a step 921, the processing module 300 initialize a variable i to zero. Here, the variable i represents an entry of the luma LUT meta_L_LUT in the [0 to N] range (N being a number equal for example to “65”, “129” or “257”). In a step 922, the processing module 300 normalizes i in the [0.0 to 1.0] range in a value inorm. In a step 923, the processing module 300 linearizes inorm in a value inormLin (inormLin = ^^ ^^ ^^ ^^ ^^ଶ.ସ^. In a step 924, the processing module 300 applies a perceptual OETF (opto- electronic transfer function) in the HDR domain to the value inormLin to obtain a value puInp. puInp is in the perceptual HDR domain. In a step 925, the processing module 300 applies the WS to the value puHdr to obtain a value puHdrWs: puHdrWs = puHdr / (1 – WS). In a step 926, the processing module 300 identifies an index p for which FTFX[p] ≤ puInp < FTFX[p+1]. The index p necessarily exists as FTFX[0] = 0 and FTFX[tmOutputFineTuningNumVal -1] = 1. In a step 927, the processing module 300 obtains a corrected value corVal corresponding to puInp by interpolation, knowing puInp, p, FTFY[p], FTFY[p+1], FTFX[p], FTFX[p+1] (f =FTFY[p+1] - FTFY[p]) / (FTFX[p+1] - FTFX[p] and corVal = FTFY[p] + f * (puHdrWs - FTFX[p])). In a step 928, following an inverse of the process of the clause 7.2.3.1.5 of the standard SL-HDR1 (ETSI TS 103433-1 V1.4.1), the processing module 300 applies a tone mapping to the corrected value corVal, to obtain a value puSdr. In a step 929, the processing module 300 applies a perceptual EOTF (Electro- Optical Transfer Function) in the HDR domain to the value puSdr to obtain a value YsdrNormLin in the linear domain. In a step 930, the processing module 300 converts back the value YsdrNormLin in the gamma domain to obtain YsdrNorm in the [0 to 1] range (YsdrNorm= ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^ / ଶ.ସ^. In a step 931, the processing module 300 increments the variable i of one unit. In a step 932, the processing module 300 determines if i ≤ N. Responsive to i ≤ N, step 932 is followed by step 922. Otherwise, the process ends in a step 933. The set of obtained pair (i, YsdrNorm) for i in [0;N] forms the luma LUT meta_L_LUT. In a first embodiment of step 43, the luma LUT slitmLUT is derived by the processing module 300 of the RITM module 110 using the luma LUT meta_itmedLUT. Fig. 10A illustrates schematically a process for obtaining the luma LUT slitmLUT according to the first embodiment. In a step 1001, the meta_itmedLUT is inversed to follow the equation eq.2. Je epConsidering that the luma LUT meta_itmedLUT-1has “1024” entries, building the meta_itmedLUT-1comprises multiplying the “65” values of the meta_itmedLUT, which are normalized in [0.0...1.0], by “1023 and, finding for each entry j of the meta_itmedLUT-1(which is a value between “0” and “1023”) a pseudo- entry in the meta_itmedLUT, i.e., an interpolated entry located between two successive actual entries of the meta_itmedLUT, which produces the exact integer value j. Given j, the first integer value i for which meta_itmedLUT [i] is just above j is determined. A value delta is computed as follows: delta = meta_itmedLUT [i] - meta_itmedLUT [i-1] and then: meta_itmedLUT-1[j] = (i - 1) + int ( (j - meta_itmedLUT [i-1]) / delta) where int(x) takes the integer part of x. meta_itmedLUT-1is necessarily “10” bits integer LUT (i.e., its output values are “10” bits), as it replaces an input luminance value in the [0…1023] range by another value which is intended to be sent to the SL-HDR1 post processor which is expecting “10” bits data. In a step 1002, the processing module 300 obtains the luma LUT slitmLUT from the luma LUT itmedLUT and the luma LUT meta_itmedLUT-1. In the case where the luma LUT itmedLUT is an integer LUT, i.e., its outputs are in the integer range[0…1023], the luma LUT slitmLUT for a luma value Y (slitmLUT[Y]) is obtained in step 1002 by addressing the itmedLUT using the value Y to obtain a value Z in the range [0…1023] (Z= itmedLUT[Y]), and then addressing the meta_itmedLUT-1using the value Z to obtain the slitmLUT[Y] value (slitmLUT[Y]= ^^ ^^ ^^ ^^_ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ି^^ ^^^). In the case where the luma LUT itmedLUT is a floating point LUT, i.e., its output is in the floating-point range [0.0…1023.0], a value Z can be found for which: Z < itmedLUT[Y] < Z+1 and then slitmLUT [Y] is obtained in step 1002 using an interpolation: slitmLUT [Y] = meta_itmedLUT-1[Z] + int ((itmedLUT[Y] – Z) * delta) with delta = meta_itmedLUT-1[Z+1] - meta_itmedLUT-1[Z] Note that we have considered full range video (i.e., the luminance values are between 0 and 1023 when encoded on 10 bits). The principle remains the same for legal range video (i.e., the luminance values are between 64 and 940 when encoded on 10 bits). In a second embodiment of step 43, the luma LUT slitmLUT is derived by the processing module 300 of the RITM module 110 using the luma LUT meta_L_LUT to follow equation Eq.3. Fig. 10B illustrates schematically a process for obtaining the luma LUT slitmLUT according to the second embodiment. In a step 1011, the processing module 300 defines a N values table SDR_N. In the following, N=65 but other values such as N=129 or N=257 are possible. To do so, the processing module 300 fix N SDR values in the Gamma domain from “0” to “1024” with a step of “16” (i.e., SDR_N[i]=16×i). These N SDR values are then evenly distributed in the SDR Gamma domain. The luma LUT meta_L_LUT being normalized in [0.0…1.0], in a step 1012, the processing module 300 multiplies the output of the normalized luma LUT meta_L_LUT by “1024” (i.e., denorm_meta_L_LUT[i]=meta_L_LUT[i]×1024 for i in [0; N]). In a step 1013, for each integer value i in the range [0…64], the processing module 300 determines a value p for which: denorm_meta_L_LUT[p] <= SDR_N[i] < denorm_meta_L_LUT[p+1] In a step 1014, the processing module 300 determines a value HDR_N[i] corresponding to the value SDR_N[i] by interpolation: HDR[i] = p + (SDR[i] – denorm_meta_L_LUT[p]) / (denorm_meta_L_LUT[p+1]) - denorm_meta_L_LUT[p]). A result of step 1011 to 1014 is a set of “65” pairs (SDR[i], HDR[i]), the SDR[i] being evenly distributed in the gamma domain. In a step 1015, the processing module 300 then constructs the luma LUT slitmLUT using interpolations. To do so, for “1025” values j in the [0…1024] range, the processing module 300 determines a value j such that: HDR[i] <= itmedLUT[j] < HDR[i+1] During step 1015, the processing module 300 then calculates a value offset and a value delta such that: offset = itmedLUT[j] - HDR[i] delta = (SDR[i+1] - SDR[i]) / (HDR[i+1] - HDR[i]) and finally: slitmLUT[j] = SDR[i] + int(offset * delta). Note that we have considered full range video. The principle remains the same for legal range video. We described above a number of embodiments. Features of these embodiments can be provided alone or in any combination. Further, embodiments can include one or more of the following features, devices, or aspects, alone or in any combination, across various claim categories and types: ^ A bitstream or signal that includes one or more of the described video content or variations thereof. ^ Creating and / or transmitting and / or receiving and / or decoding a bitstream or signal that includes one or more of the described video content, or variations thereof. ^ A TV, set-top box, cell phone, tablet, personal computer or other electronic device that performs at least one of the embodiments described, and that displays (e.g. using a monitor, screen, or other type of display) a resulting picture. ^ A TV, set-top box, cell phone, tablet, personal computer or other electronic device that tunes (e.g. using a tuner) a channel to receive a signal including a reconstructed video content, and performs at least one of the embodiments described. ^ A TV, set-top box, cell phone, tablet, or other electronic device that receives (e.g. using an antenna) a signal over the air that includes a reconstructed video content, and performs at least one of the embodiments described.

Claims

Claims 1. A method comprising: obtaining (40) picture data in a first dynamic range; determining (41) a first function allowing mapping the picture data from the first dynamic range to a second dynamic range; signaling (42) metadata allowing obtaining a second function corresponding to an approximated version of the first function in video data; determining (43) a third function from the first function and the second function such that an application of the second function to intermediate data resulting from an application of the third function to the picture data in the first dynamic range is equivalent to an application of the first function to the picture data in the first dynamic range; and signaling (44) data representative of the intermediate data in the video data.

2. The method of claim 1 wherein a dynamic range of the first dynamic range is lower than a dynamic range of the second dynamic range.

3. The method of claim 1 or 2 wherein the metadata are representative of an inverse of the first function.

4. The method of claim 1, 2 or 3 wherein the second function is an inverse of an intermediate function derived from the metadata.

5. The method of claim 4 wherein the intermediate function is a tone mapping function represented by a first look-up table derived from the metadata and the second function is an inverse tone mapping function represented by a second look-up table derived by inverting the intermediate function from the first look- up table.

6. The method of claim 4 or 5 wherein the third function is derived from the intermediate function or from the second function.

7. The method of any previous claim further comprising:obtaining (11231) chroma components from a current sample of the intermediate data using a color correction function; estimating (11232) a clipping factor based on the obtained chroma components and on a precision value; representing (11233) each obtained chroma component as a multiplication of a first sub-part depending on a luma component of the sample of the intermediate data and a second sub-part depending on a corresponding chroma component of the sample of the intermediate data and obtaining a first ratio of a correction factor to be applied to the first sub-part and a second ratio of the correction factor to be applied to the second sub-part, the correction factor being based on the clipping factor; obtaining (11234) a luma value of a sample of a corrected intermediate data corresponding to the sample of the intermediate data using a division of the first sub- part by the correction factor to a power equal to the first ratio; and for each chroma component, obtaining (11235) a chroma value for the sample of the corrected intermediate data corresponding to the sample of the intermediate data by dividing the second sub-part of the chroma component by the correction factor to a power equal to the second ratio; wherein the data representative of the intermediate data are the corrected intermediate data.

8. A device comprising an electronic circuitry configured for: obtaining (40) picture data in a first dynamic range; determining (41) a first function allowing mapping the picture data from the first dynamic range to a second dynamic range; signaling (42) metadata allowing obtaining a second function corresponding to an approximated version of the first function in video data; determining (43) a third function from the first function and the second function such that an application of the second function to intermediate data resulting from an application of the third function to the picture data in the first dynamic range is equivalent to an application of the first function to the picture data in the first dynamic range; and signaling (44) data representative of the intermediate data in the video data.

9. The device of claim 8 wherein a dynamic range of the first dynamic range is lower than a dynamic range of the second dynamic range.

10. The device of claim 8 or 9 wherein the metadata are representative of an inverse of the first function.

11. The device of claim 8, 9 or 10 wherein the second function is an inverse of an intermediate function derived from the metadata.

12. The device of claim 11 wherein the intermediate function is a tone mapping function represented by a first look-up table derived from the metadata and the second function is an inverse tone mapping function represented by a second look-up table derived by inverting the intermediate function from the first look- up table.

13. The device of claim 11 or 12 wherein the third function is derived from the intermediate function or from the second function.

14. The device of any previous claim from claim 8 to 13 wherein the electronic circuitry is further configured for: obtaining (11231) chroma components from a current sample of the intermediate data using a color correction function; estimating (11232) a clipping factor based on the obtained chroma components and on a precision value; representing (11233) each obtained chroma component as a multiplication of a first sub-part depending on a luma component of the sample of the intermediate data and a second sub-part depending on a corresponding chroma component of the sample of the intermediate data and obtaining a first ratio of a correction factor to be applied to the first sub-part and a second ratio of the correction factor to be applied to the second sub-part, the correction factor being based on the clipping factor; obtaining (11234) a luma value of a sample of a corrected intermediate data corresponding to the sample of the intermediate data using a division of the first sub- part by the correction factor to a power equal to the first ratio; andfor each chroma component, obtaining (11235) a chroma value for the sample of the corrected intermediate data corresponding to the sample of the intermediate data by dividing the second sub-part of the chroma component by the correction factor to a power equal to the second ratio; wherein the data representative of the intermediate data are the corrected intermediate data.

15. Non-transitory information storage medium storing program code instructions for implementing the method according to any previous claim from claim 1 to 7.

16. A computer program comprising program code instructions for implementing the method according to any previous claim from claim 1 to 7.

17. A signal generated by the method of any previous claim from claim 1 to 7 or by the device of any previous claim from claim 8 to 14.

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