Patent Publication Number: US-2013230101-A1

Title: Methods for encoding and decoding an image, and corresponding devices

Description:
This application claims priority under 35 USC §119 from United Kingdom Applications No. 1203706.5 filed on Mar. 2, 2012 and No. 1217459.5 filed on Sep. 28, 2012, each of which are incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The present invention concerns methods for encoding and decoding an image comprising blocks of pixels, and associated encoding devices. 
     The invention is particularly useful for the encoding of digital video sequences made of images or “frames”. 
     BACKGROUND OF THE INVENTION 
     Video compression algorithms, such as those standardized by the standardization organizations ITU, ISO, and SMPTE, exploit the spatial and temporal redundancies of images in order to generate bitstreams of data of smaller size than original video sequences. These powerful video compression tools, known as spatial (or intra) and temporal (or inter) predictions, make the transmission and/or the storage of video sequences more efficient. 
     Video encoders and/or decoders (codecs) are often embedded in portable devices with limited resources, such as cameras or camcorders. Conventional embedded codecs can process at best high definition (HD) digital videos, i.e 1080×1920 pixel frames. 
     Real time encoding is however limited by the limited resources of the portable devices, especially regarding slow access to the working memory (e.g. random access memory, or RAM) and regarding the central processing unit (CPU). 
     This is particularly striking for the encoding of ultra-high definition (UHD) digital videos that are about to be handled by the latest cameras. This is because the amount of pixel data to encode or to consider for spatial or temporal prediction is huge. 
     UHD is typically four times (4 k2 k pixels) the definition of an HD video which is the current standard definition video. Furthermore, very ultra high definition, which is sixteen times that definition (i.e. 8 k4 k pixels), is even being considered in a more long-term future. 
     SUMMARY OF THE INVENTION 
     Faced with these encoding constraints in terms of limited power and memory access bandwidth, the inventors provide a UHD codec with low complexity based on scalable encoding. 
     Basically, the UHD video is encoded into a base layer and one or more enhancement layers. 
     The base layer results from the encoding of a reduced version of the UHD images, in particular having a HD resolution, with a standard existing codec (e.g. H.264 or HEVC—High Efficiency Video Coding). As stated above, the compression efficiency of such a codec relies on spatial and temporal predictions. 
     Further to the encoding of the base layer, an enhancement image is obtained from subtracting an interpolated (or up-scaled) decoded image of the base layer from the corresponding original UHD image. The enhancement images, which are residuals or pixel differences with UHD resolution, are then encoded into an enhancement layer. 
       FIG. 1  illustrates such approach at the encoder  10 . 
     An input raw video  11 , in particular a UHD video, is down-sampled  12  to obtain a so-called base layer, for example with HD resolution, which is encoded by a standard base video coder  13 , for instance H.264/AVC or HEVC. This results in a base layer bit stream  14 . 
     To generate the enhancement layer, the encoded base layer is decoded  15  and up-sampled  16  into the initial resolution (UHD in the example) to obtain the up-sampled decoded base layer. 
     The latter is then subtracted  17 , in the pixel domain, from the original raw video to get the residual enhancement layer X. 
     The information contained in X is the error or pixel difference due to the base layer encoding and the up-sampling. It is also known as a “residual”. 
     A conventional block division is then applied, for instance a homogenous 8×8 block division (but other divisions with non-constant block size are also possible). 
     Next, a DCT transform  18  is applied to each block to generate DCT blocks forming the DCT image X DCT  having the initial UHD resolution. 
     This DCT image X DCT  is encoded in X DCT,Q   ENC  by an enhancement video encoding module  19  into an enhancement layer bit stream  20 . 
     The encoded bit-stream EBS resulting from the encoding of the raw video  11  is made of:
         the base layer bit-stream  14  produced by the base video encoder  13 ;   the enhancement layer bit-stream  20  encoded by the enhancement video encoder  19 ; and   parameters  21  determined and used by the enhancement video encoder.       

     Examples of those parameters are given here below. 
       FIG. 2  illustrates the associated processing at the decoder  30  receiving the encoded bit-stream EBS. 
     Part of the processing consists in decoding the base layer bit-stream  14  by the standard base video decoder  31  to produce a decoded base layer. This decoded base layer is up-sampled  32  into the initial resolution, i.e. UHD resolution. 
     In another part of the processing, both the enhancement layer bit-stream  20  and the parameters  21  are used by the enhancement video decoding module  33  to generate a dequantized DCT image  X   Q     −1     DEC . The image  X   Q     −1     DEC  is the result of the quantization and then the inverse quantization on the image X DCT . 
     An inverse DCT transform  34  is then applied to each block of the image X to obtain the decoded residual  X   IDCT,Q     −1     DEC  (of UHD resolution) in the pixel domain. 
     This decoded residual  X   IDCT,Q     −1     DEC  is added  35  to the up-sampled decoded base layer to obtain decoded images of the video. 
     Filter post-processing, for instance with a deblocking filter  36 , is finally applied to obtain the decoded video  37  which is output by the decoder  30 . 
     Reducing UHD encoding complexity relies on simplifying the encoding of the enhancement images at the enhancement video encoding module  19  compared to the conventional encoding scheme. 
     To that end, the inventors dispense with the temporal prediction and possibly the spatial prediction when encoding the UHD enhancement images. This is because the temporal prediction is very expensive in terms of memory bandwidth consumption, since it often requires accessing other enhancement images. 
     While this simplification reduces by 80% the slow memory random access bandwidth consumption during the encoding process, not using those powerful video compression tools may deteriorate the compression efficiency, compared to the conventional standards. 
     In this respect, the inventors have developed several additional tools for increasing the efficiency of the encoding of those enhancement images. 
       FIG. 3  illustrates an embodiment of the enhancement video encoding module  19  (or “enhancement layer encoder”) that is provided by the inventors. 
     In this embodiment, the enhancement layer encoder models  190  the statistical distribution of the DCT coefficients within the DCT blocks of a current enhancement image by fitting a parametric probabilistic model. 
     This fitted model becomes the channel model of DCT coefficients and the fitted parameters are output in the parameter bit-stream  21  coded by the enhancement layer encoder. As will become more clearly apparent below, a channel model may be obtained for each DCT coefficient position within a DCT block, i.e. each type of coefficient or each DCT channel, based on fitting the parametric probabilistic model onto the corresponding collocated DCT coefficients throughout all the DCT blocks of the image X DCT  or of part of it. 
     Based on the channel models, quantizers may be chosen  191  from a pool of pre-computed quantizers dedicated to each DCT channel as further explained below. 
     The chosen quantizers are used to perform the quantization  192  of the DCT image X DCT  to obtain the quantized DCT image X DCT,Q . 
     Lastly, an entropy encoder  193  is applied to the quantized DCT image X DCT,Q  to compress data and generate the encoded DCT image X DCT,Q   ENC  which constitutes the enhancement layer bit-stream  20 . 
     The associated enhancement video decoder  33  is shown in  FIG. 4 . 
     From the received parameters  21 , the channel models are reconstructed and quantizers are chosen  330  from the pool of quantizers. As further explained below, quantizers used for dequantization may be selected at the decoder side using a process similar to the selection process used at the encoder side, based on parameters defining the channel models (which parameters are received in the data stream). Alternatively, the parameters transmitted in the data stream could directly identify the quantizers to be used for the various DCT channels. 
     An entropy decoder  331  is applied to the received enhancement layer bit-stream  20  (  X =  X   DCT,Q   ENC ) to obtain the quantized DCT image  X   DEC . 
     A dequantization  332  is then performed by using the chosen quantizers, to obtain a dequantized version of the DCT image  X   Q     −1     DEC . 
     The channel modeling and the selection of quantizers are some of the additional tools as introduced above. 
     As will become apparent from the explanation below, those additional tools may be used for the encoding of any image, regardless of the enhancement nature of the image, and furthermore regardless of its resolution. 
     As briefly introduced above, the invention is particularly advantageous when encoding images without prediction. 
     According to a first aspect, the invention provides a method for encoding a video sequence comprising at least one frame comprising a plurality of blocks of pixels, comprising the steps of:
         determining a frame merit and a distortion at the frame level such that a video merit, computed based on said distortion and said frame merit, corresponds to a target video merit;   determining, for each block of said plurality of blocks, a block merit for the concerned block based on the frame merit;   transforming, for each block of the plurality of blocks, pixel values for the concerned block into a set of coefficients each having a coefficient type;   selecting coefficient types based, for each coefficient, on an initial encoding merit for said coefficient type and on the block merit for the concerned block;   quantizing the selected coefficients into quantized symbols; and   encoding the quantized symbols.       

     The frame merit can thus be chosen such that the encoding provided when using this frame merit meets the target video merit, which can for instance be selected by the user. When used over several frames in particular, encoding is thus correctly distributed between the frames in order to meet this target video merit. In this respect, the various frames may be several luminance frames, possibly representing multiple views for a same image, or luminance and chrominance frames as explained below. 
     As further explained in the description given below, each block may have a particular block type and, for each block, the block merit may then be determined based on the frame merit and on a number of blocks per area unit for the block type of the concerned block, which makes it possible to correctly distribute encoding between the various blocks. 
     The steps of determining the frame merit and the distortion at the frame level, of determining, for each block of said plurality of blocks, the block merit and of selecting coefficients may in practice be performed using an iterative process including the following steps:
         determining, for each block of said plurality of blocks, a possible block merit for the concerned block based on a possible frame merit;   for each block of said plurality of blocks, selecting coefficient types based, for each coefficient type, on an initial encoding merit for said coefficient type and on the possible block merit for the concerned block;   for each block of said plurality of blocks, selecting, for each selected coefficient type, a possible quantizer based on the possible block merit for the concerned block; and   determining an obtained distortion at the frame level resulting from using the selected quantizers;   until an obtained video merit, computed based on the obtained distortion and the possible frame merit, corresponds to a target video merit.       

     In such a process, the possible frame merit may converge (during the various iterations of the iterative process) towards the determined frame merit, for instance according to a dichotomy scheme as described below. 
     In such processes, a coefficient type may, for instance, be selected if the initial encoding merit for this coefficient type is greater than the possible block merit for the concerned block. For each selected coefficient type, a quantizer may be selected based on the possible block merit, for instance such that the merit for further encoding the concerned coefficient (i.e. of encoding with a finer quantizer) equals the possible block merit. This provides a balanced distribution of encoding between coefficients. 
     In the case where the frame is a luminance frame, the video sequence may also comprise at least one corresponding colour frame (for instance a U frame and a V frame as described below); the method may then comprise at least one step of determining a colour frame merit. 
     In such a context, when the colour frame comprises a plurality of colour blocks, the method may comprise the steps of:
         determining, for each colour block of said plurality of colour blocks, a colour block merit for the concerned colour block based on the colour frame merit;   transforming, for each colour block of the plurality of blocks, pixel values for the concerned colour block into a set of coefficients each having a coefficient type;   selecting coefficient types based, for each coefficient, on an initial encoding merit for said coefficient type and on the colour block merit for the concerned colour block;   for each block of said plurality of colour blocks, selecting, for each selected coefficient type, a quantizer based on the colour block merit for the concerned colour block;   for each selected coefficient type, quantizing the coefficient having the concerned type into a quantized symbol using the selected quantizer for the concerned coefficient type; and   encoding the quantized symbols.       

     The advantages mentioned above also apply in this case to colour frames. 
     The step of determining the colour frame merit may use a balancing parameter. 
     For instance, the step of determining a frame merit and a distortion at the frame level is such that a product of the determined distortion at the frame level and of the target video merit essentially equals the determined frame merit and the step of determining the colour frame merit is such that a product of a corresponding distortion for the colour frame and of the target video merit essentially equals a product of the balancing parameter and the determined colour frame merit. This provides a balance between the luminance component (luminance frame) and the concerned chrominance component (colour frame) which is adjustable thanks to the balancing parameter. 
     When two colour components are used (such as U and V), this may apply to each colour component, possibly with a specific colour frame merit for each colour component; the two colour frame merits may be separately computed based on the above, as explained below. 
     According to another possible embodiment, the frame merit determined for the luminance frame and the colour frame merit may be determined based on a fixed relationship between the distortion at the frame level for the luminance frame and a distortion at the frame level for the colour frame. The distribution of encoding between luminance frames and colour frames may thus be controlled thanks to this fixed relationship. 
     The video merit may estimate a ratio between a variation of the Peak-Signal-to-Noise-Ratio caused by further encoding the luminance frame and an associated variation of the rate for the luminance and colour frames. This type of ratio is generally taken into consideration when estimating the rate-distortion balance of a coding mode. 
     In a general manner, the video merit may estimate a ratio between a variation of the Peak-Signal-to-Noise-Ratio caused by further encoding at least said frame and an associated variation of the rate for at least said frame. 
     On the other hand, determining an initial coefficient encoding merit for a given coefficient type includes for instance estimating a ratio between a distortion variation provided by encoding a coefficient having the given type and a rate increase resulting from encoding said coefficient. 
     According to a possible embodiment, the step of determining a frame merit and a distortion at the frame level uses a balancing parameter. This balancing parameter makes possible for instance to adjust the desired balancing of quality between the various components (i.e. the luminance Y and each of the colour components U,V) 
     The step of determining a frame merit and a distortion at the frame level is for instance such that a product of the determined distortion at the frame level and of the target video merit essentially equals a product of the balancing parameter and the determined frame merit, as further explained below. 
     The method may include a step of sending the determined frame merit. The frame merit may then be easily used at the receiver side, i.e. at the decoder, as now explained. 
     The invention also provides a method for encoding a video sequence comprising at least one frame comprising a plurality of blocks of pixels, comprising the steps of:
         determining a frame merit and a corresponding distortion at the frame level such that said distortion corresponds to a target distortion;   determining, for each block of said plurality of blocks, a block merit for the concerned block based on the frame merit;   transforming, for each block of the plurality of blocks, pixel values for the concerned block into a set of coefficients each having a coefficient type;   selecting coefficient types based, for each coefficient, on an initial encoding merit for said coefficient type and on the block merit for the concerned block;   quantizing the selected coefficients into quantized symbols; and   encoding the quantized symbols.       

     As in the embodiment described below, the steps of determining the frame merit and the corresponding distortion at the frame level, of determining, for each block of said plurality of blocks, the block merit and of selecting coefficients may be performed using an iterative process including the following steps:
         determining, for each block of said plurality of blocks, a possible block merit for the concerned block based on a possible frame merit;   for each block of said plurality of blocks, selecting coefficient types based, for each coefficient type, on an initial encoding merit for said coefficient type and on the possible block merit for the concerned block;   for each block of said plurality of blocks, selecting, for each selected coefficient type, a possible quantizer based on the possible block merit for the concerned block; and   determining an obtained distortion at the frame level resulting from using the selected quantizers;   until the obtained distortion corresponds to the target distortion.       

     The invention also provides a method for encoding a video sequence comprising at least one frame comprising a plurality of blocks of pixels, comprising the steps of:
         determining a frame merit and a corresponding rate at the frame level such that said rate corresponds to a target rate;   determining, for each block of said plurality of blocks, a block merit for the concerned block based on the frame merit;   transforming, for each block of the plurality of blocks, pixel values for the concerned block into a set of coefficients each having a coefficient type;   selecting coefficient types based, for each coefficient, on an initial encoding merit for said coefficient type and on the block merit for the concerned block;   quantizing the selected coefficients into quantized symbols; and   encoding the quantized symbols.       

     As in the embodiment described below, the steps of determining the frame merit and the corresponding rate at the frame level, of determining, for each block of said plurality of blocks, the block merit and of selecting coefficients may be performed using an iterative process including the following steps:
         determining, for each block of said plurality of blocks, a possible block merit for the concerned block based on a possible frame merit;   for each block of said plurality of blocks, selecting coefficient types based, for each coefficient type, on an initial encoding merit for said coefficient type and on the possible block merit for the concerned block;   for each block of said plurality of blocks, selecting, for each selected coefficient type, a possible quantizer based on the possible block merit for the concerned block; and   determining an obtained rate at the frame level resulting from using the selected quantizers;   until the obtained rate corresponds to the target rate.       

     According to a second aspect, the invention provides a method for decoding data representing a video sequence comprising at least one frame comprising a plurality of blocks of pixels, each block having a block type, comprising the steps of:
         receiving the data and a frame merit;   decoding data associated with a block among said plurality of blocks into a set of symbols each corresponding to a coefficient type, said block having a given block type;   determining a block merit based on the received frame merit and on a number of blocks of the given block type per area unit;   selecting coefficient types based, for each coefficient type, on a coefficient encoding merit prior to encoding, for said coefficient type, and on the block merit;   for selected coefficient types, dequantizing symbols into dequantized coefficients having a coefficient type among the selected coefficient types; and   transforming dequantized coefficients into pixel values in the spatial domain for said block.       

     The selection of symbols to be dequantized and their corresponding coefficient type are thus determined in a manner comparable to what is done at the encoder side and is thus consistent with encoding. 
     Each block may have a particular block type and said block merit may then be determined based on the received frame merit and on a number of blocks per area unit for the block type of the concerned block, as was done at encoding as mentioned above. 
     As noted above, a coefficient type is selected for instance if the initial encoding merit for this coefficient type is greater than the block merit. It may also be provided a step of selecting, for each selected coefficient type, a quantizer based on the block merit; dequantizing a symbol having a particular coefficient type may then use the quantizer selected for the particular coefficient type. 
     In the possible case where the frame is a luminance frame and where the video sequence comprises at least one corresponding colour frame, the method may comprise a step of receiving a colour frame merit. 
     In this context, the colour frame may comprise a plurality of colour blocks and the method may comprise the steps of:
         decoding data associated with a colour block among said plurality of colour blocks into a set of symbols each corresponding to a coefficient type, said block having a particular block type;   determining a colour block merit based on the received colour frame merit and on a number of blocks of the particular block type per area unit;   selecting coefficient types based, for each coefficient type, on a coefficient encoding merit prior to encoding, for said coefficient type, and on the colour block merit;   for selected coefficient types, dequantizing symbols into dequantized coefficients having a coefficient type among the selected coefficient types; and   transforming dequantized coefficients into pixel values in the spatial domain for said colour block.       

     The invention further provides a device for encoding a video sequence comprising at least one frame comprising a plurality of blocks of pixels, comprising:
         a module for determining a frame merit and a distortion at the frame level such that a video merit, computed based on said distortion and said frame merit, corresponds to a target video merit;   a module for determining, for each block of said plurality of blocks, a block merit for the concerned block based on the frame merit;   a module for transforming, for each block of the plurality of blocks, pixel values for the concerned block into a set of coefficients each having a coefficient type;   a module for selecting coefficient types based, for each coefficient, on an initial encoding merit for said coefficient type and on the block merit for the concerned block;   a module for quantizing the selected coefficients into quantized symbols; and   a module for encoding the quantized symbols.       

     As provided above, the module for determining a frame merit and a distortion at the frame level may for instance be configured such that a product of the determined distortion at the frame level and of the target video merit essentially equals a product of a balancing parameter and the determined frame merit. 
     In the case where the above-mentioned frame is a luminance frame and where a colour frame is also used, the module for determining a frame merit and a distortion at the frame level may be configured such that a product of the determined distortion at the frame level and of the target video merit essentially equals the determined frame merit, and the module for determining a colour frame merit (to be used for the colour frame as explained above) may be configured such that a product of a corresponding distortion for the colour frame and of the target video merit essentially equals a product of a balancing parameter and the determined colour frame merit. 
     At the decoder side, it is proposed a device for decoding data representing a video sequence comprising at least one frame comprising a plurality of blocks of pixels, each block having a block type, comprising:
         a module for receiving the data and a frame merit;   a module for decoding data associated with a block among said plurality of blocks into a set of symbols each corresponding to a coefficient type, said block having a given block type;   a module for determining a block merit based on the received frame merit and on a number of blocks of the given block type per area unit;   a module for selecting coefficient types based, for each coefficient type, on a coefficient encoding merit prior to encoding, for said coefficient type, and on the block merit;   a module for dequantizing, for selected coefficient types, symbols into dequantized coefficients having a coefficient type among the selected coefficient types; and   a module for transforming dequantized coefficients into pixel values in the spatial domain for said block.       

     Optional features proposed above in connection with the encoding method may also apply to the decoding method, the encoding device and the decoding device just mentioned. 
     The invention also provides information storage means, possibly totally or partially removable, able to be read by a computer system, comprising instructions for a computer program adapted to implement an encoding or decoding method as mentioned above, when this program is loaded into and executed by the computer system. 
     The invention also provides a computer program product able to be read by a microprocessor, comprising portions of software code adapted to implement an encoding or decoding method as mentioned above, when it is loaded into and executed by the microprocessor. 
     The invention also provides an encoding device for encoding an image substantially as herein described with reference to, and as shown in,  FIGS. 1 and 3  of the accompanying drawings. 
     The invention also provides a decoding device for decoding an image substantially as herein described with reference to, and as shown in,  FIGS. 2 and 4  of the accompanying drawings. 
     According to another aspect of the present invention, there is provided a method of encoding video data comprising:
         receiving video data having a first resolution,   downsampling the received first-resolution video data to generate video data having a second resolution lower than said first resolution, and encoding the second resolution video data to obtain video data of a base layer having said second resolution; and   decoding the base layer video data, upsampling the decoded base layer video data to generate decoded video data having said first resolution, forming a difference between the generated decoded video data having said first resolution and said received video data having said first resolution to generate residual data, and compressing the residual data to generate video data of an enhancement layer.       

     Preferably, the compression of the residual data employs a method embodying the aforesaid first aspect of the present invention. 
     According to yet another aspect, the invention provides a method of decoding video data comprising:
         decoding video data of a base layer to generate decoded base layer video data having a second resolution, lower than a first resolution, and upsampling the decoded base layer video data to generate upsampled video data having the first resolution;   decompressing video data of an enhancement layer to generate residual data having the first resolution; and   forming a sum of the upsampled video data and the residual data to generate enhanced video data.       

     Preferably, the decompression of the residual data employs a method embodying the aforesaid second aspect of the present invention. 
     In one embodiment the encoding of the second resolution video data to obtain video data of a base layer having said second resolution and the decoding of the base layer video data are in conformity with HEVC. 
     In one embodiment, the first resolution is UHD and the second resolution is HD. As already noted, it is proposed that the compression of the residual data does not involve temporal prediction and/or that the compression of the residual data also does not involve spatial prediction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other particularities and advantages of the invention will also emerge from the following description, illustrated by the accompanying drawings, in which: 
         FIG. 1  schematically shows an encoder for a scalable codec; 
         FIG. 2  schematically shows the corresponding decoder; 
         FIG. 3  schematically illustrates the enhancement video encoding module of the encoder of  FIG. 1 ; 
         FIG. 4  schematically illustrates the enhancement video decoding module of the encoder of  FIG. 2 ; 
         FIG. 5  illustrates an example of a quantizer based on Voronoi cells; 
         FIG. 6  shows the correspondence between data in the spatial domain (pixels) and data in the frequency domain; 
         FIG. 7  illustrates an exemplary distribution over two quanta; 
         FIG. 8  shows exemplary rate-distortion curves, each curve corresponding to a specific number of quanta; 
         FIG. 9  shows the rate-distortion curve obtained by taking the upper envelope of the curves of  FIG. 8 ; 
         FIG. 10  depicts several rate-distortion curves obtained for various possible parameters of the DCT coefficient distribution; 
         FIG. 11  shows an exemplary embodiment of an encoding process according to the teachings of the invention at the block level; 
         FIG. 12  shows an exemplary embodiment of an encoding process according to the teachings of the invention at the frame level; 
         FIG. 13  shows an exemplary embodiment of an encoding process according to the teachings of the invention at the level of a video sequence; 
         FIG. 14  shows an alternative embodiment for an encoding process at the level of a video sequence; and 
         FIG. 15  shows a particular hardware configuration of a device able to implement methods according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION 
     For the detailed description below, focus is made on the encoding of a UHD video as introduced above with reference to  FIGS. 1 to 4 . It is however to be recalled that the invention applies to the encoding of any image from which a probabilistic distribution of transformed block coefficients can be obtained (e.g. statistically). In particular, it applies to the encoding of an image without temporal prediction and possibly without spatial prediction. 
     Referring again to  FIG. 3 , a low resolution version of the initial image has been encoded into an encoded low resolution image, referred above as the base layer; and a residual enhancement image has been obtained by subtracting an interpolated decoded version of the encoded low resolution image from said initial image. 
     The encoding of the residual enhancement image is now described, first with reference to  FIG. 11  focusing on steps performed at the block level. 
     Conventionally, that residual enhancement image is to be transformed, using for example a DCT transform, to obtain an image of transformed block coefficients. In the Figure, that image is referenced X DCT , which comprises a plurality of DCT blocks, each comprising DCT coefficients. 
     As an example, the residual enhancement image has been divided into blocks B k , each having a particular block type. Several block types may be considered, owing in particular to various possible sizes for the block. Other parameters than the size may be used to distinguish between block types. 
     In particular, as there may be a big disparity of activity (or energy) between blocks with the same size, a segmentation of a frame by using only block size is not fine enough to obtain an optimal performance of classification of parts of the frame. This is why it is proposed to add a label to the block size in order to distinguish various levels and/or characteristics of a block activity. 
     It is proposed for instance to use only square blocks, here blocks of dimensions 32×32, 16×16 and 8×8, and the following block types for luminance residual frames, each block type being defined by a size and a label (corresponding to an index of energy for instance, but possibly also to other parameters as explained below):
         32×32 label 1;   32×32 label 2;   etc.   32×32 label N 32 ;   16×16 label 1 (e.g. bottom);   16×16 label 2 (e.g. low);   etc.;   16×16 label N is ;   8×8 label 1 (e.g. low);   8×8 label 2;   etc.;   8×8 label N 8  (e.g. high).       

     There are thus N 32  block types of size 32×32, N 16  block types of size 16×16 and N 8  block types of size 8×8. The choice of the parameters N 32 , N 16 , N 8  depends on the residual frame content and, as a general rule, high quality coding requires more block types than low quality coding. 
     The choice of the block size is performed here by computing the integral L 2  of a morphological gradient I (measuring residual activity, e.g. residual morphological activity) on each 32×32 block, before applying the DCT transform. (Such a morphological gradient corresponds to the difference between a dilatation and an erosion of the luminance residual frame, as explained for instance in “ Image Analysis and Mathematical Morphology” , Vol. 1, by Jean Serra, Academic Press, Feb. 11, 1984.) If the integral computed for a block is higher than a predetermined threshold, the concerned block is divided into four smaller, here 16×16-, blocks; this process is applied on each obtained 16×16 block to decide whether or not it is divided into 8×8 blocks (top-down algorithm). 
     Once the block size of a given block is decided, the block type of this block is determined (step S 2 ) based on the morphological integral I computed for this block, for instance here by comparing the morphological integral with thresholds defining three bands of residual activity (i.e. three indices of energy) for each possible size (as exemplified above, bottom, low or normal residual activity for 16×16-blocks and low, normal, high residual activity for 8×8-blocks). 
     It may be noted that the morphological gradient is used in the present example to measure the residual activity but that other measures of the residual activity may be used, instead or in combination, such as local energy or Laplace&#39;s operator. 
     In a possible embodiment, the decision to attribute a given label to a particular block (once its size is determined as above) may be based not only on the magnitude of the integral I, but also on the ratio of vertical activity vs. horizontal activity, e.g. thanks to the ratio I h /I v , where I h  is the L 2  integral of the horizontal morphological gradient and I v  is the L 2  integral of the vertical morphological gradient. 
     For instance, the concerned block will be attributed a label (i.e. a block type) depending on whether the ratio I h /I v  is below 0.5 (corresponding to a block with residual activity oriented in the vertical direction), between 0.5 and 2 (corresponding to a block with non-oriented residual activity) and above 2 (corresponding to a block with residual activity oriented in the horizontal direction). 
     It is proposed here that chrominance blocks each have a block type inferred from the block type of the corresponding luminance block in the frame. For instance chrominance block types can be inferred by dividing in each direction the size of luminance block types by a factor depending on the resolution ratio between the luminance and the chrominance. 
     In the present case where use is made of 4:2:0 videos, where chrominance (U and V) frames are down-sampled by a factor two both vertically and horizontally, compared to the corresponding luminance frame. The blocks in chrominance frames have a size (among 16×16, 8×8 and 4×4) and a label both inferred from the size and label of the corresponding block in the luminance frame. 
     In addition, it is proposed here to define the block type in function of its size and an index of the energy, also possibly considering orientation of the residual activity. Other characteristics can also be considered such as for example the encoding mode used for the collocated block of the base layer, referred below as to the “base coding mode”. Typically, Intra blocks of the base layer do not behave the same way as Inter blocks, and blocks with a coded residual in the base layer do not behave the same way as blocks without such a residual (i.e. Skipped blocks). 
     A DCT transform is then applied to each of the concerned blocks (step S 4 ) in order to obtain a corresponding block of DCT coefficients. 
     Within a block, the DCT coefficients are associated with an index i (e.g. i=1 to 64), following an ordering used for successive handling when encoding, for example. 
     Blocks are grouped into macroblocks MB k . A very common case for so-called 4:2:0 YUV video streams is a macroblock made of 4 blocks of luminance Y, 1 block of chrominance U and 1 block of chrominance V. Here too, other configurations may be considered. 
     To simplify the explanations, only the coding of the luminance component is described here with reference to  FIG. 11 . However, the same approach can be used for coding the chrominance components. In addition, it will be further explained with reference to  FIG. 13  how to process luminance and chrominance in relation with each other. 
     Starting from the image X DCT , a probabilistic distribution P of each DCT coefficient is determined using a parametric probabilistic model at step S 6 . This is referenced  190  in  FIG. 3 . 
     Since, in the present example, the image X DCT  is a residual image, i.e. information is about a noise residual, it is efficiently modelled by Generalized Gaussian Distributions (GGD) having a zero mean: DCT (X)≈GGD(α/β), 
     where α,β are two parameters to be determined and the GGD follows the following two-parameter distribution: 
     
       
         
           
             
               
                 GGD 
                  
                 
                   ( 
                   
                     α 
                     , 
                     β 
                     , 
                     x 
                   
                   ) 
                 
               
               := 
               
                 
                   β 
                   
                     2 
                      
                     α 
                      
                     
                         
                     
                      
                     
                       Γ 
                        
                       
                         ( 
                         
                           1 
                           / 
                           β 
                         
                         ) 
                       
                     
                   
                 
                  
                 
                   exp 
                    
                   
                     ( 
                     
                       - 
                       
                         
                            
                           
                             x 
                             / 
                             α 
                           
                            
                         
                         β 
                       
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
     and where Γ is the well-known Gamma function: Γ(z)=∫ 0   ∞ t z-1 e −1 dt 
     The DCT coefficients cannot be all modelled by the same parameters and, practically, the two parameters α, β depend on:
         the video content. This means that the parameters must be computed for each image or for every group of n images for instance;   the index i of the DCT coefficient within a DCT block B k . Indeed, each DCT coefficient has its own behaviour. A DCT channel is thus defined for the DCT coefficients collocated (i.e. having the same index) within a plurality of DCT blocks (possibly all the blocks of the image). A DCT channel can therefore be identified by the corresponding coefficient index i. For illustrative purposes, if the residual enhancement image X DCT  is divided into 8×8 pixel blocks, the modelling  190  has to determine the parameters of 64 DCT channels for each base coding mode.   the block type defined above. The content of the image, and then the statistics of the DCT coefficients, may be strongly related to the block type because, as explained above, the block type is selected in function of the image content, for instance to use large blocks for parts of the image containing little information.       

     In addition, since the luminance component Y and the chrominance components U and V have dramatically different source contents, they must be encoded in different DCT channels. For example, if it is decided to encode the luminance component Y on one channel and to encode jointly the chrominance components UV on another channel, 64 channels are needed for the luminance of a block type of size 8×8 and 16 channels are needed for the joint UV chrominance (made of 4×4 blocks) in a case of a 4:2:0 video where the chrominance is down-sampled by a factor two in each direction compared to the luminance. Alternatively, one may choose to encode U and V separately and 64 channels are needed for Y, 16 for U and 16 for V. 
     At least 64 pairs of parameters for each block type may appear as a substantial amount of data to transmit to the decoder (see parameter bit-stream  21 ). However, experience proves that this is quite negligible compared to the volume of data needed to encode the residuals of Ultra High Definition (4 k2 k or more) videos. As a consequence, one may understand that such a technique is preferably implemented on large videos, rather than on very small videos because the parametric data would take too much volume in the encoded bitstream. 
     For sake of simplicity of explanation, a set of DCT blocks corresponding to the same block type are now considered. The invention may then be applied to each set corresponding to each block type. 
     To obtain the two parameters α i , β i  defining the probabilistic distribution P i  for a DCT channel i, the Generalized Gaussian Distribution model is fitted onto the DCT block coefficients of the DCT channel, i.e. the DCT coefficients collocated within the DCT blocks of the same block type. Since this fitting is based on the values of the DCT coefficients, the probabilistic distribution is a statistical distribution of the DCT coefficients within a considered channel i. 
     For example, the fitting may be simply and robustly obtained using the moment of order k of the absolute value of a GGD: 
     
       
         
           
             
               
                 
                   
                     M 
                     k 
                     
                       
                         α 
                         i 
                       
                       , 
                       
                         β 
                         i 
                       
                     
                   
                   := 
                     
                    
                   
                     
                       E 
                        
                       
                         ( 
                         
                           
                              
                             
                               GGD 
                                
                               
                                 ( 
                                 
                                   
                                     α 
                                     i 
                                   
                                   , 
                                   
                                     β 
                                     i 
                                   
                                 
                                 ) 
                               
                             
                              
                           
                           k 
                         
                         ) 
                       
                     
                     
                       ( 
                       
                         k 
                         ∈ 
                         
                           R 
                           + 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       ∫ 
                       
                         - 
                         ∞ 
                       
                       ∞ 
                     
                      
                     
                       
                         
                            
                           x 
                            
                         
                         k 
                       
                        
                       
                         GGD 
                          
                         
                           ( 
                           
                             
                               α 
                               i 
                             
                             , 
                             
                               β 
                               i 
                             
                             , 
                             x 
                           
                           ) 
                         
                       
                        
                       
                           
                       
                        
                       
                          
                         x 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         
                           α 
                           i 
                           k 
                         
                          
                         
                           Γ 
                            
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                               / 
                               
                                 β 
                                 i 
                               
                             
                             ) 
                           
                         
                       
                       
                         Γ 
                          
                         
                           ( 
                           
                             1 
                             / 
                             
                               β 
                               i 
                             
                           
                           ) 
                         
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     Determining the moments of order 1 and of order 2 from the DCT coefficients of channel i makes it possible to directly obtain the value of parameter β i : 
     
       
         
           
             
               
                 M 
                 2 
               
               
                 
                   ( 
                   
                     M 
                     1 
                   
                   ) 
                 
                 2 
               
             
             = 
             
               
                 
                   Γ 
                    
                   
                     ( 
                     
                       1 
                       / 
                       
                         β 
                         i 
                       
                     
                     ) 
                   
                 
                  
                 
                   Γ 
                    
                   
                     ( 
                     
                       3 
                       / 
                       
                         β 
                         i 
                       
                     
                     ) 
                   
                 
               
               
                 
                   Γ 
                    
                   
                     ( 
                     
                       2 
                       / 
                       
                         β 
                         i 
                       
                     
                     ) 
                   
                 
                 2 
               
             
           
         
       
     
     The value of the parameter β i  can thus be estimated by computing the above ratio of the two first and second moments, and then the inverse of the above function of β i . 
     Practically, this inverse function may be tabulated in memory of the encoder instead of computing Gamma functions in real time, which is costly. 
     The second parameter a, may then be determined from the first parameter β i  and the second moment, using the equation: M 2 =σ 2 =α i   2 Γ(3/β i )/Γ(1/β i ). 
     The two parameters α i , β i  being determined for the DCT coefficients i, the probabilistic distribution P i  of each DCT coefficient i is defined by 
     
       
         
           
             
               
                 P 
                 i 
               
                
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 GGD 
                  
                 
                   ( 
                   
                     
                       α 
                       i 
                     
                     , 
                     
                       β 
                       i 
                     
                     , 
                     x 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     β 
                     i 
                   
                   
                     2 
                      
                     
                       α 
                       i 
                     
                      
                     
                       Γ 
                        
                       
                         ( 
                         
                           1 
                           / 
                           
                             β 
                             i 
                           
                         
                         ) 
                       
                     
                   
                 
                  
                 
                   
                     exp 
                      
                     
                       ( 
                       
                         - 
                         
                           
                              
                             
                               x 
                               / 
                               
                                 α 
                                 i 
                               
                             
                              
                           
                           
                             β 
                             i 
                           
                         
                       
                       ) 
                     
                   
                   . 
                 
               
             
           
         
       
     
     Referring to  FIG. 3 , a quantization  193  of the DCT coefficients is to be performed in order to obtain quantized symbols or values. As explained below, it is proposed here to first determine a quantizer per DCT channel so as to optimize a rate-distortion criterion. 
       FIG. 5  illustrates an exemplary Voronoi cell based quantizer. 
     A quantizer is made of M Voronoi cells distributed along the values of the DCT coefficients. Each cell corresponds to an interval [t m ,t m+1 ], called quantum Q m . 
     Each cell has a centroid c m , as shown in the Figure. 
     The intervals are used for quantization: a DCT coefficient comprised in the interval [t m ,t m+1 ] is quantized to a symbol a m  associated with that interval. 
     For their part, the centroids are used for de-quantization: a symbol a m  associated with an interval is de-quantized into the centroid value c m  of that interval. 
     The quality of a video or still image may be measured by the so-called Peak-Signal-to-Noise-Ratio or PSNR, which is dependent upon a measure of the L2-norm of the error of encoding in the pixel domain, i.e. the sum over the pixels of the squared difference between the original pixel value and the decoded pixel value. It may be recalled in this respect that the PSNR may be expressed in dB as: 
     
       
         
           
             
               10. 
                
               
                 
                   log 
                   10 
                 
                 ( 
                 
                   
                     MAX 
                     2 
                   
                   MSE 
                 
                 ) 
               
             
             , 
           
         
       
     
     where MAX is the maximal pixel value (in the spatial domain) and MSE is the mean squared error (i.e. the above sum divided by the number of pixels concerned). 
     However, as noted above, most of video codecs compress the data in the DCT-transformed domain in which the energy of the signal is much better compacted. 
     The direct link between the PSNR and the error on DCT coefficients is now explained. 
     For a residual block, we note ψ n  its inverse DCT (or IDCT) pixel base in the pixel domain as shown on  FIG. 6 . If one uses the so-called IDCT III for the inverse transform, this base is orthonormal: ∥ψ n ∥=1. 
     On the other hand, in the DCT domain, the unity coefficient values form a base σ n  which is orthogonal. One writes the DCT transform of the pixel block X as follows: 
     
       
         
           
             
               
                 X 
                 DCT 
               
               = 
               
                 
                   ∑ 
                   n 
                 
                  
                 
                     
                 
                  
                 
                   
                     d 
                     n 
                   
                    
                   
                     ϕ 
                     n 
                   
                 
               
             
             , 
           
         
       
     
     where d n  is the value of the n-th DCT coefficient. A simple base change leads to the expression of the pixel block as a function of the DCT coefficient values: 
     
       
         
           
             X 
             = 
             
               
                 IDCT 
                  
                 
                   ( 
                   
                     X 
                     DCT 
                   
                   ) 
                 
               
               = 
               
                 
                   IDCT 
                    
                   
                     
                       ∑ 
                       n 
                     
                      
                     
                         
                     
                      
                     
                       
                         d 
                         n 
                       
                        
                       
                         ϕ 
                         n 
                       
                     
                   
                 
                 = 
                 
                   
                     
                       ∑ 
                       n 
                     
                      
                     
                         
                     
                      
                     
                       
                         d 
                         n 
                       
                        
                       
                         IDCT 
                          
                         
                           ( 
                           
                             ϕ 
                             n 
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       ∑ 
                       n 
                     
                      
                     
                         
                     
                      
                     
                       
                         d 
                         n 
                       
                        
                       
                         
                           ψ 
                           n 
                         
                         . 
                       
                     
                   
                 
               
             
           
         
       
     
     If the value of the de-quantized coefficient d n  after decoding is denoted d Q   n , one sees that (by linearity) the pixel error block is given by: 
     
       
         
           
             
               ɛ 
               X 
             
             = 
             
               
                 ∑ 
                 n 
               
                
               
                   
               
                
               
                 
                   ( 
                   
                     
                       d 
                       n 
                     
                     - 
                     
                       d 
                       Q 
                       n 
                     
                   
                   ) 
                 
                  
                 
                   ψ 
                   n 
                 
               
             
           
         
       
     
     The mean L 2 -norm error on all blocks, is thus: 
     
       
         
           
             
               E 
                
               
                 ( 
                 
                   
                      
                     
                       ɛ 
                       X 
                     
                      
                   
                   2 
                   2 
                 
                 ) 
               
             
             = 
             
               
                 E 
                 ( 
                 
                   
                     ∑ 
                     n 
                   
                    
                   
                       
                   
                    
                   
                     
                        
                       
                         
                           d 
                           n 
                         
                         - 
                         
                           d 
                           Q 
                           n 
                         
                       
                        
                     
                     2 
                   
                 
                 ) 
               
               = 
               
                 
                   
                     ∑ 
                     n 
                   
                    
                   
                       
                   
                    
                   
                     E 
                      
                     
                       ( 
                       
                         
                            
                           
                             
                               d 
                               n 
                             
                             - 
                             
                               d 
                               Q 
                               n 
                             
                           
                            
                         
                         2 
                       
                       ) 
                     
                   
                 
                 = 
                 
                   
                     ∑ 
                     n 
                   
                    
                   
                       
                   
                    
                   
                     D 
                     n 
                     2 
                   
                 
               
             
           
         
       
     
     where D n   2  is the mean quadratic error of quantization on the n-th DCT coefficient, or squared distortion for this type of coefficient. The distortion is thus a measure of the distance between the original coefficient (here the coefficient before quantization) and the decoded coefficient (here the dequantized coefficient). 
     It is thus proposed below to control the video quality by controlling the sum of the quadratic errors on the DCT coefficients. In particular, this control is preferable compared to the individual control of each of the DCT coefficient, which is a priori a sub-optimal control. 
     In the embodiment described here, it is proposed to determine (i.e. to select in step  191  of  FIG. 3 ) a set of quantizers (to be used each for a corresponding DCT channel), the use of which results in a mean quadratic error having a target value D t   2  while minimizing the rate obtained. This corresponds to step S 16  in  FIG. 11 . 
     In view of the above correspondence between PSNR and the mean quadratic error D n   2  on DCT coefficients, these constraints can be written as follows: 
     
       
         
           
             
               
                 
                   
                     minimize 
                      
                     
                         
                     
                      
                     R 
                   
                   = 
                   
                     
                       
                         ∑ 
                         n 
                       
                        
                       
                           
                       
                        
                       
                         
                           
                             R 
                             n 
                           
                            
                           
                             ( 
                             
                               D 
                               n 
                             
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                           s 
                           . 
                           t 
                           . 
                           
                               
                           
                            
                           
                             
                               ∑ 
                               n 
                             
                              
                             
                                 
                             
                              
                             
                               D 
                               n 
                               2 
                             
                           
                         
                       
                     
                     = 
                     
                       D 
                       t 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   A 
                   ) 
                 
               
             
           
         
       
     
     where R is the total rate made of the sum of individual rates R n  each DCT coefficient. In case the quantization is made independently for each DCT coefficient, the rate R n  only on the distortion D n  of the associated n-th DCT coefficient. 
     It may be noted that the above minimization problem (A) may only be fulfilled by optimal quantizers which are solution of the problem 
       minimize  R   n ( D   n ) s.t.E (|d n   −d   Q   n | 2 )= D   n   2   (B).
 
     This statement is simply proven by the fact that, assuming a first quantizer would not be optimal following (B) but would fulfil (A), then a second quantizer with less rate but the same distortion can be constructed (or obtained). So, if one uses this second quantizer, the total rate R has been diminished without changing the total distortion Σ n D n   2 ; this is in contradiction with the first quantifier being a minimal solution of the problem (A). 
     As a consequence, the rate-distortion minimization problem (A) can be split into two consecutive sub-problems without losing the optimality of the solution:
         first, determining optimal quantizers and their associated rate-distortion curves R n (D n ) following the problem (B), which will be done in the present case for GGD channels as explained below;   second, by using optimal quantizers, the problem (A) is changed into the problem (A_opt):       

     
       
         
           
             
               minimize 
                
               
                   
               
                
               R 
             
             = 
             
               
                 
                   ∑ 
                   n 
                 
                  
                 
                     
                 
                  
                 
                   
                     
                       R 
                       n 
                     
                      
                     
                       ( 
                       
                         D 
                         n 
                       
                       ) 
                     
                   
                    
                   
                       
                   
                    
                   
                     s 
                     . 
                     t 
                     . 
                     
                         
                     
                      
                     
                       
                         ∑ 
                         n 
                       
                        
                       
                           
                       
                        
                       
                         D 
                         n 
                         2 
                       
                     
                   
                 
               
               = 
               
                 
                   D 
                   t 
                   2 
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 
                   
                     R 
                     n 
                   
                    
                   
                     ( 
                     
                       D 
                       n 
                     
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 is 
                  
                 
                     
                 
                  
                 optimal 
                  
                 
                     
                 
                  
                 
                   
                     ( 
                     A_opt 
                     ) 
                   
                   . 
                 
               
             
           
         
       
     
     Based on this analysis, it is proposed as further explained below:
         to compute off-line (step S 8  in  FIG. 11 ) optimal quantizers adapted to possible probabilistic distributions of each DCT channel (thus resulting in the pool of quantizers of  FIG. 3 );   to select (step S 16 ) one of these pre-computed optimal quantizers for each DCT channel (i.e. each type of DCT coefficient) such that using the set of selected quantizers results in a global distortion corresponding to the target distortion D t   2  with a minimal rate (i.e. a set of quantizers which solves the problem A_opt).       

     It is now described a possible embodiment for the first step S 8  of computing optimal quantizers for possible probabilistic distributions, here Generalised Gaussian Distributions. 
     It is proposed to change the previous complex formulation of problem (B) into the so-called Lagrange formulation of the problem: for a given parameter λ&gt;0, we determine the quantization in order to minimize a cost function such as D 2 +λR. We thus get an optimal rate-distortion couple (D λ ,R λ ). In case of a rate control (i.e. rate minimization) for a given target distortion Δ, the optimal parameter λ&gt;0 is determined by 
     
       
         
           
             
               λ 
               
                 Δ 
                 t 
               
             
             = 
             
               
                 
                   arg 
                    
                   
                       
                   
                    
                   min 
                 
                 
                   λ 
                   , 
                   
                     
                       D 
                       λ 
                     
                     ≤ 
                     
                       Δ 
                       t 
                     
                   
                 
               
                
               
                   
               
                
               
                 R 
                 λ 
               
             
           
         
       
     
     (i.e. the value of λ for which the rate is minimum while fulfilling the constraint on distortion) and the associated minimum rate is 
     
       
         
           
             
               R 
               
                 Δ 
                 t 
               
             
             = 
             
               
                 R 
                 
                   λ 
                   
                     Δ 
                     t 
                   
                 
               
               . 
             
           
         
       
     
     As a consequence, by solving the problem in its Lagrange formulation, for instance following the method proposed below, it is possible to plot a rate distortion curve associating a resulting minimum rate to each distortion value (Δ t   R Δ     t   ) which may be computed off-line as well as the associated quantization, i.e. quantizer, making it possible to obtain this rate-distortion pair. 
     It is precisely proposed here to formulate problem (B) into a continuum of problems (B_lambda) having the following Lagrange formulation 
       minimize  D   n   2   +λR   n ( D   n ) s.t.E (| x−d   m ∥ 2 )= D   n   2   (B_lambda).
 
     The well-known Chou-Lookabaugh-Gray algorithm is a good practical way to perform the required minimization. It may be used with any distortion distance d; we describe here a simplified version of the algorithm for the L 2 -distance. This is an iterative process from any given starting guessed quantization. 
     As noted above, this algorithm is performed here for each of a plurality of possible probabilistic distributions (in order to obtain the pre-computed optimal quantizers for the possible distributions to be encountered in practice), and for a plurality of possible numbers M of quanta. It is described below when applied for a given probabilistic distribution P and a given number M of quanta. 
     In this respect, as the parameter alpha α (or equivalently the standard deviation σ of the Generalized Gaussian Definition) can be moved out of the distortion parameter D n   2  because it is a homothetic parameter, only optimal quantizers with unity standard deviation σ=1 need to be determined in the pool of quantizers. 
     Taking advantage of this remark, in the proposed embodiment, the GGD representing a given DCT channel will be normalized before quantization (i.e. homothetically transformed into a unity standard deviation GGD), and will be de-normalized after de-quantization. Of course, this is possible because the parameters (in particular here the parameter α or equivalently the standard deviation σ) of the concerned GGD model are sent to the decoder in the video bit-stream. 
     Before describing the algorithm itself, the following should be noted. 
     The position of the centroids c m  is such that they minimize the distortion δ m   2  inside a quantum, in particular one must verify that ∂ c     m   δ m   2 =0 (as the derivative is zero at a minimum). 
     As the distortion δ m  of the quantization, on the quantum Q m , is the mean error E(d(x;c m )) for a given distortion function or distance d, the distortion on one quantum when using the L 2 -distance is given by δ m   2 =∫ Q     m   ∥x−c m | 2 P(x)dx and the nullification of the derivative thus gives: c m =∫ Q     m   xP(x)dx/P m , where P m  is the probability of x to be in the quantum Q m  and is simply the following integral P m =∫ Q     m   P(x)dx. 
     Turning now to minimization of the cost function C=D 2 +λR, and considering that the rate reaches the entropy of the quantized data: 
     
       
         
           
             
               R 
               = 
               
                 - 
                 
                   
                     ∑ 
                     
                       m 
                       = 
                       1 
                     
                     M 
                   
                    
                   
                       
                   
                    
                   
                     
                       P 
                       m 
                     
                      
                     
                       log 
                       2 
                     
                      
                     
                       P 
                       m 
                     
                   
                 
               
             
             , 
           
         
       
     
     the nullification of the derivatives of the cost function for an optimal solution can be written as: 
       0=∂ t     m−1     C=∂   t     m+1   [Δ m   2   −λP   m  ln  P   m +Δ m+1   2   −λP   m+1  ln  P   m+1 ]
 
     Let us set  P =P(t m+1 ) the value of the probability distribution at the point t m+1 . From simple variational considerations, see  FIG. 7 , we get 
       ∂ t     m+1     P   m   =  P  and ∂   t     m+1     P   m+1   =−  P .  
 
     Then, a bit of calculation leads to 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       
                         t 
                         
                           m 
                           + 
                           1 
                         
                       
                     
                      
                     
                       Δ 
                       m 
                       2 
                     
                   
                   = 
                   
                     
                       ∂ 
                       
                         t 
                         
                           m 
                           + 
                           1 
                         
                       
                     
                      
                     
                       
                         ∫ 
                         
                           t 
                           m 
                         
                         
                           t 
                           
                             m 
                             + 
                             1 
                           
                         
                       
                        
                       
                         
                           
                              
                             
                               x 
                               - 
                               
                                 c 
                                 m 
                               
                             
                              
                           
                           2 
                         
                          
                         
                           P 
                            
                           
                             ( 
                             x 
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           x 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         P 
                         _ 
                       
                        
                       
                         
                            
                           
                             
                               t 
                               
                                 m 
                                 + 
                                 1 
                               
                             
                             - 
                             
                               c 
                               m 
                             
                           
                            
                         
                         2 
                       
                     
                     + 
                     
                       
                         ∫ 
                         
                           t 
                           m 
                         
                         
                           t 
                           
                             m 
                             + 
                             1 
                           
                         
                       
                        
                       
                         
                           
                             ∂ 
                             
                               t 
                               
                                 m 
                                 + 
                                 1 
                               
                             
                           
                            
                           
                             
                                
                               
                                 x 
                                 - 
                                 
                                   c 
                                   m 
                                 
                               
                                
                             
                             2 
                           
                         
                          
                         
                           P 
                            
                           
                             ( 
                             x 
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           x 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         P 
                         _ 
                       
                        
                       
                         
                            
                           
                             
                               t 
                               
                                 m 
                                 + 
                                 1 
                               
                             
                             - 
                             
                               c 
                               m 
                             
                           
                            
                         
                         2 
                       
                     
                     - 
                     
                       2 
                        
                       
                         
                           ∂ 
                           
                             t 
                             
                               m 
                               + 
                               1 
                             
                           
                         
                          
                         
                           c 
                           m 
                         
                       
                        
                       
                         
                           ∫ 
                           
                             t 
                             m 
                           
                           
                             t 
                             
                               m 
                               + 
                               1 
                             
                           
                         
                          
                         
                           
                             ( 
                             
                               x 
                               - 
                               
                                 c 
                                 m 
                               
                             
                             ) 
                           
                            
                           
                             P 
                              
                             
                               ( 
                               x 
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           
                              
                             x 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       P 
                       _ 
                     
                      
                     
                       
                          
                         
                           
                             t 
                             
                               m 
                               + 
                               1 
                             
                           
                           - 
                           
                             c 
                             m 
                           
                         
                          
                       
                       2 
                     
                   
                 
               
             
           
         
       
     
     as well as 
       ∂ t     m+1   Δ m+1   2   =−P|t   m+1   −c   m+1 | 2 .
 
     As the derivative of the cost is now explicitly calculated, its cancellation gives: 
     
       
         
           
             
               0 
               = 
               
                 
                   
                     P 
                     _ 
                   
                    
                   
                     
                        
                       
                         
                           t 
                           
                             m 
                             + 
                             1 
                           
                         
                         - 
                         
                           d 
                           m 
                         
                       
                        
                     
                     2 
                   
                 
                 - 
                 
                   λ 
                    
                   
                     P 
                     _ 
                   
                    
                   
                       
                   
                    
                   ln 
                    
                   
                       
                   
                    
                   
                     P 
                     m 
                   
                 
                 - 
                 
                   λ 
                    
                   
                       
                   
                    
                   
                     P 
                     m 
                   
                    
                   
                     
                       P 
                       _ 
                     
                     
                       P 
                       m 
                     
                   
                 
                 - 
                 
                   
                     P 
                     _ 
                   
                    
                   
                     
                        
                       
                         
                           t 
                           
                             m 
                             + 
                             1 
                           
                         
                         - 
                         
                           d 
                           
                             m 
                             + 
                             1 
                           
                         
                       
                        
                     
                     2 
                   
                 
                 + 
                 
                   λ 
                    
                   
                     P 
                     _ 
                   
                    
                   
                       
                   
                    
                   ln 
                    
                   
                       
                   
                    
                   
                     P 
                     
                       m 
                       + 
                       1 
                     
                   
                 
                 + 
                 
                   λ 
                    
                   
                       
                   
                    
                   
                     P 
                     m 
                   
                    
                   
                     
                       P 
                       _ 
                     
                     
                       P 
                       m 
                     
                   
                 
               
             
             , 
           
         
       
     
     which leads to a useful relation between the quantum boundaries t m ,t m+1  and the centroids 
     
       
         
           
             
               
                 c 
                 m 
               
                
               
                 : 
               
                
               
                   
               
                
               
                 t 
                 
                   m 
                   + 
                   1 
                 
               
             
             = 
             
               
                 
                   
                     c 
                     m 
                   
                   + 
                   
                     c 
                     
                       m 
                       + 
                       1 
                     
                   
                 
                 2 
               
               - 
               
                 λ 
                  
                 
                   
                     
                       
                         ln 
                          
                         
                             
                         
                          
                         
                           P 
                           
                             m 
                             + 
                             1 
                           
                         
                       
                       - 
                       
                         ln 
                          
                         
                             
                         
                          
                         
                           P 
                           m 
                         
                       
                     
                     
                       2 
                        
                       
                         ( 
                         
                           
                             c 
                             
                               m 
                               + 
                               1 
                             
                           
                           - 
                           
                             c 
                             m 
                           
                         
                         ) 
                       
                     
                   
                   . 
                 
               
             
           
         
       
     
     Thanks to these formulae, the Chou-Lookabaugh-Gray algorithm can be implemented by the following iterative process: 
     1. Start with arbitrary quanta Q m  defined by a plurality of limits t m    
     2. Compute the probabilities P m  by the formula P m =∫ Q     m   P(x)dx 
     3. Compute the centroids c m  by the formula c m =∫ Q     m   xP(x)dx/P m    
     4. Compute the limits t m  of new quanta by the formula 
     
       
         
           
             
               t 
               
                 m 
                 + 
                 1 
               
             
             = 
             
               
                 
                   
                     c 
                     m 
                   
                   + 
                   
                     c 
                     
                       m 
                       + 
                       1 
                     
                   
                 
                 2 
               
               - 
               
                 λ 
                  
                 
                   
                     
                       ln 
                        
                       
                           
                       
                        
                       
                         P 
                         
                           m 
                           + 
                           1 
                         
                       
                     
                     - 
                     
                       ln 
                        
                       
                           
                       
                        
                       
                         P 
                         m 
                       
                     
                   
                   
                     2 
                      
                     
                       ( 
                       
                         
                           c 
                           
                             m 
                             + 
                             1 
                           
                         
                         - 
                         
                           c 
                           m 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     5. Compute the cost C=D 2 +λR by the formula 
     
       
         
           
             C 
             = 
             
               
                 
                   ∑ 
                   
                     m 
                     = 
                     1 
                   
                   M 
                 
                  
                 
                     
                 
                  
                 
                   Δ 
                   m 
                   2 
                 
               
               - 
               
                 λ 
                  
                 
                     
                 
                  
                 
                   P 
                   m 
                 
                  
                 ln 
                  
                 
                     
                 
                  
                 
                   P 
                   m 
                 
               
             
           
         
       
     
     6. Loop to 2. until convergence of the cost C 
     When the cost C has converged, the current values of limits t m  and centroids c m  define a quantization, i.e. a quantizer, with M quanta, which solves the problem (B_lambda), i.e. minimizes the cost function for a given value λ, and has an associated rate value R λ  and an distortion value D λ . 
     Such a process is implemented for many values of the Lagrange parameter λ (for instance 100 values comprised between 0 and 50). It may be noted that for λ equal to 0, there is no rate constraint, which corresponds to the so-called Lloyd quantizer. 
     In order to obtain optimal quantizers for a given parameter β of the corresponding GGD, the problems (B_lambda) are to be solved for various odd (by symmetry) values of the number M of quanta and for the many values of the parameter λ. A rate-distortion diagram for the optimal quantizers with varying M is thus obtained, as shown on  FIG. 8 . 
     It turns out that, for a given distortion, there is an optimal number M of needed quanta for the quantization associated to an optimal parameter λ. In brief, one may say that optimal quantizers of the general problem (B) are those associated to a point of the upper envelope of the rate-distortion curves making this diagram, each point being associated with a number of quanta (i.e. the number of quanta of the quantizer leading to this point of the rate-distortion curve). This upper envelope is illustrated on  FIG. 9 . At this stage, we have now lost the dependency on λ of the optimal quantizers: for a given rate (or a given distortion) corresponds only one optimal quantizer whose number of quanta M is fixed. 
     Based on observations that the GGD modelling provides a value of β almost always between 0.5 and 2 in practice, and that only a few discrete values are enough for the precision of encoding, it is proposed here to tabulate β every 0.1 in the interval between 0.2 and 2.5. Considering these values of β (i.e. here for each of the 24 values of β taken in consideration between 0.2 and 2.5), rate-distortion curves, depending on β, are obtained (step S 10 ) as shown on  FIG. 10 . It is of course possible to obtain according to the same process rate-distortion curves for a larger number of possible values of β. 
     Each curve may in practice be stored in the encoder in a table containing, for a plurality of points on the curve, the rate and distortion (coordinates) of the point concerned, as well as features defining the associated quantizer (here the number of quanta and the values of limits t m  and centroids c m  for the various quanta). For instance, a few hundreds of quantizers may be stored for each β up to a maximum rate, e.g. of 5 bits per DCT coefficient, thus forming the pool of quantizers mentioned in  FIG. 3 . It may be noted that a maximum rate of 5 bits per coefficient in the enhancement layer makes it possible to obtain good quality in the decoded image. Generally speaking, it is proposed to use a maximum rate per DCT coefficient equal or less than 10 bits, for which value near lossless coding is provided. 
     Before turning to the selection of quantizers (step S 16 ), for the various DCT channels and among these optimal quantizers stored in association with their corresponding rate and distortion when applied to the concerned distribution (GGD with a specific parameter β), it is proposed here to select which part of the DCT channels are to be encoded. 
     Based on the observation that the rate decreases monotonously as a function of the distortion induced by the quantizer, precisely in each case in the manner shown by the curves just mentioned, it is possible to write the relationship between rate and distortion as follows: R n =f n (−ln(D n /σ n )), 
     where σ n  is the normalization factor of the DCT coefficient, i.e. the GGD model associated to the DCT coefficient has σ n  for standard deviation, and where f n ′≧0 in view of the monotonicity just mentioned. 
     In particular, without encoding (equivalently zero rate) leads to a quadratic distortion of value σ n   2  and we deduce that 0=f n (0). 
     Finally, one observes that the curves are convex for parameters β lower than two: β≦2 f n ″≧0. 
     It is proposed here to consider the merit of encoding a DCT coefficient. 
     More encoding basically results in more rate R n  (in other words, the corresponding cost) and less distortion D n   2  (in other words the resulting gain or advantage). 
     Thus, when dedicating a further bit to the encoding of the video (rate increase), it should be determined on which DCT coefficient this extra rate is the most efficient. In view of the analysis above, an estimation of the merit M of encoding may be obtained by computing the ratio of the benefit on distortion to the cost of encoding: 
     
       
         
           
             
               M 
               n 
             
             := 
             
               
                  
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       D 
                       n 
                       2 
                     
                   
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       R 
                       n 
                     
                   
                 
                  
               
               . 
             
           
         
       
     
     Considering the distortion decreases by an amount ε, then a first order development of distortion and rates gives 
     
       
         
           
             
               
                 ( 
                 
                   D 
                   - 
                   ɛ 
                 
                 ) 
               
               2 
             
             = 
             
               
                 D 
                 2 
               
               - 
               
                 2 
                  
                 ɛ 
                  
                 
                     
                 
                  
                 D 
               
               + 
               
                 o 
                  
                 
                   ( 
                   ɛ 
                   ) 
                 
               
             
           
         
       
       
         
           and 
         
       
       
         
           
             
               
                 
                   
                     R 
                      
                     
                       ( 
                       
                         D 
                         - 
                         ɛ 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       f 
                       n 
                     
                      
                     
                       ( 
                       
                         - 
                         
                           ln 
                            
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   D 
                                   - 
                                   ɛ 
                                 
                                 ) 
                               
                               / 
                               σ 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       f 
                       n 
                     
                      
                     
                       ( 
                       
                         
                           - 
                           
                             ln 
                              
                             
                               ( 
                               
                                 D 
                                 / 
                                 σ 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           ln 
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 ɛ 
                                 / 
                                 D 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       f 
                       n 
                     
                      
                     
                       ( 
                       
                         
                           - 
                           
                             ln 
                              
                             
                               ( 
                               
                                 D 
                                 / 
                                 σ 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           ɛ 
                           / 
                           D 
                         
                         + 
                         
                           o 
                            
                           
                             ( 
                             ɛ 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         f 
                         n 
                       
                        
                       
                         ( 
                         
                           - 
                           
                             ln 
                              
                             
                               ( 
                               
                                 D 
                                 / 
                                 σ 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ɛ 
                        
                       
                           
                       
                        
                       
                         
                           
                             f 
                             ′ 
                           
                            
                           
                             ( 
                             
                               - 
                               
                                 ln 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     / 
                                     σ 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                         / 
                         
                           D 
                           . 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     As a consequence, the ratio of the first order variations provides an explicit formula for the merit of encoding: 
     
       
         
           
             
               
                 M 
                 n 
               
                
               
                 ( 
                 
                   D 
                   n 
                 
                 ) 
               
             
             = 
             
               
                 
                   2 
                    
                   
                     D 
                     n 
                     2 
                   
                 
                 
                   
                     f 
                     n 
                     ′ 
                   
                    
                   
                     ( 
                     
                       - 
                       
                         ln 
                          
                         
                           ( 
                           
                             
                               D 
                               n 
                             
                             / 
                             
                               σ 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
     If the initial merit M n   0  is defined as the merit of encoding at zero rate, i.e. before any encoding, this initial merit M n   0  can thus be expressed as follows using the preceding formula: 
     
       
         
           
             
               M 
               n 
               0 
             
             := 
             
               
                 
                   M 
                   n 
                 
                  
                 
                   ( 
                   
                     σ 
                     n 
                   
                   ) 
                 
               
               = 
               
                 
                   2 
                    
                   
                     σ 
                     n 
                     2 
                   
                 
                 
                   
                     f 
                     n 
                     ′ 
                   
                    
                   
                     ( 
                     0 
                     ) 
                   
                 
               
             
           
         
       
     
     (because as noted above no encoding leads to a quadratic distortion of value σ n   2 ). 
     It is thus possible, starting from the pre-computed and stored rate-distortion curves, to determine the function f n  associated with a given DCT channel and to compute the initial merit M n   0  of encoding the corresponding DCT coefficient (the value f n ′(0) being determined by approximation thanks to the stored coordinates of rate-distortion curves). 
     It may further be noted that, for β lower than two (which is in practice almost always true), the convexity of the rate distortion curves teaches us that the merit is an increasing function of the distortion. 
     In particular, the initial merit is thus an upper bound of the merit: M n (D n )≦M n   0 . 
     It will now be shown that, when satisfying the optimisation criteria defined above, all encoded DCT coefficients in the block have the same merit after encoding. Furthermore, this does not only apply to one block only, but as long as the various functions f n  used in each DCT channel are the unchanged, i.e. in particular for all blocks in a given block type. Hence the common merit value for encoded DCT coefficients will now be referred to as the merit of the block type. 
     The above property of equal merit after encoding may be shown for instance using the Karush-Kuhn-Tucker (KKT) necessary conditions of optimality. In this goal, the quality constraint 
     
       
         
           
             
               
                 ∑ 
                 n 
               
                
               
                   
               
                
               
                 D 
                 n 
                 2 
               
             
             = 
             
               D 
               t 
               2 
             
           
         
       
     
     can De rewritten as h=0 with 
     
       
         
           
             
               h 
               ( 
               
                 
                   D 
                   1 
                 
                 , 
                 
                   D 
                   2 
                 
                 , 
                 … 
               
                
               
                   
               
               ) 
             
             := 
             
               
                 
                   ∑ 
                   n 
                 
                  
                 
                     
                 
                  
                 
                   D 
                   n 
                   2 
                 
               
               - 
               
                 
                   D 
                   t 
                   2 
                 
                 . 
               
             
           
         
       
     
     The distortion of each DCT coefficient is upper bounded by the distortion without coding: D n ≦σ n , and the domain of definition of the problem is thus a multi-dimensional box Q={(D 1 , D 2 , . . . ); D n ≦σ n }={(D 1 , D 2 , . . . ); g n ≦0}, defined by the functions g n (D n ):=D n −σ n . 
     Thus, the problem can be restated as follows: 
       minimize  R ( D   1   , D   2 , . . . ) s.t.h= 0 ,g   n ≦0  (A_opt′).
 
     Such an optimization problem under inequality constrains can effectively be solved using so-called Karush-Kuhn-Tucker (KKT) necessary conditions of optimality. 
     In this goal, the relevant KKT function Λ is defined as follows: 
     
       
         
           
             
               Λ 
               ( 
               
                 
                   D 
                   1 
                 
                 , 
                 
                   D 
                   2 
                 
                 , 
                 … 
                  
                 
                     
                 
                 , 
                 λ 
                 , 
                 
                   μ 
                   1 
                 
                 , 
                 
                   μ 
                   2 
                 
                 , 
                 … 
               
                
               
                   
               
               ) 
             
             := 
             
               R 
               - 
               
                 λ 
                  
                 
                     
                 
                  
                 h 
               
               - 
               
                 
                   ∑ 
                   n 
                 
                  
                 
                     
                 
                  
                 
                   
                     μ 
                     n 
                   
                    
                   
                     
                       g 
                       n 
                     
                     . 
                   
                 
               
             
           
         
       
     
     The KKT necessary conditions of minimization are
         stationarity: dΛ=0,   equality: h=0,   inequality: g n ≦0,   dual feasibility: μ n ≦0,   saturation: μ n g n =0.       

     It may be noted that the parameter λ in the KKT function above is unrelated to the parameter λ used above in the Lagrange formulation of the optimization problem meant to determine optimal quantizers. 
     If g n =0, the n-th condition is said to be saturated. In the present case, it indicates that the n-th DCT coefficient is not encoded. 
     By using the specific formulation R n =f n (−ln(D n /σ n )) of the rate depending on the distortion discussed above, the stationarity condition gives: 
       0=∂ D     n   Λ=∂ D     n     R   n −λ∂ D     n     h−μ   n ∂ D     n     g   n   =−f   n   ′/D   n −2 λD   n −μ n ,
 
       i.e. 2 λD   n   2 =−μ n   D   n   −f   n ′.
 
     By summing on n and taking benefit of the equality condition, this leads to 
     
       
         
           
             
               2 
                
               λ 
                
               
                   
               
                
               
                 D 
                 t 
                 2 
               
             
             = 
             
               
                 - 
                 
                   
                     ∑ 
                     n 
                   
                    
                   
                       
                   
                    
                   
                     
                       μ 
                       n 
                     
                      
                     
                       D 
                       n 
                     
                   
                 
               
               - 
               
                 
                   ∑ 
                   n 
                 
                  
                 
                     
                 
                  
                 
                   
                     f 
                     n 
                     ′ 
                   
                   . 
                   
                     
                       ( 
                       * 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     In order to take into account the possible encoding of part of the coefficients only as proposed above, the various possible indices n are distributed into two subsets:
         the set I 0 ={n;μ n =0} of non-saturated DCT coefficients (i.e. of encoded DCT coefficients) for which we have μ n D n =0 and D n   2 =f n ′/2λ, and   the set I + ={n;μ n &gt;0} of saturated DCT coefficients (i.e. of DCT coefficients not encoded) for which we have μ n D n =−f n ′−2λσ n   2 .       

     From (*), we deduce 
     
       
         
           
             
               2 
                
               λ 
                
               
                   
               
                
               
                 D 
                 t 
                 2 
               
             
             = 
             
               
                 
                   - 
                   
                     
                       ∑ 
                       
                         I 
                         + 
                       
                     
                      
                     
                         
                     
                      
                     
                       
                         μ 
                         n 
                       
                        
                       
                         D 
                         n 
                       
                     
                   
                 
                 - 
                 
                   
                     ∑ 
                     n 
                   
                    
                   
                       
                   
                    
                   
                     f 
                     n 
                     ′ 
                   
                 
               
               = 
               
                 
                   
                     ∑ 
                     
                       I 
                       + 
                     
                   
                    
                   
                     f 
                     n 
                     ′ 
                   
                 
                 + 
                 
                   2 
                    
                   λ 
                    
                   
                     
                       ∑ 
                       
                         I 
                         + 
                       
                     
                      
                     
                         
                     
                      
                     
                       σ 
                       n 
                       2 
                     
                   
                 
                 - 
                 
                   
                     ∑ 
                     n 
                   
                    
                   
                       
                   
                    
                   
                     f 
                     n 
                     ′ 
                   
                 
               
             
           
         
       
     
     and by gathering the λ&#39;s 
     
       
         
           
             
               2 
                
               
                 λ 
                 ( 
                 
                   
                     D 
                     t 
                     2 
                   
                   - 
                   
                     
                       ∑ 
                       
                         I 
                         + 
                       
                     
                      
                     
                         
                     
                      
                     
                       σ 
                       n 
                       2 
                     
                   
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   I 
                   0 
                 
               
                
               
                   
               
                
               
                 
                   f 
                   n 
                   ′ 
                 
                 . 
               
             
           
         
       
     
     As a consequence, for a non-saturated coefficient (nεI 0 ), i.e. a coefficient to be encoded, we obtain: 
     
       
         
           
             
               D 
               n 
               2 
             
             = 
             
               
                 ( 
                 
                   
                     D 
                     t 
                     2 
                   
                   - 
                   
                     
                       ∑ 
                       
                         I 
                         + 
                       
                     
                      
                     
                         
                     
                      
                     
                       σ 
                       n 
                       2 
                     
                   
                 
                 ) 
               
                
               
                 
                   
                     f 
                     n 
                     ′ 
                   
                    
                   
                     ( 
                     
                       - 
                       
                         ln 
                          
                         
                           ( 
                           
                             
                               D 
                               n 
                             
                             / 
                             
                               σ 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     ) 
                   
                 
                 / 
                 
                   
                     ∑ 
                     
                       m 
                       ∈ 
                       
                         I 
                         0 
                       
                     
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         f 
                         m 
                         ′ 
                       
                        
                       
                         ( 
                         
                           - 
                           
                             ln 
                              
                             
                               ( 
                               
                                 
                                   D 
                                   m 
                                 
                                 / 
                                 
                                   σ 
                                   m 
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     This formula for the distortion makes it possible to rewrite the above formula giving the merit M n (D n ) as follows for non-saturated coefficients: 
     
       
         
           
             
               
                 M 
                 n 
               
                
               
                 ( 
                 
                   D 
                   n 
                 
                 ) 
               
             
             = 
             
               2. 
                
               
                 
                   ( 
                   
                     
                       D 
                       t 
                       2 
                     
                     - 
                     
                       
                         ∑ 
                         
                           I 
                           + 
                         
                       
                        
                       
                           
                       
                        
                       
                         σ 
                         n 
                         2 
                       
                     
                   
                   ) 
                 
                 / 
                 
                   
                     ∑ 
                     
                       m 
                       ∈ 
                       
                         I 
                         0 
                       
                     
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         f 
                         m 
                         ′ 
                       
                        
                       
                         ( 
                         
                           - 
                           
                             ln 
                              
                             
                               ( 
                               
                                 
                                   D 
                                   m 
                                 
                                 / 
                                 
                                   σ 
                                   m 
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     Clearly, the right side of the equality does not depend on the DCT channel n concerned. Thus, for a block type k, for any DCT channel n for which coefficients are encoded, the merit associated with said channel after encoding is the same: M n =m k . 
     Another proof of the property of common merit after encoding is the following: supposing that there are two encoded DCT coefficients with two different merits M1&lt;M2, if an infinitesimal amount of rate from coefficient 1 is put on coefficient 2 (which is possible because coefficient 1 is one of the encoded coefficients and this does not change the total rate), the distortion gain on coefficient 2 would then be strictly bigger than the distortion loss on coefficient 1 (because M1&lt;M2). This would thus provide a better distortion with the same rate, which is in contradiction with the optimality of the initial condition with two different merits. 
     As a conclusion, if the two coefficients 1 and 2 are encoded and if their respective merits M1 and M2 are such that M1&lt;M2, then the solution is not optimal. 
     Furthermore, all non-coded coefficients have a merit smaller than the merit of the block type (i.e. the merit of coded coefficients after encoding). 
     In view of the property of equal merits of encoded coefficients when optimisation is satisfied, it is proposed here to encode only coefficients for which the initial encoding merit 
     
       
         
           
             
               M 
               n 
               0 
             
             = 
             
               
                 2 
                  
                 
                   σ 
                   n 
                   2 
                 
               
               
                 
                   f 
                   n 
                   ′ 
                 
                  
                 
                   ( 
                   0 
                   ) 
                 
               
             
           
         
       
     
     is greater than a predetermined target block merit m k . 
     For each coefficient to be encoded, the quantization to be performed is selected to obtain the target block merit as the merit of the coefficient after encoding: first, the corresponding distortion, which is thus such that 
     
       
         
           
             
               
                 
                   M 
                   n 
                 
                  
                 
                   ( 
                   
                     D 
                     n 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     2 
                      
                     
                       D 
                       n 
                       2 
                     
                   
                   
                     
                       f 
                       n 
                       ′ 
                     
                      
                     
                       ( 
                       
                         - 
                         
                           ln 
                            
                           
                             ( 
                             
                               
                                 D 
                                 n 
                               
                               / 
                               
                                 σ 
                                 n 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
                 = 
                 
                   m 
                   k 
                 
               
             
             , 
           
         
       
     
     can be found by dichotomy using stored rate-distortion curves (step S 14 ); the quantizer associated (see steps S 8  and S 10  above) with the distortion found is then selected (step S 16 ). 
     Then, quantization is performed at step S 18  by the chosen (or selected) quantizers to obtain the quantized data X DCT,Q  representing the DCT image. Practically, these data are symbols corresponding to the index of the quantum (or interval or Voronoi cell in 1D) in which the value of the concerned coefficient of X DCT  falls in. 
     The entropy coding of step S 20  may be performed by any known coding technique like VLC coding or arithmetic coding. Context adaptive coding (CAVLC or CABAC) may also be used. 
     The encoded data can then be transmitted together with parameters allowing in particular the decoder to use the same quantizers as those selected and used for encoding as described above. 
     According to a first possible embodiment, the transmitted parameters may include the parameters defining the distribution for each DCT channel, i.e. the parameter α (or equivalently the standard deviation σ) and the parameter β computed at the encoder side for each DCT channel, as shown in step S 22 . 
     Based on these parameters received in the data stream, the decoder may deduce the quantizers to be used (a quantizer for each DCT channel) thanks to the selection process explained above at the encoder side (the only difference being that the parameters β for instance are computed from the original data at the encoder side whereas they are received at the decoder side). 
     Dequantization (step  332  of  FIG. 4 ) can thus be performed with the selected quantizers (which are the same as those used at encoding because they are selected the same way). 
     According to a second possible embodiment, the transmitted parameters may include a flag per DCT channel indicating whether the coefficients of the concerned DCT channel are encoded or not, and, for encoded channels, the parameters β and the standard deviation σ (or equivalently the parameter α). This helps minimizing the amount of information to be sent because channel parameters are sent only for encoded channels. According to a possible variation, in addition to flags indicating whether the coefficients of a given DCT channel are encoded or not, information can be transmitted that designates, for each encoded DCT channel, the quantizer used at encoding. In this case, there is thus no need to perform a quantizer selection process at the decoder side. 
     Dequantization (step  332  of  FIG. 4 ) can thus be performed at the decoder by use of the identified quantizers for DCT channels having a received flag indicating the DCT channel was encoded. 
       FIG. 12  shows the encoding process implemented in the present example at the level of the frame, which includes in particular determining the target block merit for the various block types. 
     First, the frame is segmented at step S 30  into a plurality of blocks each having a given block type k, for instance in accordance with the process described above based on residual activity. 
     A parameter k designating the block type currently considered is then initialised at step S 32 . 
     The target block merit m k  for the block type k currently considered is the computed at step S 34  based on a predetermined frame merit m F  and on a number of blocks v k  of the given block type per area unit, here according to the formula: 
         m   k   =v   k   ·m   F . 
     For instance, one may choose the area unit as being the area of a 16×16 block, i.e. 256 pixels. In this case, v k =1 for block types of size 16×16, v k =4 for block types of size 8×8 etc. One also understands that the method is not limited to square blocks; for instance v k =2 for block types of size 16×8. 
     This type of computation makes it possible to obtain a balanced encoding between block types, i.e. here a common merit of encoding per pixel (equal to the frame merit m F ) for all block types. 
     This is because the variation of the pixel distortion Δδ P,k   2  for the block type k is the sum 
     
       
         
           
             
               ∑ 
               codedn 
             
              
             
                 
             
              
             
               Δ 
                
               
                   
               
                
               
                 D 
                 
                   n 
                   , 
                   k 
                 
                 2 
               
             
           
         
       
     
     of the distortion variations provided by the various encoded DCT coefficients, and can thus be rewritten as follows thanks to the (common) block merit: 
     
       
         
           
             
               Δδ 
               
                 P 
                 , 
                 k 
               
               2 
             
             = 
             
               
                 
                   m 
                   k 
                 
                 . 
                 
                   
                     ∑ 
                     codedn 
                   
                    
                   
                       
                   
                    
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       R 
                       
                         n 
                         , 
                         k 
                       
                     
                   
                 
               
               = 
               
                 
                   
                     m 
                     k 
                   
                   . 
                   Δ 
                 
                  
                 
                     
                 
                  
                 
                   R 
                   k 
                 
               
             
           
         
       
     
     (where ΔR k  is the rate variation for a block of type k). Thus, the merit of encoding per pixel is: 
     
       
         
           
             
               
                 Δδ 
                 
                   P 
                   , 
                   k 
                 
                 2 
               
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   U 
                   k 
                 
               
             
             = 
             
               
                 
                   
                     
                       m 
                       k 
                     
                     . 
                     Δ 
                   
                    
                   
                       
                   
                    
                   
                     R 
                     k 
                   
                 
                 
                   
                     
                       v 
                       k 
                     
                     . 
                     Δ 
                   
                    
                   
                       
                   
                    
                   
                     R 
                     k 
                   
                 
               
               = 
               
                 m 
                 F 
               
             
           
         
       
     
     (where U k  is the rate per area unit for the block type concerned) and has a common value over the various block types. 
     Blocks having the block type k currently considered are then each encoded by the process described above with reference to  FIG. 11  using the block merit m k  just determined as the target block merit in step S 14  of  FIG. 11 . 
     The next block type is then considered by incrementing k (step S 38 ), checking whether all block types have been considered (step S 40 ) and looping to step S 34  if all block types have not been considered. 
     If all block types have been considered, the whole frame has been processed (step S 42 ), which ends the encoding process at the frame level presented here. 
       FIG. 13  shows the encoding process implemented according to a first embodiment at the level of the video sequence, which includes in particular determining the frame merit for luminance frames Y as well as for chrominance frames U,V of the video sequence. 
     The process shown in  FIG. 13  applies to a specific frame and is to be applied to each frame of the video sequence concerned. However, it may be provided as a possible variation that quantizers are determined based on one frame and used for that frame and a predetermined number of the following frames. 
     The frame is first segmented into blocks each having a block type at step S 50 , in a similar manner as was explained above for step S 30 . As mentioned above, the segmentation is determined based on the residual activity of the luminance frame Y and is also applied to the chrominance frames U,V. 
     A DCT transform is then applied (step S 52 ) to each block thus defined. The DCT transform is adapted to the type of the block concerned, in particular to its size. 
     Parameters representative of the statistical distribution of coefficients (here α i , β i  as explained above) are then computed (step S 54 ) both for luminance frames and for chrominance frames, in each case for each block type, each time for the various coefficient types. 
     A loop is then entered (at step S 58  described below) to determine by dichotomy a luminance frame merit m Y  and a chrominance frame merit m UV  linked by the following relationship: 
     
       
         
           
             
               
                 
                   1 
                   
                     
                       μ 
                       VIDEO 
                     
                     . 
                     
                       D 
                       Y 
                       2 
                     
                   
                 
                 - 
                 
                   2 
                   
                     m 
                     UV 
                   
                 
               
               = 
               
                 1 
                 
                   m 
                   Y 
                 
               
             
             , 
           
         
       
     
     where μ VIDEO  is a selectable video merit obtained for instance based on user selection of a quality level at step S 56  and D Y   2  is the frame distortion for the luminance frame after encoding and decoding. 
     Each of the determined luminance frame merit m Y  and chrominance frame merit m UV  may then be used as the frame merit m F  in a process similar to the process described above with reference to  FIG. 12 , as further explained below. 
     The relationship given above makes it possible to adjust (to the value) μ VIDEO  the local video merit defined as the ratio between the variation of the PSNR (already defined above) of the luminance ΔPSNR Y  and the corresponding variation of the total rate ΔR YUV  (including not only luminance but also chrominance frames). This ratio is generally considered when measuring the efficiency of a coding method. 
     This relationship is also based on the following choices made in the present embodiment: 
     the quality of luminance frames is the same as the quality of chrominance frames: 
         D   Y   2   =D   UV   2 =( D   U   2   +D   V   2 )/2; 
     the merit of U chrominance frames is the same as the merit of V chrominance frames: m U =m V =m UV . 
     As explained above, the merit m F  of encoding per pixel is the same whatever the block in a frame and the relationship between distortion and rate thus remains valid at the frame level (by summing over the frame the distortions of the one hand and the rates on the other hand, each corresponding distortion and rate defining a constant ratio m F ): ΔD Y   2 =m Y ·ΔR Y , ΔD U   2 =m UV ·ΔR U  and ΔD V   2 =m UV ·ΔR V , where ΔR Y , Δ U  and ΔR V  are the rate variations respectively for the luminance frame, the U chrominance frame and the V chrominance frame. 
     Thus, 
     
       
         
           
             
               Δ 
                
               
                   
               
                
               
                 R 
                 YUV 
               
             
             = 
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       D 
                       Y 
                       2 
                     
                   
                   
                     m 
                     Y 
                   
                 
                 + 
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       D 
                       U 
                       2 
                     
                   
                   
                     m 
                     UV 
                   
                 
                 + 
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       D 
                       V 
                       2 
                     
                   
                   
                     m 
                     UV 
                   
                 
               
               = 
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   
                     D 
                     Y 
                     2 
                   
                   . 
                   
                     ( 
                     
                       
                         1 
                         
                           m 
                           Y 
                         
                       
                       + 
                       
                         2 
                         
                           m 
                           UV 
                         
                       
                     
                     ) 
                   
                   . 
                 
               
             
           
         
       
     
     As the PSNR is the logarithm of the distortion D Y   2 , its variation ΔPSNR Y  can be written as follows at the first order: 
     
       
         
           
             
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   PSNR 
                   Y 
                 
               
               = 
               
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     D 
                     Y 
                     2 
                   
                 
                 
                   D 
                   Y 
                   2 
                 
               
             
             , 
           
         
       
     
     and the video merit can thus be restated as follows based on the above assumptions and remarks: 
     
       
         
           
             
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   PSNR 
                   Y 
                 
               
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   R 
                   YUV 
                 
               
             
             = 
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       PSNR 
                       Y 
                     
                   
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       R 
                       Y 
                     
                   
                 
                  
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       R 
                       Y 
                     
                   
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       R 
                       YUV 
                     
                   
                 
               
               = 
               
                 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         
                           D 
                           Y 
                           2 
                         
                         . 
                         
                           m 
                           Y 
                         
                       
                     
                     
                       
                         
                           D 
                           Y 
                           2 
                         
                         . 
                         Δ 
                       
                        
                       
                           
                       
                        
                       
                         D 
                         Y 
                         2 
                       
                     
                   
                    
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         D 
                         Y 
                         2 
                       
                     
                     
                       
                         
                           m 
                           Y 
                         
                         . 
                         Δ 
                       
                        
                       
                           
                       
                        
                       
                         
                           D 
                           Y 
                           2 
                         
                          
                         
                           ( 
                           
                             
                               1 
                               
                                 m 
                                 Y 
                               
                             
                             + 
                             
                               2 
                               
                                 m 
                                 UV 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 = 
                 
                   
                     1 
                     
                       
                         D 
                         Y 
                         2 
                       
                       . 
                       
                         ( 
                         
                           
                             1 
                             
                               m 
                               Y 
                             
                           
                           + 
                           
                             2 
                             
                               m 
                               UV 
                             
                           
                         
                         ) 
                       
                     
                   
                   . 
                 
               
             
           
         
       
     
     This ratio is equal to the chosen value μ VIDEO  when the above relationship 
     
       
         
           
             ( 
             
               
                 
                   1 
                   
                     
                       μ 
                       VIDEO 
                     
                     . 
                     
                       D 
                       Y 
                       2 
                     
                   
                 
                 - 
                 
                   2 
                   
                     m 
                     UV 
                   
                 
               
               = 
               
                 1 
                 
                   m 
                   Y 
                 
               
             
             ) 
           
         
       
     
     is satisfied. 
     Going back to the loop process implemented to determine the luminance frame merit m Y  and the chrominance frame merit m UV  as mentioned above, a lower bound m L   Y  and an upper bound m U   Y  for the luminance frame merit are initialized at step S 58  at predetermined values. The lower bound m L   Y  and the upper bound m U   Y  define an interval, which includes the luminance frame merit and which will be reduced in size (divided by two) at each step of the dichotomy process. At initialization step S 58 , the lower bound m L   Y  may be chosen as strictly positive but small, corresponding to a nearly lossless encoding, while the upper bound m U   Y  is chosen for instance greater than all initial encoding merits (over all DCT channels and all block types). 
     A temporary luminance frame merit m Y  is computed (step S 60 ) as equal to 
     
       
         
           
             
               
                 m 
                 L 
                 Y 
               
               + 
               
                 m 
                 U 
                 Y 
               
             
             2 
           
         
       
     
     (i.e. in the middle of the interval). 
     A block merit is then computed at step S 62  for each of the various block types, as explained above with reference to  FIG. 12  (see in particular step S 34 ) according to the formula: m k =v k ·m Y . Block merits are computed based on the temporary luminance frame merit defined above. The next steps are thus based on this temporary value which is thus a tentative value for the luminance frame merit. 
     For each block type k in the luminance frame, the distortions D n,k,Y   2  after encoding of the various DCT channels n are then determined at step S 64  in accordance with what was described with reference to  FIG. 11 , in particular step S 14 , based on the block merit m k  just computed and on optimal rate-distortion curves determined beforehand at step S 67 , in the same manner as in step S 10  of  FIG. 11 . 
     The frame distortion for the luminance frame D Y   2  can then be determined at step S 66  by summing over the block types thanks to the formula: 
     
       
         
           
             
               
                 D 
                 Y 
                 2 
               
               = 
               
                 
                   
                     ∑ 
                     k 
                   
                    
                   
                       
                   
                    
                   
                     
                       ρ 
                       k 
                     
                     . 
                     
                       δ 
                       
                         P 
                         , 
                         k 
                         , 
                         Y 
                       
                       2 
                     
                   
                 
                 = 
                 
                   
                     ∑ 
                     k 
                   
                    
                   
                       
                   
                    
                   
                     
                       ρ 
                       k 
                     
                     . 
                     
                       ( 
                       
                         
                           ∑ 
                           n 
                         
                          
                         
                             
                         
                          
                         
                           D 
                           
                             n 
                             , 
                             k 
                             , 
                             Y 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             , 
           
         
       
     
     where ρ k  is the density of a block type in the frame, i.e. the ratio between the total area for blocks having the concerned block type k and the total area of the frame. 
     It is then sought, for instance by dichotomy at step S 68  and also based on optimal rate-distortion curves predetermined at step S 67 , a temporary chrominance frame merit m UV  such that the distortions after encoding D n,k,U   2 , D n,k,V   2 , implementing a process according to  FIG. 12  using m UV  as the frame merit, result in chrominance frame distortions D U   2 , D V   2  satisfying D Y   2 =(D U   2 +D V   2 )/2. 
     It may be noted in this respect that the relationship between distortions of the DCT channels and the frame distortion, given above for the luminance frame, is also valid for each of the chrominance frames U,V. 
     It is then checked at step S 70  whether the interval defined by the lower bound m L   Y  and the upper bound m U   Y  have reached a predetermined required accuracy α, i.e. whether m U   Y −m L   Y &lt;α. 
     If this is not the case, the dichotomy process will be continued by selecting one of the first half of the interval and the second half of the interval as the new interval to be considered, depending on the sign of 
     
       
         
           
             
               
                 1 
                 
                   m 
                   Y 
                 
               
               - 
               
                 1 
                 
                   
                     μ 
                     VIDEO 
                   
                   . 
                   
                     D 
                     Y 
                     2 
                   
                 
               
               + 
               
                 2 
                 
                   m 
                   UV 
                 
               
             
             , 
           
         
       
     
     which will thus converge towards zero such that the relationship defined above is satisfied. The lower bound m L   Y  and the upper bound m U   Y  are adapted consistently with the selected interval (step S 72 ) and the process loops at step S 60 . 
     If the required accuracy is reached, the process continues at step S 74  where quantizers are selected in a pool of quantizers predetermined at step S 65  and associated with points of the optimal rate-distortion curves already used (see explanations relating to step S 8  in  FIG. 11 ), based on the distortions values D n,k,Y   2 , D n,k,U   2 , D n,k,V   2  obtained during the last iteration of the dichotomy process (steps S 64  and S 68  described above). 
     The coefficients of the blocks of the frames (which coefficients where computed at step S 52 ) are then quantized at step S 76  using the selected quantizers. 
     The quantized coefficients are then entropy encoded at step S 78 . 
     A bit stream to be transmitted is then computed based on encoded coefficients (step S 82 ). The bit stream also includes parameters α i , β i  representative of the statistical distribution of coefficients computed at step S 54 , as well as frame merits m Y , m UV  determined at step S 60  and S 68  during the last iteration of the dichotomy process. 
     Transmitting the frame merits makes it possible to select the quantizers for dequantization at the decoder according to a process similar to  FIG. 12  (with respect to the selection of quantizers), without the need to perform the dichotomy process. 
     It may be noted that the process just mentioned can be adapted to the case where luminance frames are considered (i.e. without any colour component) by simply removing the terms relating to colour components, such as setting the term m UV  to infinity (practically, the term 
     
       
         
           
             2 
             
               m 
               UV 
             
           
         
       
     
     is removed in step S 72 ), and not performing step S 68 . Such a process thus makes it possible to obtain the frame merit m Y , and the corresponding block merits m k , based on a predetermined (e.g. user selected) video merit μ VIDEO . 
       FIG. 14  shows an encoding process according to a second possible embodiment, which includes in particular determining the frame merit for luminance component Y as well as for each of chrominance components U,V for each frame of the video sequence. 
     It is proposed in the present embodiment to consider the following video quality function: 
         Q ( R   Y   ,R   U   ,R   V )= PSNR   Y +θ U   ·PSNR   U +θ V   ·PSNR   V ,
 
     where R* is the rate for the component * of a frame, PSNR* is the PSNR for the component * of a frame, and θ U , θ V  are balancing parameters provided by the user in order to select the acceptable degree of distortion in the concerned chrominance component (U or V) relative to the degree of distortion in the luminance component. 
     In order to unify the explanations in the various components, use is made below of θ Y =1 and the video quality function considered here can thus be rewritten as: 
         Q ( R   Y   ,R   U   ,R   V )=θ Y   ·PSNR   Y +θ U   ·PSNR   U +θ V   ·PSNR   V .
 
     As already noted, the PSNR is the logarithm of the frame distortion: PSNR*=ln(D* 2 ) (D* 2  being the frame distortion for the frame of the component *) and it can thus be written at the first order that 
     
       
         
           
             
               Δ 
                
               
                   
               
                
               
                 PSNR 
                 * 
               
             
             = 
             
               
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     D 
                     * 
                     2 
                   
                 
                 
                   D 
                   * 
                   2 
                 
               
               . 
             
           
         
       
     
     As the merit m F  of encoding per pixel is the same whatever the block in a frame, the relationship between distortion and rate thus remains valid at the frame level (by summing over the frame the distortions of the one hand and the rates on the other hand, each corresponding distortion and rate defining a constant ratio m F ) and it can be written that: ΔD* 2 =m*·ΔR*. 
     The variation of the video quality Q defined above depending on the attribution of the rate R* to a given component * can thus be estimated to: 
     
       
         
           
             
               
                 ∂ 
                 Q 
               
               
                 ∂ 
                 
                   R 
                   * 
                 
               
             
             = 
             
               
                 
                   
                     θ 
                     * 
                   
                   . 
                   
                     m 
                     * 
                   
                 
                 
                   D 
                   * 
                   2 
                 
               
               . 
             
           
         
       
     
     It is proposed in the process below to encode the residual data such that no component is favoured compared to another one (taking into account the video quality function Q), i.e. such that 
     
       
         
           
             
               
                 ∂ 
                 Q 
               
               
                 ∂ 
                 
                   R 
                   Y 
                 
               
             
             = 
             
               
                 
                   ∂ 
                   Q 
                 
                 
                   ∂ 
                   
                     R 
                     U 
                   
                 
               
               = 
               
                 
                   
                     ∂ 
                     Q 
                   
                   
                     ∂ 
                     
                       R 
                       V 
                     
                   
                 
                 . 
               
             
           
         
       
     
     As described below, the encoding process will thus be designed to obtain a value μ VIDEO  (target merit) for this common merit, which value defines the video merit and is selectable by the user. In view of the above formulation for 
     
       
         
           
             
               
                 ∂ 
                 Q 
               
               
                 ∂ 
                 
                   R 
                   * 
                 
               
             
             , 
           
         
       
     
     the process below is thus designed such that: 
     
       
         
           
             
               
                 μ 
                 VIDEO 
               
               = 
               
                 
                   
                     
                       θ 
                       Y 
                     
                     . 
                     
                       m 
                       Y 
                     
                   
                   
                     D 
                     Y 
                     2 
                   
                 
                 = 
                 
                   
                     
                       
                         θ 
                         U 
                       
                       . 
                       
                         m 
                         U 
                       
                     
                     
                       D 
                       U 
                       2 
                     
                   
                   = 
                   
                     
                       
                         θ 
                         V 
                       
                       . 
                       
                         m 
                         V 
                       
                     
                     
                       D 
                       V 
                       2 
                     
                   
                 
               
             
             , 
           
         
       
     
     i.e. to obtain, for each of the three components, a frame merit m* such that the function e(m*)=μ VIDEO ·D* 2 (m*)−θ*·m* is null (the distortion at the frame level being here noted D* 2 (m*) in order to explicit the fact that it depends on the frame merit m*). 
     The process shown in  FIG. 14  applies to a particular component, denoted * below, of a specific frame and is to be applied to each of the three components Y, U, V of a frame to be encoded. 
     If the component * being processed is a luminance component, the concerned frame is first segmented into blocks each having a block type at step S 77 , in a similar manner as was explained above for step S 30 . This is because, as already mentioned, it is proposed here that the segmentation is determined based on the residual activity of the luminance frame Y and is also applied to the chrominance frames U,V. According to a possible variation, the segmentation could be determined independently for the various components. 
     A DCT transform is then applied (step S 79 ) to each block thus defined in the processed component of the concerned frame. 
     Parameters representative of the statistical distribution of coefficients (here α i , β i  as explained above) are then computed (step S 83 ) for each block type, each time for the various coefficient types. As noted above, this applies to a given component * only. 
     Before entering a loop implemented to determine the frame merit m*, a lower bound m L * and an upper bound m U * for the frame merit are initialized at step S 84  at predetermined values. The lower bound m L * and the upper bound m U * define an interval, which includes the sought frame merit and which will be reduced in size (divided by two) at each step of the dichotomy process. At initialization step S 84 , the lower bound m L * may be chosen as strictly positive but small, corresponding to a nearly lossless encoding, while the upper bound m U * is chosen for instance greater than all initial encoding merits (over all DCT channels and all block types). 
     A temporary luminance frame merit m* is computed (step S 86 ) as equal to 
     
       
         
           
             
               
                 m 
                 L 
                 * 
               
               + 
               
                 m 
                 U 
                 * 
               
             
             2 
           
         
       
     
     (i.e. in the middle of the interval). 
     A block merit is then computed at step S 88  for each of the various block types, as explained above with reference to  FIG. 12  (see in particular step S 34 ) according to the formula: m k =v k ·m*. Block merits are computed based on the temporary frame merit defined above. The next steps are thus based on this temporary value which is thus a tentative value for the frame merit for the concerned component *. 
     For each block type k in the frame, the distortions D n,k   2 * after encoding of the various DCT channels n are then determined at step S 88  in accordance with what was described with reference to  FIG. 11 , in particular step S 14 , based on the block merit m k  just computed and on optimal rate-distortion curves determined beforehand at step S 89 , in the same manner as in step S 10  of  FIG. 11 . 
     The frame distortion for the luminance frame D* 2  can then be determined at step S 92  by summing over the block types thanks to the formula: 
     
       
         
           
             
               
                 D 
                 * 
                 2 
               
               = 
               
                 
                   
                     ∑ 
                     k 
                   
                    
                   
                       
                   
                    
                   
                     
                       ρ 
                       k 
                     
                     . 
                     
                       δ 
                       
                         P 
                         , 
                         k 
                         , 
                         * 
                       
                       2 
                     
                   
                 
                 = 
                 
                   
                     ∑ 
                     k 
                   
                    
                   
                       
                   
                    
                   
                     
                       ρ 
                       k 
                     
                     . 
                     
                       ( 
                       
                         
                           ∑ 
                           n 
                         
                          
                         
                             
                         
                          
                         
                           D 
                           
                             n 
                             , 
                             k 
                             , 
                             * 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             , 
           
         
       
     
     where ρ k  is the density of a block type in the frame, i.e. the ratio between the total area for blocks having the concerned block type k and the total area of the frame. 
     It is then checked at step S 94  whether the interval defined by the lower bound m L * and the upper bound m U * have reached a predetermined required accuracy α, i.e. whether m U *−m L *&lt;α. 
     If this is not the case, the dichotomy process will be continued by selecting one of the first half of the interval and the second half of the interval as the new interval to be considered, depending on the sign of e(m*), i.e. here the sign of μ VIDEO ·D* 2 (m*)−θ*·m*, which will thus converge towards zero as required to fulfill the criterion defined above. It may be noted that the selected video merit μ VIDEO  (see selection step S 81 ) and, in the case of chrominance frames U, V, the selected balancing parameter θ* (i.e. θ U  or θ V ) are introduced at this stage in the process for determining the frame merit m*. 
     The lower bound m L * and the upper bound m U * are adapted consistently with the selected interval (step S 98 ) and the process loops at step S 86 . 
     If the required accuracy is reached, the process continues at step S 96  where quantizers are selected in a pool of quantizers predetermined at step S 87  and associated with points of the optimal rate-distortion curves already used (see explanations relating to step S 8  in  FIG. 11 ), based on the distortions values D n,k   2 * obtained during the last iteration of the dichotomy process (step S 90  described above). 
     The coefficients of the blocks of the frames (which coefficients where computed at step S 79 ) are then quantized at step S 100  using the selected quantizers. 
     The quantized coefficients are then entropy encoded at step S 102 . 
     A bit stream to be transmitted is then computed based on encoded coefficients (step S 104 ). The bit stream also includes parameters α i , β i  representative of the statistical distribution of coefficients, which parameters were computed at step S 83  The process just described for determining optimal quantizers uses a function e(m*) resulting in an encoded frame having a given video merit (denoted μ VIDEO  above), with the possible influence of balancing parameters θ*. 
     As a possible variation, it is possible to use a different function e(m*), which will result in the encoded frame fulfilling a different criterion. For instance, if it is sought to obtain a target distortion D t   2 , the function e(m*)=D* 2 (m*)−D t   2  could be used instead. 
     In a similar manner, if it is sought to control the rate of a frame (for a given component) to a target rate R t , the function e(m*)=R*(m*)−R t  could be used. In this case, step S 90  would include determining the rate for encoding each of the various channels (also considering each of the various blocks) using the rate-distortion curves (S 89 ) and step S 92  would include summing the determined rates to obtain the rate R* for the frame. 
     In addition, although the process of  FIG. 14  has been described in the context of a video sequence with three colour components, it also applies in the context of a video sequence with a single colour component, e.g. luminance, in which case no balancing parameter is used (θ*=1, which is by the way the case for the luminance component in the example just described where θ Y  was defined as equal to 1). 
     With reference now to  FIG. 15 , a particular hardware configuration of a device for encoding or decoding images able to implement methods according to the invention is now described by way of example. 
     A device implementing the invention is for example a microcomputer  50 , a workstation, a personal digital assistant, or a mobile telephone connected to various peripherals. According to yet another embodiment of the invention, the device is in the form of a photographic apparatus provided with a communication interface for allowing connection to a network. 
     The peripherals connected to the device comprise for example a digital camera  64 , or a scanner or any other image acquisition or storage means, connected to an input/output card (not shown) and supplying image data to the device. 
     The device  50  comprises a communication bus  51  to which there are connected:
         a central processing unit CPU  52  taking for example the form of a microprocessor;   a read only memory  53  in which may be contained the programs whose execution enables the methods according to the invention. It may be a flash memory or EEPROM;   a random access memory  54 , which, after powering up of the device  50 , contains the executable code of the programs of the invention necessary for the implementation of the invention. As this memory  54  is of random access type (RAM), it provides fast access compared to the read only memory  53 . This RAM memory  54  stores in particular the various images and the various blocks of pixels as the processing is carried out (transform, quantization, storage of the reference images) on the video sequences;   a screen  55  for displaying data, in particular video and/or serving as a graphical interface with the user, who may thus interact with the programs according to the invention, using a keyboard  56  or any other means such as a pointing device, for example a mouse  57  or an optical stylus;   a hard disk  58  or a storage memory, such as a memory of compact flash type, able to contain the programs of the invention as well as data used or produced on implementation of the invention;   an optional diskette drive  59 , or another reader for a removable data carrier, adapted to receive a diskette  63  and to read/write thereon data processed or to process in accordance with the invention; and   a communication interface  60  connected to the telecommunications network  61 , the interface  60  being adapted to transmit and receive data.       

     In the case of audio data, the device  50  is preferably equipped with an input/output card (not shown) which is connected to a microphone  62 . 
     The communication bus  51  permits communication and interoperability between the different elements included in the device  50  or connected to it. The representation of the bus  51  is non-limiting and, in particular, the central processing unit  52  unit may communicate instructions to any element of the device  50  directly or by means of another element of the device  50 . 
     The diskettes  63  can be replaced by any information carrier such as a compact disc (CD-ROM) rewritable or not, a ZIP disk or a memory card. Generally, an information storage means, which can be read by a micro-computer or microprocessor, integrated or not into the device for processing a video sequence, and which may possibly be removable, is adapted to store one or more programs whose execution permits the implementation of the method according to the invention. 
     The executable code enabling the coding device to implement the invention may equally well be stored in read only memory  53 , on the hard disk  58  or on a removable digital medium such as a diskette  63  as described earlier. According to a variant, the executable code of the programs is received by the intermediary of the telecommunications network  61 , via the interface  60 , to be stored in one of the storage means of the device  50  (such as the hard disk  58 ) before being executed. 
     The central processing unit  52  controls and directs the execution of the instructions or portions of software code of the program or programs of the invention, the instructions or portions of software code being stored in one of the aforementioned storage means. On powering up of the device  50 , the program or programs which are stored in a non-volatile memory, for example the hard disk  58  or the read only memory  53 , are transferred into the random-access memory  54 , which then contains the executable code of the program or programs of the invention, as well as registers for storing the variables and parameters necessary for implementation of the invention. 
     It will also be noted that the device implementing the invention or incorporating it may be implemented in the form of a programmed apparatus. For example, such a device may then contain the code of the computer program(s) in a fixed form in an application specific integrated circuit (ASIC). 
     The device described here and, particularly, the central processing unit  52 , may implement all or part of the processing operations described in relation with  FIGS. 1 to 13 , to implement methods according to the present invention and constitute devices according to the present invention. 
     The above examples are merely embodiments of the invention, which is not limited thereby.