Abstract:
A method for texture compressing images having a plurality of color components (R, G, B) includes defining color representatives for use in encoding by defining groups of colors for each color component (R,G,B), and selecting a representative median color for the group. Each group ideally includes 3 to 15 increasing colors. The method includes computing, for each group, an error between each member of the group and the representative median color of the group. Typically, the error is computed as the sum of the absolute differences (SAD) between each member of the group and the representative median color of the group.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to texture compression techniques. 
   2. Background of Invention 
   Compression and decompression intended to minimize the memory size needed to store 2D textures is a promising field of application for these techniques in the 3D graphic domain. This possible field of use is becoming more and more significant as the dimensions and number of these textures tend to increase in real applications. The level of detail tends to increase as required by some applications, such as 3D games, and, without the help of such techniques, memory size and bandwidth for access would tend to require increasing performance levels hardly sustainable in mobile, ultra low power, handheld systems. More to the point, these techniques are becoming increasingly important in wireless phone architectures with 3D games processing capabilities. 
   For example, assuming a texture dimension of 512×512 pixels 16 bit/color each and a depth of 3, the amount of memory needed is 1.5 M bytes. Assuming 20-30 frames per second, the memory bandwidth is 30 to 45 Mbytes/s. 
   Additional background information on this topic can be gathered from “Real-Time Rendering” by Tomas Akenine-Möller and Eric Haines, A. K. Peters Ltd, 2 nd  edition, ISBN 1568811829. 
   A well-known solution in this scenario was developed by the company S3; the related algorithm is designated S3TC (where TC stands for Texture Compression). 
   This has become a widely used de-facto standard and is included in the Microsoft DirectX libraries with adhoc API support. 
   Compression is performed off-line at compile time and the textures are stored in the main memory. Decompression processes act to compress textures accessing the memory run-time. This means that only decompression is implemented in hardware form while compression is not. 
   Important parameters for the decompression engine are: steps needed to decompress textures and possible parallel operation; low latency between data-access-from-memory and data-out-from the decompression engine. 
   In order to better understand operation of the S3TC algorithm one may refer to an image in RGB format, where each color component R (Red) or G (Green) or B (Blue) is a sub-image composed by N pixels in the horizontal dimension and M pixels in vertical dimension. If each color component is coded with P bits, the number of bits per image is N*M*3*P. 
   For example, assuming N=M=256 and P=8, then the resulting size is 1,572,864 bits. If each sub-image R or G or B is decomposed in not-overlapped blocks of Q pixels in the horizontal dimension and S pixel in the vertical dimension, the number of blocks per sub-image is (N*M)/(Q*S) while per image is [3(NM/(Q*S(WM)] and the number of bits per block is [3*(Q*S)]*P. If, for example Q=S=4 and P=8, then the resulting size of each block is 384 bits. If the number of bits per channel is R=5, G=6, B=5 then the resulting size of each block per image is (4*4)*(5+6+5)=256 bits. The S3TC algorithm is able to compress such an amount of data by 6 times when R=8, G=8, B=8 and 4 times when R=5, G=6, B=5. 64 bits compose the resulting compressed block always sent to decompression stage. This number is the results of the coding steps described below assuming Q=S=4. 
   To sum up, operation of the S3TC algorithm may be regarded as comprised of the following steps: 
   i) Decompose the R G B image in non overlapped Q=4*S=4 blocks of R G B colors 
   ii) Consider the following block composed by 16 pixels each one composed by R, G and B color components: 
   Pij=R ij  U G ij  U B ij  (this denotes the pixel at the ij position the R G B image, and U is the union operator) 
   
     
       
             
             
             
             
           
         
             
                 
             
           
           
             
               (R11 G11 B11) 
               (R12 G12 B12) 
               (R13 G13 B13) 
               (R14 G14 B14) 
             
             
               (R21 G21 B21) 
               (R22 G22 B22) 
               (R23 G23 B23) 
               (R24 G24 B24) 
             
             
               (R31 G31 B31) 
               (R32 G32 B32) 
               (R33 G33 B33) 
               (R34 G34 B34) 
             
             
               (R41 G41 B41) 
               (R42 G42 B42) 
               (R43 G43 B43) 
               (R44 G44 B44) 
             
             
                 
             
           
        
       
     
   
   iii) Decompose the block above in three sub-blocks called sub-block R, sub-block G and sub-block B as shown hereinbelow, each block including only one color component: 
                                               R11 R12 R13 R14   sub-block R           R21 R22 R23 R24           R31 R32 R33 R34           R41 R42 R43 R44           G11 G12 G13 G14   sub-block G           G21 G22 G23 G24           G31 G32 G33 G34           G41 G42 G43 G44           B11 B12 B13 B14   sub-block B           B21 B22 B23 B24           B31 B32 B33 B34           B41 B42 B43 B44                        
as shown in  FIG. 1 .
 
   Specifically,  FIG. 1  shows RGB blocks ordered in different planes, with a RGB block shown on the left and a corresponding de-composition shown on the right. 
   iv) Sort in ascending order each sub-block color 
   v) Detect the black color, which is a pixel made of R=0 and G=0 and B=0 
   vi) If the black color is not detected, then set a color palette made by
         a. 1st color is the minimum value of sub-block R, minimum value of sub-block G, minimum value of sub-block B.   b. 2nd color is the maximum value of sub-block R, maximum value of sub-block G, maximum value of sub-block B   c. 3 rd  is composed by (2*min R+max R)/3, (2*min G+max G)/3, (2*min B+max B)/3   d. 4 th  is composed by (min R+2*max R)/3, (min G+2*max G)/3, (min B+2*max B)/3       

   vii) Otherwise, if black color is detected then set a color palette made by
         a. 1 st  color is minimum value of sub-block R, sub-block G, sub-block B where each of them must not be equal to zero (the black color component) at the same time   b. 2 nd  color is maximum value of sub-block R, sub-block G, sub-block B   c. 3 rd  is composed by (min R+max R)/2, (min G+max G)/2, (min B+max B)/2   d. 4 th  is the black color that has R,G,B components equal to zero       

   viii) If black color is not detected, define the look-up color palette as 
   
     
       
         
           
             
               
                 
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   If black color is detected define the color palette as 
   
     
       
         
           
             
               
                 
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   ix) Associate the following 2 bits code (in boldface, under the palette) to each column of the above palette 
   
     
       
         
           
             
               
                 
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   x) For each Pij=R ij  U G ij  U B ij  (where i ranges from 1 to Q=4 and j ranges from 1 to S=4) compute the Euclidean distance Dist between it and each look-up color as defined above in vi.a,b,c,d or vii.a,b,c,d depending if black color has been detected or not. Note that the difference is within a homologue color component (between R or G or B).
 
Dist1=√(| R   ij −Min R|   2   +|G   ij −Min G|   2   +|B   ij −Min B|   2 )
 
Dist2=√(| R   ij   −Int   1   R|   2   +|G   ij   −Int   1   G|   2   +|B   ij   −Int   1   B|   2 )
 
Dist3=√(| R   ij   −Int   2   R|   2   +|G   ij   −Int   2   G|   2   +|B   ij   −Int   2   B|   2 )
 
Dist4=√(| R   ij −Max R|   2   +|G   ij −Max G|   2   +|B   ij −Max B|   2 )
 
   xi) For each Pij=R ij  U G ij  U B ij  find the minimum distance among Dist 1 , Dist 2 , Dist 3  and Dist 4 . For example let this be Dist 1 . 
   xii) Send to a decoder process the code associated to the color enclosed in the look-up table that has the minimum distance. If it is Dist 1  then the code is 00. 
   xiii) The decoder receives for each Q*S block as shown in  FIG. 2 
         a. 2 bits code for each Pij that are addresses to the look-up table   b. MinR MinG MinB   c. MaxR MaxG MaxB       

   xiv) If Min is received before Max by the decoder, then black has been detected by the encoder otherwise not 
   xv) As shown in  FIG. 2 , the decoder operates as described in steps vi or vii depending on black color detection
         a. Int 1 R Int 1 G Int 1 B   b. Int 2 R Int 2 G Int 2 B       

   xvi) As shown in  FIG. 2 , the decoder addresses a look-up table with 2 bits code associated to each Pij and replaces it with the color stored in the look-up table color palette. Specifically ST, LUT, and CT indicate the source text, the look-up table, and the compressed text, respectively. 
     FIG. 3  shows how the data sent to the decoder are arranged in a bitstream and if the black color is not detected, while  FIG. 4  shows the opposite case. 
   As stated before, the compression ratio is 6:1 or 4:1. This is because if colors are in R=8 G=8 B=8 format then 384 bits are coded with 64 (384/64=6) and if colors are in R=5 G=6 B=5 format then 256 bits are coded with 64 (256/64=4). 
   As shown in  FIGS. 3 and 4 , the sum of all the bits amounts to 64. 
   SUMMARY OF THE INVENTION 
   However satisfactory the prior art solution considered in the foregoing may be, the need is felt for alternative texture compression/decompression techniques. The aim of the present invention is thus to provide such an alternative technique. 
   According to the present invention such an object is achieved by means of a method having the features set forth in the claims that follow. The invention also encompasses the decoding process as well as corresponding apparatus in the form of either a dedicated processor or a suitably programmed general-purpose computer (such as a DSP). In that respect the invention also relates to a computer program product directly loadable into the memory of a digital computer and including software code portions for performing the method of the invention when the product is run on a computer. 
   In brief, the presently preferred embodiment of the invention differs, in one of its aspects, from the S3TC algorithm in the way the reference colors are selected to construct the look-up table. The way of choosing these colors is made adaptive and consists in creating groups of colors for each color component R,G,B and select at first a group from which a representative color for this group is derived. Preferably, each group is composed by any number of colors between 3 up to 15 members. For each of them the median color is chosen as the representative color of the group to which it belongs. For sake of clarity, the median of a set of numbers put in ascending order is the number located in the middle position of them. 
   For example if the set is (1, 3, 5, 6, 20) then the median is the 3 rd  value (from right) and is equal to 5. 
   For each group, an error is computed as the sum of the absolute differences (SAD) between each group member and the representative (the median value of the group) color. 
   Still preferably, at least two different criteria are used to select the group first and then extract from this group a representative color. 
   The former is to select the group that minimizes the error as defined before, assuming each group comprised of the lower colors sorted in ascending order. The same applies for the groups comprised of the higher colors. 
   The latter accrues the error computed separately for the two groups in all possible combinations and then provides for finding the minimum of the composite error. 
   Groups that include only the minimum color or the maximum color are not considered during the processing which are, instead, the reference colors for S3TC. 
   The arrangement disclosed herein detects black colors. Also the encoding steps, the bitstream composition and the decoding steps are different if compared to S3TC. 

   
     BRIEF DESCRIPTIONS OF THE DRAWINGS 
     The invention will now be described, by way of example only, with reference to the annexed figures of drawing, wherein: 
       FIGS. 1 to 4  pertain to the prior as described above; 
       FIG. 5  shows R or G or B sub-blocks sorted from left to right in ascending order in a possible embodiment of the invention; 
       FIG. 6  shows examples of groups in respective sets as well as examples of computed errors; 
       FIGS. 7 and 8  show possible variants of the arrangement described herein; and 
       FIG. 9  is a block diagram of a pipeline arrangement to evaluate the performance of the compression and decompression techniques described herein. 
   

   DETAILED DESCRIPTION 
   The presently preferred embodiment of the invention differs, in one of its aspects, from the S3TC algorithm in the way the reference colors are selected to construct the look-up table. The way of choosing these colors is made adaptive and consists in creating groups of colors for each color component R,G,B and select at first a group from which a representative color for this group is derived. Preferably, each group is composed by any number of colors between 3 up to 15 members. For each of them the median color is chosen as the representative color of the group to which it belongs. For sake of clarity, the median of a set of numbers put in ascending order is the number located in the middle position of them. 
   For example if the set is (1, 3, 5, 6, 20) then the median is the 3 rd  value (from right) and is equal to 5. 
   For each group, an error is computed as the sum of the absolute differences (SAD) between each group member and the representative (the median value of the group) color. 
   Still preferably, at least two different criteria are used to select the group first and then extract from this group a representative color. 
   The former is to select the group that minimizes the error as defined before, assuming each group comprised of the lower colors sorted in ascending order. The same applies for the groups comprised of the higher colors. 
   The latter accrues the error computed separately for the two groups in all possible combinations and then provides for finding the minimum of the composite error. 
   Groups that include only the minimum color or the maximum color are not considered during the processing which are, instead, the reference colors for S3TC. 
   The arrangement disclosed herein detects black colors. Also the encoding steps, the bitstream composition and the decoding steps are different if compared to S3TC. 
   An embodiment of the invention will now be described by using the approach previously adopted for describing the S3TC arrangement and assuming Q=S=4. 
   i) Decompose the R G B image in non overlapped Q=4 S=4 blocks of R G B colors 
   ii) Consider the following 4×4 block composed of 16 pixels each one composed by R, G and B components: 
   Pij=R ij  U G ij  U B ij  (this again denotes the pixel at the ij position in the R G B image, where U is the union operator) 
   
     
       
             
             
             
             
           
         
             
                 
             
           
           
             
               (R11 G11 B11) 
               (R12 G12 B12) 
               (R13 G13 B13) 
               (R14 G14 B14) 
             
             
               (R21 G21 B21) 
               (R22 G22 B22) 
               (R23 G23 B23) 
               (R24 G24 B24) 
             
             
               (R31 G31 B31) 
               (R32 G32 B32) 
               (R33 G33 B33) 
               (R34 G34 B34) 
             
             
               (R41 G41 B41) 
               (R42 G42 B42) 
               (R43 G43 B43) 
               (R44 G44 B44) 
             
             
                 
             
           
        
       
     
   
   iii) Decompose the block above in three sub-blocks called sub-block R, sub-block G and sub-block B each block including only a color component: 
   
     
       
             
             
             
           
         
             
                 
                 
             
           
           
             
                 
               R11 R12 R13 R14 
               sub-block R 
             
             
                 
               R21 R22 R23 R24 
             
             
                 
               R31 R32 R33 R34 
             
             
                 
               R41 R42 R43 R44 
             
             
                 
               G11 G12 G13 G14 
               sub-block G 
             
             
                 
               G21 G22 G23 G24 
             
             
                 
               G31 G32 G33 G34 
             
             
                 
               G41 G42 G43 G44 
             
             
                 
               B11 B12 B13 B14 
               sub-block B 
             
             
                 
               B21 B22 B23 B24 
             
             
                 
               B31 B32 B33 B34 
             
             
                 
               B41 B42 B43 B44 
             
             
                 
                 
             
           
        
       
     
   
   iv) Sort in ascending order each sub-block color R, G, B as shown in  FIG. 5 . Each number is the position in ascending order that addresses each color component R,G,B 
   v) Define two sets, each set including some groups of color for each R, G, B component independently. The left-hand portion of  FIG. 6  shows the yellow set and the red set as an example of such groups for a given color component. In the yellow set, each group includes an increasing number of colors starting from the minimum on the left and excluding the group with only the lowest color (marked with X). In the red set, each group includes a decreasing number of colors starting form the maximum on the right and excluding the group with only the highest color (marked with X). 
   vi) For each group, compute the error as the sum of absolute differences (SAD) between its median color and each color composing the group. Referring to the right hand portion of  FIG. 6 , Ei is such error associated to the yellow set (where i ranges from 1 to the number of groups belonging to yellow set) and ej (where j ranges from 1 to the number of groups belonging to red set) is the error associated to red set, where i or j is the index to address each group in the respective set 
   vii) Two sets of errors are computed, Ei and ej. Selection of the yellow group and red group (and then depending on which one is selected, the median is taken as the representative color) can occur in two ways:
         a) the yellow group is the one that has the minimum error between all Ei&#39;s and the red group is the one that has the minimum error between all ej&#39;s   b) all possible combinations of Ei+ej are computed first and then the global minimum value is found. This will select at the same time—and not separately as before—a yellow and red group that has the error that minimizes the Ei+ej number. For example E 7 +e 11  being the minimum implies the selection of 4th element as min_median reference and 14th element as max_median reference for next encoding steps       

   viii) The color representatives as defined in step vii) will be used to set the encoding step. 
   If the black color is detected, step vi) is modified in such a way that each group of color does not include the black. 
   The basic scheme described in the foregoing lends itself to a numbers of variants. 
   A first variant has only two groups of colors of 3 and 5 elements as shown in  FIG. 7 . 
   Depending on the criteria a) and b) assumed in the previous section vii two additional variants can be defined. 
   In particular, referring to  FIG. 7 , in the first of these additional variants:
         If E 3 &lt;=E 5  min_median reference 1 =element  2 , else min_median reference 1 =element  3 ,   If e 3 &lt;=e 5  max_median reference 2 =element  15  else max_median reference 2 =element  14         

   In the second variant:
         If minimum is E 3 +e 3  then min_median reference  1 =element  2  and max_median reference 2 =element  15     If minimum is E 3 +e 5  then min_median reference  1 =element  2  and max_median reference 2 =element  14     If minimum is E 5 +e 3  then min_median reference  1 =3 and max_median reference 2 =element  15     If minimum is E 5 +e 5  then min_median reference  1 =3 and max_median reference 2 =element  14         

   A further additional variant takes always as min_medianreference 1  equal to the second element and as max_median_reference — 2 equal to the 15 th , while another additional variant takes always as min_median reference  1  the 3 rd  element and max_median as reference  2  the 14 th  as shown in  FIG. 8  where the first row is related to STM-TC3 and the second is related to STM-TC 5. 
   At the end of above described variants, each one produces as a result two reference colors named: 
   1) min_medianR U min_medianG U min_medianB 
   2) max_medianR U max_medianG U max_medianB 
   where U is the union operator grouping them as a whole pixel. 
   Next, the proposed method computes a value called length as follows. 
   If the black colour (which is a pixel made of R=0 and G=0 and B=0) has not been detected:
 
Length —   R =(max_median R −min_median R )/6
 
Length —   G =(max_median G −min_median G )/6
 
Length —   B =(max_median B −min_median B )/6
 
Length=√(|Length —   R|   2 +|Length —   G|   2 +|Length —   B|   2 )
 
   where max_medianR,G,B and min_medianR,G,B are the representative colors for each selected group belonging to the red and yellow sets. 
   This is the maximum quantization error the method can compute when Pij colors are quantized during the encoding step, here described. 
   If the black color is not detected for each Pij=R ij  U G ij  U B ij  (where i range is from 1 to Q=4 and j range is from 1 to S=4) compute the Euclidean distance
 
Dist —   ij =√(| R   ij −min_median R|   2   +|G   ij −min_median G|   2   +|B   ij −min_median B|   2 )
 
   Now the encoder quantizes each color as follows:
         if Dist_ij&lt;=(Length) send to the decoder the code 00   if (Length)&lt;Dist_ij&lt;=3*Length send to the decoder the code 01   if (3*Length)&lt;Dist_ij&lt;=5*Length send to the decoder the code 10   if Dist_ij&gt;5*Length send to the decoder the code 11       

   When a block is encoded, the decoder receives a 2 bits code for each Pij as above defined, plus min_medianR U min_medianG U min_medianR plus length_R, length_G, length_B 
   Conversely, if the encoder detects the black color, then
 
Length —   R =(max_median R −min_median R )/4
 
Length —   G =(max_median G −min_median G )/4
 
Length —   B =(max_median B −min_median B )/4
 
Length=√(|Length —   R|   2 +|Length —   G|   2 +|Length —   B|   2 )
 
   for each Pij=R ij  U G ij  U B ij  (where i range is from 1 to Q=4 and j range is from 1 to S=4) quantize them as follows:
 
compute Dist  ij =√(|R ij −min_median R|   2   +|G   ij −min_median G|   2   +|B   ij −min_median B|   2 )
         if R ij =Gij=Bij=0 send to the decoder the code 00   else if R ij  or Gij or Bij not equal to 0
           if Dist ij&lt;=(Length) send to the decoder the code 01   if (Length)&lt;Dist ij&lt;=3*Length send to the decoder the code 10   if (3*Length)&lt;Dist ij send to the decoder the code 11   
               

   When a block is encoded the decoder receives 2 bits code for each Pij as above defined, plus min_medianR U min_medianG U min_medianR after length_R, length_B, length_B 
   If decoder receives min_medianR U min_medianG U min_medianR before length_R, length_B, length_B this means that the black color is not detected so the output colors will be 
   if the code is 00
         Rij=min_medianR   Gij=min_medianG   Bij=min_medianB       

   if the code is 01
         Rij=min_medianR+2*length_R   Gij=min_medianG+2*length_G   Bij=min_medianB+2*length_B       

   if the code is 10
         Rij=min_medianR+4*length_R   Gij=min_medianG+4*length_G   Bij=min_medianB+4*length_B       

   if the code is 11
         Rij=min_medianR+6*length_R   Gij=min_medianG+6*length_G   Bij=min_medianB+6*length_B       

   If the decoder receives Min_medianR U min_medianG U min_medianR after length_R, length_B, length_B it means that black color is detected so the output colors will be 
   if the code is 00
         Rij=0   Gij=0   Bij=0       

   if the code is 01
         Rij=min_medianR   Gij=min_medianG   Bij=min_medianB       

   if the code is 10
         Rij=min_medianR+2*length_R   Gij=min_medianG+2*length_G   Bij=min_medianB+2*length_B       

   if the code is 11
         Rij=min_medianR+4*length_R   Gij=min_medianG+4*length_G   Bij=min_medianB+4*length_B       

   The various arrangements described in the foregoing have been applied to the following standard images by using two formats: RGB 565 and RGB 888, where 5, 6 or 8 is the number of bits per color channel. 
   1. 256×256 (horizontal×vertical size dimension)
         Abstrwav   Chapt   Forest   Intel   Pixtest   Reference   Teleport   Topsmap       

   2. 512×512 (horizontal×vertical size dimension)
         Donut       

   3. 512×1024 (horizontal×vertical size dimension)
         Face       

   4. 640×480 (horizontal×vertical size dimension)
         Balloon       

   5. 1024×768 (horizontal×vertical size dimension)
         Yahoo       

   These pictures are a representative set on which texture compression is typicaly applied. 
   All the pictures are in true-color format or 888, while the 565 format is obtained from the 888 format by truncating the 323 lowest bits of the 888 pictures. Alternative truncating methods can be used to go from 888 to 565 such as rounding to nearest integer, Floyd-Steinberg dithering etc. These do not imply any changes in the arrangement disclosed herein. 
   To evaluate the performance of each arrangement, visual assessments and objective measures can be performed. In particular two parameters are taken as reference measures: 
   mean square error (MSE), and 
   peak signal/noise ratio (PSNR) for each RGB channel. 
     FIG. 9  shows how the measures are taken within the simulation environment. 
   Input images IS in the 888 format (called Source888) are converted at  200  into the 565 format (called Source565), then compressed at  201  and further decompressed at  202  to the 565 format. These are back converted at  203  into the 888 format to generate a first set of output images OS′ (also called Decoded888). 
   The Source-565 images from block  200  are back converted into 888 at  204  to generate a second set of output images OS″ to be used as a reference (called Source565to888). 
   A first set of PSNR values (called PSNR 888) are computed between the Source 888 IS and the Decoded888 OS′ images. A second set of PSNR (called PSNR 565) values are computed between the Source565to888 OS″ and the Decoded888 OS′ images. 
   In particular, 565 images are back reported to 888 by simple zero bit stuffing of the 323 least significant positions. 
   How the Source888 IS images are converted to the 565 format and back to the 888 foamt corresponds to techniques that are well known to the experts in this area and do not need to be described in detail here:
 
 MSE =(Σ| Pij−Paij|   2 )/( w*h )
 
where:
         Pij=source color   Paij=processed color   w, h=image width, height
 
 PSNR= 10 log 10 [(2 bpp −1) 2   /MSE ]
 
where:
   bpp=bit per color       

   The results show that all the variants of the solution disclosed herein perform significantly better than S3TC in most tests. 
   Of course, the underlying principle of the invention remaining the same, the details and embodiments may vary, also significantly, with respect to what has been described and shown by way of example only, without departing from the scope of the invention as defined by the annexed claims.