Abstract:
A method and apparatus for selecting a coding mode of intra prediction in video compression. The method adapts an alternative full search (AFS) algorithm which reduces the computations of a conventional full search (FS) method. In the method, estimated sums of predicted blocks are obtained without actually forming predictors. By comparing the estimated sums of all modes with a low bound threshold, the undesired modes are quickly eliminated, and thus the number of predictor calculations and cost evaluations that require intensive computations are decreased.

Description:
BACKGROUND 
   1. Field of the Invention 
   The present invention relates generally to a method for video compression, and more particularly, to a method of selecting a coding mode for intra-predicted block data within an image frame. 
   2. Background of the Invention 
   The ITU-T H.264 standard, which is also named MPEG-4 Part-10 Advanced Video Coding (AVC), has recently been developed as a next-generation compression tool for the coding of video content. Experimental results show that the H.264 standard provides a factor of two in compression efficiency compared to other exiting standards. Therefore, the H.264 standard is very suitable for use in the growing applications of Internet streaming, multimedia communications, and mobile televisions. 
   During the coding of a current block, to remove the spatial redundancy between its neighboring blocks, the H.264 standard provides a coding tool called “intra prediction” to form predictors from pixels around the current coding block. As shown in  FIG. 1 , according to the H.264 standard, there are a total of nine intra prediction modes for each 4 by 4 Luma block. Furthermore,  FIG. 2  shows boundary pixels (A to L, and X) that are used to form the predictors (a to p) of the 4 by 4 predicted block in each of the prediction modes. The residual between the current coding block and the predicted block, which is formed according to a prediction mode, is processed by further coding procedures, such as transformation, quantization, and entropy coding to produce a compressed bitstream. Choosing a suitable intra prediction mode is important for the performance of compression as the more similar a predicted block is to the current coding block, the smaller the resulting residual is. Therefore, the amount of information that needs to be compressed is largely decreased so that the performance of compression can be improved. 
   A number of technologies for fast-selecting the intra prediction mode and rapidly performing the intra prediction have been introduced in the market. For example, in Japan Patent No. 2004-140473, an image information coding apparatus is provided to rapidly intra-predict each block based on a pipeline process. The apparatus sequentially processes the respective blocks in a pre-determined order except for the raster scanning. 
   In U.S. patent Publication No. 2003/0206594, a method of encoding intra frame is disclosed, which provides a probability table of the prediction modes according to an expected complexity of an encoder. The probability table is adjustable so that the blocks can be coded in a low-complexity encoding by using the low-complexity subset of modes, or in a high-complexity encoding using any prediction mode. This permits a low-complexity decoder responsive to only the low-complexity subset of modes. 
   U.S. patent Publication No. 2003/0223645 discloses methods and systems for estimating a pixel prediction mode to be used in a video encoding or decoding process. This application classifies the prediction modes by five groups that are ordered in a manner with their likelihood of producing a reduced prediction error. The prediction mode order is expressed according to the positions of the blocks that are near the edges or boundaries of an image frame. 
   U.S. patent Publication No. 2004/0008771 discloses a method and device for coding a digital image using an intra-mode block prediction. The modes assigned to each combination of prediction modes may be divided into two groups. The first group includes n most probable prediction modes (where n is smaller than the overall number of available modes) and the second group includes the remaining modes. The modes in the first group are ordered according to their probability. This order may be specified as a list of modes ordered from the most probable mode to the least probable mode. The modes of the second group may be ordered in a predetermined manner, which may be specified depending on the information already available to a decoder. 
   Furthermore, one known technology selects an intra prediction mode with a reasonable computational complexity via various approaches including a partially computation of the cost function, an early termination, and a selective computation of highly probable modes to save the time of selecting the intra prediction mode. Another known technology provides a fast mode selection method by examining the most probable modes. This method is based on an assumption that the suitable prediction mode of a block is most likely in the direction of a local edge within that block. The local edge information is obtained with additional calculations for the edge feature parameters of the current coding block. For more details on the fast algorithms for intra prediction mode selection, references may be made to B. Meng and O. C. Au, “Fast intra-prediction mode selection by 4 by 4 blocks in H.264,” in Proc. Of 2003 IEEE Int. Conf. On Acoustics, Speech, and Signal Processing (ICASSP &#39;03), April 2003, and Y. D. Zhang, F. Dai, and S. X. Lin, “Fast 4 by 4 Intra-prediction Mode Selection for H.264,” in Proc. Of 2004 IEEE Int. Conf. On Multimedia and Expo (ICME &#39;04), July 2004. 
   The above technologies, however, only rely on fewer candidates of modes and roughly evaluate matching errors of the predicted blocks. Therefore, there are some difficulties in achieving an optimum selection of intra prediction modes. That is, these prior art methodologies cannot achieve maximum compression performance. 
   Furthermore, to achieve the best compression performance, each 4 by 4 block in an image frame needs to be encoded with its optimal intra prediction mode. To find the optimal intra prediction mode, a full search (FS) is commonly used for all the nine prediction modes of  FIG. 1  because of its good performance and regularity for easy implementation. In an H.264 reference program JM 7.3, a full search algorithm is developed to select the optimal mode for each 4 by 4 block. The cost measure for each mode is based on the sum of absolute difference (SAD) between the predicted block and the current coding block. Let C(i, j) and Pm(i, j) be the pixel intensities at coordinate (i, j) of the current 4 by 4 coding block (C) and the predicted 4 by 4 block (Pm) according to mode m (0≦m≦8), respectively. The sum of absolute difference between Pm and C is denoted by SAD(m), which is given by:
 
SAD( m )=ΣΣ| Pm ( i,j )− C ( i,j )|, 0≦( i,j )≦3  (1)
 
   Therefore, in the H.264 reference program, the FS method may include the following steps: 
   (1) Generating a predicted 4 by 4 block Pm according to the mode m; 
   (2) Calculating the cost of the mode m, denoted by COST(m) as given below:
 
COST( m )=SAD( m )+4* F ( QP )* MP   (2)
 
   wherein F(QP) is a function of the quantization parameter (QP) and F(QP)≧0. MP is 0 if m is the most probable mode; otherwise MP is 1. 
   (3) Repeating steps (1) and (2) for 0≦m≦8. Choosing the one that has the minimum COST(m) as the optimal intra prediction mode. 
   According to the H.264 reference program, except for the mode (0) (vertical prediction) and mode 1 (horizontal prediction), the predictors in other modes are calculated by the mathematical functions of the boundary pixels. Take the mode 2 (DC prediction) as an example. Each predictor in the DC predicted block has the same value that is calculated from (4A+4B+4C+4D+4I+4J+4K+4L+4)&gt;&gt;3, wherein {A, B, C, D, I, J, K, L} are the boundary pixels as shown in  FIG. 2 , and &gt;&gt; is a bit-wise operator for a shift-right operation. For a digital signal processor (DSP) with single operation for accumulative multiplication, the count of operations for generating DC predicted block is 9 (i.e., 8 accumulative multiplication and 1 shifting.) The expressions and the counts of operations for other 8 modes are shown in Tables I-IX, which show a total of 192 operations for generating predictors in these 9 modes. (See Table X at the end of the specification.) If fixed QP is used for each block, it takes 31 operations for COST(m) when m is the most probable mode; otherwise 32 operations are needed. As a result, the FS method would take (192+31+32*8)=479 operations for each 4 by 4 blocks. This large operation number is computationally expensive for the FS method. 
   Therefore, there is a need for a new approach to find the optimal intra prediction mode, which is computationally efficient compared to the FS method. 
   BRIEF SUMMARY OF THE INVENTION 
   An object of the present invention is to provide an alternative full search (AFS) method for the intra prediction modes. The AFS method reduces the complexity of the FS method by eliminating useless modes before calculating the cost of the predicted block for mode m (COST(m)). Therefore, the computational complexity can be reduced efficiently, while the PSNR (peak signal-to-noise ratio) and the bit-rate are approximately the same as that in the FS method. 
   In accordance with one preferred embodiment of the present invention, an apparatus for selecting a coding mode of intra prediction in video compression is provided. The apparatus includes an input port for receiving data including a current coding block, boundary pixels surrounding the current coding block, a quantization parameter, and modes of neighboring blocks; a microprocessor for determining at least one of an optimal mode and a minimum cost COSTmin used for the video compression based on the received data, and an output port for outputting the at least one of the optimal mode and COSTmin. 
   In another preferred embodiment, the apparatus further includes a means for determining the coding mode. The means for determining the coding mode includes a first calculator for calculating estimated sums of predicted blocks, a second calculator for calculating a sum of a current coding block, a comparator for comparing the estimated sums of the predicted blocks with the sum of the current coding block, and choosing a specific mode k, a generator for generating a predicted block for the mode k, and a third calculator for calculating a cost COST(k) for the mode k. 
   In the above embodiment, in the mode k, an absolute difference between the estimated sum of the predicted blocks for mode k and the sum of the current coding block has a smallest value, and a temporary minimum cost COSTmin is initiated as COST(k). Furthermore, the comparator further compares a cost COST(n) of a mode n (n≠k) with the temporary minimum cost COSTmin when the absolute difference between the estimated sum for mode n and the sum of the current block is smaller than COSTmin. If the COST(n) is smaller than the temporary COSTmin, the microprocessor updates the temporary minimum cost to the COST(n) and a temporary optimal coding mode to be the mode n. 
   A further preferred embodiment of the present invention provides a method for selecting a coding mode of intra prediction in video compression. The method includes receiving data including a current coding block, boundary pixels surrounding the current coding block, a quantization parameter, and modes of neighboring blocks, calculating estimated sums of predicted blocks for all modes, and determining an optimal coding mode based on the estimated sums of the predicted blocks. In the embodiment, the optimal coding mode includes a feature that a sum of absolute difference (SAD) between the predicted block for the optimal coding mode and the current coding block is smallest among all of the modes. 
   Another preferred embodiment further includes calculating the estimated sums of the predicted blocks for all modes, calculating a sum of the current coding block (SUMC), comparing absolute differences between the estimated sums of the predicted blocks and the sum of the current coding block (i.e., |ESUMP(m)−SUMC|), finding a mode k of which |ESUMP(k)−SUMC| is smallest among all of the modes, generating a predicted block Pk for the mode k, calculating a cost COST(k) of the predicted block Pk, and setting COST(k) and the mode k as an initial minimum cost COSTmin and an initial optimal mode. 
   The method further compares the absolute difference of the estimated sum of the mode n (n≠k) and the sum of the current coding block with the COSTmin, and if the absolute difference is smaller than the COSTmin, generates a predicted block for the mode n, calculates a cost COST(n) of the mode n, comparing the COST(n) with the COSTmin, and updates the COSTmin and the optimal mode to be COST(n) and n if the COST(n) is smaller than the COSTmin. 
   Another preferred embodiment of the present invention includes a method for calculating estimated sums of predicted blocks in a video compression application. The method includes receiving boundary pixels that are surrounding the current coding block, and calculating estimated sums of the predicted blocks according to the mathematic functions of the boundary pixels without actually forming the predicted blocks. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows nine coding modes of intra prediction for a 4 by 4 block in accordance with the H.264 standard. 
       FIG. 2  shows boundary pixels (A to L and X) that are used to form predictors (a to p) of a 4 by 4 predicted block. 
       FIG. 3  is a flow chart showing an alternative full search (AFS) method in accordance with one preferred embodiment of the present invention. 
       FIG. 4  is a block diagram of an apparatus for selecting a coding mode of intra prediction in video compression in accordance with another preferred embodiment of the present invention. 
       FIG. 5  shows a simulation result of selecting a coding mode for a CIF (352 by 288 pixels) video sequences “Akiyo” (300 frames) by means of a preferred embodiment in accordance with the present invention. 
       FIG. 6  shows a simulation result of selecting a coding mode for a CIF (352 by 288 pixels) video sequences “Foreman” (300 frames) by means of a preferred embodiment in accordance with the present invention. 
       FIG. 7  shows a simulation result of selecting a coding mode for a CIF (352 by 288 pixels) video sequences “News” (300 frames) by means of a preferred embodiment in accordance with the present invention. 
       FIG. 8  shows a simulation result of selecting a coding mode for a CIF (352 by 288 pixels) video sequences “Stefan” (300 frames) by means of a preferred embodiment in accordance with the present invention. 
       FIG. 9  shows a simulation result of selecting a coding mode for an SD (720 by 480 pixels) video sequences “Harbour” (300 frames) by means of a preferred embodiment in accordance with the present invention. 
       FIG. 10  shows a simulation result of selecting a coding mode for an SD (720 by 480 pixels) video sequences “Night” (300 frames) by means of a preferred embodiment in accordance with the present invention. 
       FIG. 11  is a diagram showing the average count of operations per frame for each video sequence by using a full search method and an alternative full search method. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   A preferred embodiment of the present invention provides an alternative full search (AFS) method for intra prediction modes. According to the preferred embodiment, the AFS method reduces the complexity of the conventional FS method by eliminating useless modes before calculating the cost of the predicted block for mode m (COST(m)). A criterion of the elimination is based on a lower bound of SAD(m), which can be obtained by an estimated sum of a predicted block Pm for mode m without actually generating the block Pm. Here, SAD(m) is the sum of absolute difference between the predicted block Pm and a current 4 by 4 block C. Therefore, the AFS method reduces the computational complexity efficiently, while the PSNR (peak signal-to-noise ratio) and bit-rate are substantially maintained at the same levels achieved with the FS method. 
   In the conventional block-matching method, by employing a successive elimination algorithm (SEA) for motion estimation, the full search approach that uses the SAD as the matching criterion can be efficiently sped up. Based on a mathematical triangle inequality used in the SEA, the SEA excludes many candidates from calculating the SAD by evaluating the lower bounds of the SAD. For more details on SEA for motion estimation, reference may be made to W. Li and E. Salari, “Successive elimination algorithm for motion estimation.” IEEE Trans, Image Processing, Vol. 4, pp. 105-107, Jan. 1995. 
   The present invention extends the concept of SEA to find out the best matching intra-prediction block, and the mathematical inequality in the SEA is modified by:
 
SAD( m )=ΣΣ| Pm ( i,j )− C ( i,j )|≧|SUMP( m )−SUMC|,  (3)
 
SUMC=ΣΣ C ( i,j ),  (4)
 
SUMP( m )=ΣΣ Pm ( i,j ),  (5)
 
   wherein C(i, j) and Pm(i, j) are the pixel intensities at coordinate (i, j) of a current coding block C and the predicted block Pm according to mode m, respectively, and SUMP(m) and SUMC are the actual sum of the predicted blocks according to mode m and the sum of the current coding block, respectively. 
   According to the inequality of (3), if there is a mode k of which the SAD(k) is the minimum value of all, it guarantees that SAD(m)≧|SUMP(m)−SUMC|&gt;SAD(k) when m≠k. Therefore, the calculations of SAD(m) can be eliminated when |SUMP(m)−SUMC| is larger than the specific lower bound, thereby saving 31 operations. 
   However, in most of the modes, the total operations for SUMP(m) are larger than 31. Take the mode 5 as the example. As shown in Table X, it first takes 36 operations to generate P5, and then it takes 15 operations to calculate SUMP(5). As a result, it totally needs (36+15)=51 operations to obtain SUMP(5). This amount of operations, however, is still considerably large. Therefore, it would be desirable to reduce the operations for SUMP(m). 
   In accordance with the present invention, the SUMP(m) in inequality of (3) is replaced by an estimate value, which is obtained without the cost of generating Pm. As the predictors (a-p) are generated from the boundary pixels (A-L and X), as shown in  FIG. 2 , the SUMP(m) can be estimated by a mathematic function of these pixels directly. The estimated sum of the predicted block according to mode m is denoted by ESUMP(m) and is calculated by the following equation:
 
ESUMP( m )=((Σ( WCm ( i,j )* BP ( i,j )))+ RCm )&gt;&gt; SRm&lt;&lt;SLm,  
 
   wherein BP(i, j) is the intensity of the boundary pixel at coordinate (i, j) that are surrounding the current coding block, WCm(i, j) is the weighting constant of BP(i, j) for a mode m, RCm is the rounding constant for a mode m, SRm and SLm are the numbers of shift-right and shift-left operations for a mode m, respectively, and symbols &gt;&gt; and &lt;&lt; are bit-wise operators for shift-right and shift-left operations, respectively. 
   Table XI shows the expressions for ESUMP(m) for all of the modes. In Table XI, the symbols &gt;&gt; and &lt;&lt; are bit-wise operators for shift-right and shift-left operations, respectively. As shown in Table XI, the counts of operations for calculating ESUMP(m) are smaller than those of SUMP(m). 
   To quickly obtain the lower bound of SAD, the inequality of (3) can be modified to:
 
SAD( m )≧|ESUMP( m )−SUMC|
 
           (SAD( m )+4* F ( QP )* MP )≧|ESUMP( m )−SUMC|
 
         COST( m )≧|ESUMP( m )−SUMC|.  (6)

   From the above inequality of (6), the AFS method of the preferred embodiment of the present invention skips the calculations of COST(m) if |ESUMP(m)−SUMC| is larger than the current minimum cost to reduce the computations. 
   The details of the AFS method in accordance with one preferred embodiment of the present invention are described with reference to  FIG. 3 . Flow chart  30  illustrates steps of selecting an optimal coding mode of intra prediction for video compression. 
   In accordance with the present invention, the AFS method first chooses an initial optimal mode and an initial minimum cost (COSTmin) as basic data. To do so, as shown at step  301 , process  30  first calculates all of the estimated sums for all modes. 
   At step  302 , all of the estimated sums are compared with the sum of the current coding block SUMC and mode k, that the absolute difference |ESUMP(k)−SUMC| is smallest among all of the modes, is chosen. Next, at step  303 , the predicted block Pk for mode k is generated and its cost COST(k) is calculated. 
   At step  304 , after Pk and COST(k) are obtained, the process sets the initial value of COSTmin to be COST(k) and the initial optimal mode to be k. 
   Next, at step  305 , the process calculates the estimated sum of the predicted block for another mode n where n≠k, and determines if the absolute difference |ESUMP(n)−SUMC| is smaller than COSTmin. If not, the method skips the calculation of mode n, as shown at step  307 . Otherwise, the process goes to step  306 . 
   At step  306 , the process generates predicted block Pn for mode n and its cost COST(n). 
   At step  308 , the process decides whether COST(n) is smaller than the COSTmin. If so, the process updates the COSTmin to be COST(n) and the optimal mode to be n, as shown at step  309 . Otherwise, the process goes to step  310 . 
   At step  310 , if all of the modes are checked, a final optimal mode is determined, as shown at step  311  and the process ends. If not all of the modes are checked, the process repeats steps  305  to  309  until all of the modes are checked and a final optimal mode is determined. 
   From the process described above, the calculations for deciding the optimal coding mode are efficiently reduced. For example, if COST(0) is the smallest of all and mode 0 is also the most probable mode, the method would only take (60+15+9+31)=115 operations to find the optimal intra prediction mode, wherein 60 is the total operations of calculating the estimated sums, 15 is the operations for SUMC, 9 is the operations for |ESUMP(m)−SUMC| for all of the modes, and 31 is the operations needed to calculate the cost COST(0). Accordingly, the computational complexity of the AFS method of the present invention is decreased efficiently as compared with the conventional FS method that requires 479 operations. 
     FIG. 4  shows an apparatus  40  for selecting a coding mode of intra prediction in video compression in accordance with another preferred embodiment of the present invention. In the preferred embodiment, apparatus  40  receives and analyzes subsequent video image frames to select a best coding mode of the intra prediction. 
   As shown, apparatus  40  includes input port  41  for receiving data including a current coding block, boundary pixels of the current coding block, a quantization parameter, and modes of neighboring blocks, and output port  47  for outputting a selected optimal mode and a minimum cost after analysis. The boundary pixels of the current block are then processed by calculator A  42  for calculating an estimated sum of predicted block for a mode. As described above, the estimated sum of the predicted block is calculated according to the equations shown in Table XI. Apparatus  40  further includes calculator B  43  for calculating the sum of the current coding block (SUMC) according the equation (4) described above. Initially, all of the estimated sums of the predicted blocks for all modes are calculated. Comparator  44  compares the absolute differences between the estimated sums and the sum of the current coding block, and then chooses mode k of which the absolute difference is smallest among all of the modes as an initial mode. 
   Apparatus  40  further includes generator  45  for generating a predicted block Pk for mode k and calculator C  46  calculates the cost COST(k) according to the above equation (2) after Pk is generated. The cost COST(k) is then set as an initial minimum cost COSTmin. Preferably, the initial minimum cost COSTmin and the initial mode k are stored in memory  48 . 
   After the initial optimal mode and minimum cost are set, calculator A  42  continues calculating an estimated sum of predicted block for mode n (ESUMP(n)), where n≠k. Comparator  44  again compares the absolute difference between ESUMP(n) and SUMC. If |ESUMP(n)−SUMC| is smaller than COSTmin stored in memory  48 , comparator  44  outputs a signal to enable generator  45  to generate predicted block Pn and calculator C  46  to calculate COST(n). In this case, if COST(n) is smaller than COSTmin, the optimal mode and the minimum cost in memory  48  are updated to be mode n and COST(n). 
   The above procedures continues until all of the modes are calculated and compared. At the end, the final optimal mode and COSTmin are output by output port  47  to another apparatus (not shown) for further processing. 
   Although in the above embodiment, apparatus  40  includes various elements, it is known in the art that apparatus  40  can be embodied as a single microprocessor or multiple microprocessors depending on the applications. 
   The above AFS method and apparatus can be preferably embodied into the H.264 reference program JM 7.3. To prove the superiority of the AFS method in accordance with the present invention to the conventional FS method, four CIF (352 by 288 pixels) video sequences, “Akiyo”, “Foreman”, “News”, and “Stefan”, and two SD (720 by 480 pixels) video sequences, “Harbour” and “Night” are used to evaluate the performance of the AFS method of the present invention. These video sequences are encoded as I-frames and using fixed quantization parameter (QP) for each frame. In each frame, the partition of block is fixed to 4 by 4 pixels. Simulations with various QP values are also examined. The results of the experiments are shown in  FIGS. 5-10 , respectively. 
     FIGS. 5-10  show the performance comparisons between the conventional FS method and the AFS method of the present invention in terms of peak signal-to-noise ratio (PSNR, unit is dB) and bit-rate (unit is Kbps). The results show that the performance of compression for the AFS method is almost the same as the conventional FS method. However, the operations required for additions and shifts used in the AFS method is much less than those required in the conventional FS method, as described above. 
     FIG. 11  shows the average count of operations per frame for each video sequence by using the conventional FS method and the AFS method. As shown in this figure, the complexity of the AFS method (i.e., the operations required for accumulative multiplication, additions and shifts) is between 48% and 71% of the operations needed by the conventional FS method, whereas the PSNR and bit-rate of the AFS method is approximately equal to that of the conventional FS method. 
   Furthermore, Table XII shows the accuracy of estimating the sums of the predicted blocks by using the AFS method of the present invention. Simulation results are given in terms of the average of |ESUMP(m)−SUMP(m)| for each mode m when QP is 24. From Table XII, the simulation results show that the differences between the estimated and actual sums of the predicted blocks are very small. That is, the present method can quickly obtain the estimated sums without actually generating the predicted blocks, whereby further reducing the computational complexity. 
   The foregoing disclosure of the preferred embodiments of the present invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many variations and modifications of the embodiments described herein will be apparent to one of ordinary skill in the art in light of the above disclosure. The scope of the invention is to be defined only by the claims appended hereto, and by their equivalents. 
   Further, in describing representative embodiments of the present invention, the specification may have presented the method and/or process of the present invention as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process of the present invention should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the present invention. 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE I 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 0 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               0 
               e, e, i, m 
               A 
               0 
               0 
             
             
                 
               b, f, j, n 
               B 
               0 
             
             
                 
               c, g, k, o 
               C 
               0 
             
             
                 
               d, h, l, o 
               D 
               0 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE II 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 1 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               1 
               a, b, c, d 
               I 
               0 
               0 
             
             
                 
               e, f, g, h 
               J 
               0 
             
             
                 
               i, j, k, l 
               K 
               0 
             
             
                 
               m, n, o, p 
               L 
               0 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE III 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 2 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               2 
               a, b, c, d, e, f, 
               (A + B + C + D + 
               9 
               9 
             
             
                 
               g, h, i, j, k, l, 
               I + J + K + L + 4)&gt;&gt;3 
             
             
                 
               m, n, o, p 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE IV 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 3 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               3 
               a 
               (A + C + 2B + 2)&gt;&gt;2 
               3 
               27 
             
             
                 
               b, e 
               (B + D + 2C + 2)&gt;&gt;2 
               4 
             
             
                 
               c, f, i 
               (C + E + 2D + 2)&gt;&gt;2 
               4 
             
             
                 
               d, g, j, m 
               (D + F + 2E + 2)&gt;&gt;2 
               4 
             
             
                 
               h, k, n 
               (E + G + 2F + 2)&gt;&gt;2 
               4 
             
             
                 
               l, o 
               (F + H + 2G + 2)&gt;&gt;2 
               4 
             
             
                 
               p 
               (G + 3H + 2)&gt;&gt;2 
               4 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE V 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 4 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               4 
               m 
               (L + 2K + J + 2)&gt;&gt;2 
               4 
               28 
             
             
                 
               i, n 
               (K + 2J + I + 2)&gt;&gt;2 
               4 
             
             
                 
               e, j, o 
               (J + 2I + X + 2)&gt;&gt;2 
               4 
             
             
                 
               a, f, k, p 
               (I + 2X + A + 2)&gt;&gt;2 
               4 
             
             
                 
               b, g, l 
               (X + 2A + B + 2)&gt;&gt;2 
               4 
             
             
                 
               c, h 
               (A + 2B + C + 2)&gt;&gt;2 
               4 
             
             
                 
               d 
               (B + 2C + D + 2)&gt;&gt;2 
               4 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE VI 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 5 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               5 
               a, j 
               (X + A + 1)&gt;&gt;1 
               3 
               36 
             
             
                 
               b, k 
               (A + B + 1)&gt;&gt;1 
               3 
             
             
                 
               c, l 
               (B + C + 1)&gt;&gt;1 
               3 
             
             
                 
               d 
               (C + D + 1)&gt;&gt;1 
               3 
             
             
                 
               e, n 
               (I + 2X + A + 2)&gt;&gt;2 
               4 
             
             
                 
               f, o 
               (X + 2A + B + 2)&gt;&gt;2 
               4 
             
             
                 
               g, p 
               (A + 2B + C + 2)&gt;&gt;2 
               4 
             
             
                 
               d 
               (B + 2C + D + 2)&gt;&gt;2 
               4 
             
             
                 
               i 
               (X + 2I + J + 2)&gt;&gt;2 
               4 
             
             
                 
               m 
               (I + 2J + K + 2)&gt;&gt;2 
               4 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE VII 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 6 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               6 
               a, g 
               (X + I + 1)&gt;&gt;1 
               3 
               36 
             
             
                 
               b, h 
               (I + 2X + A + 2)&gt;&gt;2 
               4 
             
             
                 
               c 
               (X + 2A + B + 2)&gt;&gt;2 
               4 
             
             
                 
               d 
               (A + 2B + C + 2)&gt;&gt;2 
               4 
             
             
                 
               e, k 
               (I + J + 1)&gt;&gt;1 
               3 
             
             
                 
               f, l 
               (X + 2I + J + 2)&gt;&gt;2 
               4 
             
             
                 
               i, o 
               (J + K + I)&gt;&gt;1 
               3 
             
             
                 
               j, p 
               (I + 2J + K + 2)&gt;&gt;2 
               4 
             
             
                 
               m 
               (K + L + 1)&gt;&gt;1 
               3 
             
             
                 
               n 
               (J + 2K + L + 2)&gt;&gt;2 
               4 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE VIII 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 7 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               7 
               a 
               (A + B + 1)&gt;&gt;1 
               3 
               35 
             
             
                 
               b, i 
               (B + C + 1)&gt;&gt;1 
               3 
             
             
                 
               c, j 
               (C + D + 1)&gt;&gt;1 
               3 
             
             
                 
               d, k 
               (D + E + 1)&gt;&gt;1 
               3 
             
             
                 
               l 
               (E + F + 1)&gt;&gt;1 
               3 
             
             
                 
               e 
               (A + 2B + C + 2)&gt;&gt;2 
               4 
             
             
                 
               f, m 
               (B + 2C + D + 2)&gt;&gt;2 
               4 
             
             
                 
               g, n 
               (C + 2D + E + 2)&gt;&gt;2 
               4 
             
             
                 
               h, o 
               (D + 2E + F + 2)&gt;&gt;2 
               4 
             
             
                 
               p 
               (E + 2F + G + 2)&gt;&gt;2 
               4 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE IX 
             
           
           
             
                 
             
             
               Expressions for generating predictors in mode 8 
             
           
        
         
             
                 
                 
               Expression for 
               Count of 
                 
             
             
               Mode 
               Predictor 
               Generating Predictor 
               Operations 
               Total 
             
             
                 
             
             
               8 
               a 
               (I + J + I)&gt;&gt;1 
               3 
               21 
             
             
                 
               b 
               (I + 2J + K + 2)&gt;&gt;2 
               4 
             
             
                 
               c, e 
               (J + K + 1)&gt;&gt;1 
               3 
             
             
                 
               d, f 
               (J + 2K + L + 2)&gt;&gt;2 
               4 
             
             
                 
               g, i 
               (K + L + 1)&gt;&gt;1 
               3 
             
             
                 
               h, j 
               (K + 2L + L + 2)&gt;&gt;2 
               4 
             
             
                 
               k, l, m, n, o, p 
               L 
               0 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE X 
             
           
           
             
                 
             
             
               Complexity for generating the 4 by 4 predicted block Pm 
             
             
               according to mode m 
             
           
        
         
             
                 
                 
               Count of 
             
             
                 
               Mode 
               Operations 
             
             
                 
               (m) 
               for Pm 
             
             
                 
                 
             
           
        
         
             
                 
               0 
               0 
             
             
                 
               1 
               0 
             
             
                 
               2 
               9 
             
             
                 
               3 
               27 
             
             
                 
               4 
               28 
             
             
                 
               5 
               36 
             
             
                 
               6 
               36 
             
             
                 
               7 
               35 
             
             
                 
               8 
               21 
             
             
                 
               Total: 
               192 operations 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE XI 
             
           
           
             
                 
             
             
               Present expressions and complexity for calculating ESUMP(m) 
             
           
        
         
             
               Mode 
                 
               Count of 
             
             
               (m) 
               Expression for ESUMP(m) 
               Operations 
             
             
                 
             
           
        
         
             
               0 
               (4A + 4B + 4C + 4D) 
               3 
             
             
               1 
               (4I + 4J + 4K + 4L) 
               3 
             
             
               2 
               (ESUMP(0) + ESUMP(1) + 
               4 
             
             
                 
               16)&gt;&gt;5&lt;&lt;4 
             
             
               3 
               (A + 4B + 8C + 12D + 14E + 12F + 
               9 
             
             
                 
               8G + 5H + 8)&gt;&gt;2 
             
             
               4 
               (12A + 8B + 4C + D + 12I + 8J + 
               10 
             
             
                 
               4K + L + 14X + 8)&gt;&gt;2 
             
             
               5 
               (16A + 15B + 10C + 3D + 5I + 3J + 
               9 
             
             
                 
               K + 11X + 8)&gt;&gt;2 
             
             
               6 
               (5A + 3B + C + 16I + 15J + 10K + 
               9 
             
             
                 
               3L + 11X + 8)&gt;&gt;2 
             
             
               7 
               (3A + 10B + 15C + 16D + 13E + 
               8 
             
             
                 
               6F + G + 8)&gt;&gt;2 
             
             
               8 
               (3I + 10J + 15K + 36L + 4)&gt;&gt;2 
               5 
             
             
               Total: 
                 
               60 operations 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
           
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE XII 
             
           
           
             
                 
             
             
               Average of absolute difference between 
             
             
               ESUMP(m) and SUMP(m) when QP is 24 
             
           
        
         
             
               Se- 
               Intra Prediction Mode (m) 
             
           
        
         
             
               quence 
               0 
               1 
               2 
               3 
               4 
               5 
               6 
               7 
               8 
             
             
                 
             
             
               Akiyo 
               0.00 
               0.00 
               0.00 
               1.67 
               1.58 
               1.23 
               1.22 
               1.41 
               1.07 
             
             
               Fore- 
               0.00 
               0.00 
               0.00 
               1.51 
               1.53 
               1.28 
               1.29 
               1.29 
               1.19 
             
             
               man 
             
             
               News 
               0.00 
               0.00 
               0.00 
               1.66 
               1.58 
               1.26 
               1.26 
               1.40 
               1.11 
             
             
               Stefan 
               0.00 
               0.00 
               0.00 
               1.58 
               1.56 
               1.34 
               1.37 
               1.42 
               1.21 
             
             
               Harbour 
               0.00 
               0.00 
               0.00 
               1.44 
               1.51 
               1.39 
               1.30 
               1.29 
               1.27 
             
             
               Night 
               0.00 
               0.00 
               0.00 
               1.53 
               1.54 
               1.26 
               1.27 
               1.29 
               1.18