Chan, YL

Siu, WC

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FAST INTERFRAME TRANSFORM CODING BASED ON CHARACTERISTICS OF TRANSFORM COEFFICIENTS AND FRAME DIFFERENCE Yui-Lam CH-AN and Wan-Chi SIU Department of‘ Electronic Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Tel : (852)-27666229 ABSTRACT The interframe transform coding has been seldom used in practice because of the considerable computational complexity. To reduce the computational complexity, a fast algorithm is proposed in this paper. The al- gorithm reduces the number of operations by limiting the calculation of transform coefficients without siginif- icant quality degradation based on the distribution of transform coefficients. Then, different modes of trans- formation are performed according to  frame difference. This proposed fast interframe coding, like the MPElG, has an asymmetric property with decoding being much faster than encoding. Computer simulations show that this fast algorithm can significantly reduce the comlpu- tational burden in interframe transform coding and is even faster than the MPEG-like coding. 1. INTRODUCTION An interframe discrete cosine transform(DCT) of a block can reduce both the spatial and temporal correlation of the picture elements[l,2]. Besides, the interframe DCT is more suitable in “quick search mode” than the inter- frame hybrid transform/DPCM coding, and also it, is less sensitive to  channel errors [3]. However, the inter- frame transform coding has been seldom used in prac- tice because of the considerable computational com- plexity and the requirement of extensive memory. The three dimensional discrete cosine transform(3D-DC;T) of an 8 x 8 x 8 pixel block, being a separable transform, can be implemented by a series of 1D-DCT along each dimension. Totally 192 1D-DCT per block are required to  perform. To reduce the computational complexity, a fast algorithm is proposed in this paper. The algo- rithm reduces the number of operations by limiting the calculation of transform coefficients based on the prop- erty of the distribution of the transform coefficients. - Acknowledgement : This work was supported by The Croucher Foundation PolyU340/055. Fax : (852)-23628439 And then, only low frequency coefficients are calculated in temporal DCT(a1ong temporal direction) based on the frame difference. This proposed algorithm, like the MPEG, has an asymmetric property with decoding be- ing much faster than encoding. Computer simulations show that this fast algorithm can significantly reduce the computational burden in interframe transform cod- ing without significant quality degradation and is even faster than the MPEG-like coder. 2. THREE DIMENSIONAL DISCRETE COSINE TRANSFORM(3D-DCT) For interframe transform coding, each image sequence is divided into 8 x 8 x 8 pixels and a forward 3D-DCT is carried out on each block, defined as follows: 0-7803-2570-2/95 $4.00 01995 IEEE 449 -- -., (2k  + 1). ( 2 j  + 1). (ai + l )w 16 cos R 16 cos T cos R 16 where z ( k ,  j, i )  is the pixel value in the image sequeiice and C(n)  = & for n = 0, otherwise C(n) = 1. In this paper, Lee’s algorithm [4] is used to perform the ID- DCT. The number of real additions and real multiplica- tions for an N-point sequence of the Lee’s algorithm is ( y ) l o g z N  - N + 1 and ($f)logaN recpectively. The 3D-DCT, being a separable transform, can be imple- mented by cascading three 1D-DCT along each dimen- sion. Totally 192 1D-DCT are required to perform. So the numbers of operations, for N=8, are 5568(129 x ‘29) real additions and 2304(192 x 12) real multiplications. 3. A FRAMEWORK OF PROPOSED FAST ALGORITHM 3.1. 3D-DCT’s coefficients distribution In image sequences of the real world, block motion is usually modest in speed, smooth in the spatial domain Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on June 30,2010 at 08:06:06 UTC from IEEE Xplore.  Restrictions apply. Io00 3500 3000 2500 5 2000 : 1500 1000 500 0 w40-20-10 0 i o  20 30 40 50 magnitude Figure 1: 3D-DCT’s coefficient distribution of X( 1,2,2).  and varying slowly in the temporal domain. This prop- erty has several implications: one of them is related to the magnitude distribution of the coefficients of the SD-DCT; it says that the distribution of the high fre- quency coefficients tends to  zero after quantization. In the block with still motion, the coefficients except the first frame tend to  zero. Even, in the block with modest motion, the coefficients in the third, forth, etc.. frames also tend to  zero, as illustrated in figure 1. 3.2. Low frequency DCT coefficient calculation To perform the three dimensional discrete cosine trans- form coding, the number of operations required is of- ten too high. However, based on the property dis- cussed above, it is unnecessary to calculate all coef- ficients in each block(in low or modest motion block). In other words, the most useful information about the signal is kept by the low frequency, therefore, only low- frequency DCT coefficients are necessary to be com- puted in large portion of the block. In this section, we will discuss the computational save for calculating only low frequency coefficients based on Lee’s algorithm. Figures 2 and 3 show the flowgraphs of the one dimen- sional forward and inverse discrete cosine transforms for only calculating low frequency coefficients respec- tively. The numbers of operations in various lengths for obtaining the required coefficients are shown in ta- ble l. It is seen that the computational complexity will be greatly reduced, especially for the inverse transform. x(0) W) X(2) x(3) x(7) x(6) x(5) x ( 4  (3) Figure 2: Signal flowgraphs for computing forward 8- length DCT to produce only (a) one output coefficient and (b) two output coefficients. NO) X(1) x(2) q30 x(7) X(a) ~ ( 5 )  ~ ( 4 )  (b> Figure 3: Signal flowgraphs for computing inverse 8- length DCT with only (a) one input coefficient and (b) two input coefficients available. 3.3. Motion Detection Table 1: Number of operations for n coefficients of 8- The basic idea of motion detection is to find the degree of motion in the block. In this paper, we propose to use the frame difference to  identify the degree of motion. The frame difference(FD) of each block is defined as: F D  = y,y,y, ( I ( k +  l , j , i )  - I(k,j,i)l where I ( k ,  j ,  i) is the pixel value in the image sequence. length DCT 7 7 6  a=o j = o  k = O  450 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on June 30,2010 at 08:06:06 UTC from IEEE Xplore.  Restrictions apply. 4. THE NEW PROPOSED ALGORITHM Encoding Class add. mult. Considering all discussions above, we can now propose a fast 3D-DCT coding and decoding scheme. Decoding max. number max. number of mult,. of add. 4.1. Description of encoding Since, a large number of transform coefficients are equal to  zero after quantization, it is not necessary to  calcu- late all transform coefficients in order to  reduce the computational burden. Based on the frame difference of each block, all image blocks are classified into one of the following four classes, where 3 is the predefined threshold for i=1,2 and 3. Class 1(FD < T1):they can be identified as non moving blocks by the motion detector. They usually belong to  the unchanged area like the background in images. In other words, the pixel value of each frame is nearly equal, so only the first frame 2D-DCT is needed to  perform(16 1D-DCT). Classes 2(Tl 5 F D  < T2):these blocks are origi- nally identified as low moving blocks. Their transform coefficients except the ones in the first frame are nearly zero after 3D-DCT. For such blocks, all eight frames 2D-DCT are performed, and only the lowest coefficient in temporal DCT is calculated as shown in figure 2(a). Classes 3(Tz 5 F D  < T3):these blocks are identified as modest moving blocks. But, their transform coeffi- cients except the ones in the first and second frames are nearly zero. For such blocks, all eight frames 2D-DCT are performed, and the first and second low-frequency coefficients in temporal DCT are calculated as shown in figure 2(b). Class 4(T3 FD):these blocks are considered as high moving block, a large number of transform coef- ficients have significant value. So all coefficients are required to  calculate. The transformed block is quantized and scanned ac- cording to first spatial, second temporal zig-zag scan- ning. Then, a VLC is applied and finally the encoding signal is transmitted. 4.2. Description of decoding The bitstream goes through the VLC decoding, and onward to  inverse first spatial, second temporal zig-zag scanning and inverse quantization. Before performing each separate inverse 1D-DCT, coefficients in each row, column and temporal direc- tion are scanned. Different modes of 1D-DCT are per- formed as summarized below. 1. If all coefficients are equal to  zero, no inverse 1D- DCT operation is required. Otherwise, the oper- ation is processed to step(2). 464 1824 832 5568 2303 2. If only the lowest frequency coefficient has value, the inverse 1D-DCT is calculated as shown in fig- ure 3(a). Otherwise, the operation is processed to  step(3). 3. If only the first and second lowest frequency coef- ficients are not equal to zero, the inverse 1D-DCT is calculated as shown in figure 3(b). Otherwise, the operation is processed to step(4). 4. A fully inverse 1D-DCT is needed to  perform. 5. COMPUTATIONAL COMPLEXITY Different classes perform different modes of forward 3D-DCT in encoding. The numbers of operations in different classes are shown in table 2. In decoding, the number of operations is based on the number of zero coefficients in the block. The number of addi- tions and multiplications required are 14N2 + 2’9N3 and 7Nz + 12N3 respectively, where Nz is the num- ber of inverse 1D-DCT of figure 3(b) required and N3 is the number of fully inverse 1D-DCT required within the block. The maximum number of operations is also shown in table 2. From table 2, an asymmetric prop- erty with decoding much faster than encoding is shown. The number of additions required for calculating FD per block is 847. 6. EXPERIMENTAL RESULTS A series of computer simulations have been conducted to  evaluate the performance of our proposed algorithm. The video sequences “football” , “table tennis” and “salesman” have been used. Table 3 shows the nuniber of blocks in different classes. The computational save compared with the conventional 3D-DCT with frame difference classification is shown in table 4. The com- putational complexity is significantly reduced by, about 45 1 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on June 30,2010 at 08:06:06 UTC from IEEE Xplore.  Restrictions apply. 7. CONCLUSIONS foot ball table tennis Table 3: Number of blocks in different classes 1097 1830 4 2132 1830 2493 4726 1 1556 I 2179 1 916 4814 I 1582 1 1737 1 734 Table 4: Comput,at,ional save in encoding and decoding Table 5: Number of operations in our proposed coding algorithm and MPEG like coding151 with 8 x 8 block size and w=8. MPEG like coding Encoding Decoding Our Droposed algorithm I I 1 salesman I 4940 1 1637 I 1183 I 498 1 25%-32% and 60%-78%, in encoding and decoding re- spectively, with only 0.2-0.5 dB degradation. The computational complexity of our proposed cod- ing algorithm is also compared with the MPEG like coder[5]. The comparisons presented in this paper are based on a MPEG coding with IPPPPPPP group of picture (GOP). In MPEG coding, it requires 8 for- ward 2D-DCT, 7 inverse 2D-DCT and 128 x 7 pixel additions/subtractions for one GOP. Besides, it also re- quires 7 ( N x N )  x ( 2 ~ + 1 ) ~  additions for full search with the maximum displacement w for one GOP. In decod- ing, it only requires 8 inverse 2D-DCT and 64 x 7 pixel additions for one GOP. Table 5 compares the compu- tational complexity of our proposed algorithm and the MPEG-like coding. It shows that our proposed algo- rithm is much faster than the MPEG method especially in decoding, while in table 5, the numbers of additions and multiplications of our proposed algorithm in de- coding are 1.91-3.52 and 1.67-3.08 times less than that for t,he MPEG-like coder respectively, and the numbers of additions and multiplications of our proposed algo- rithm are about 3.2 and 1.8 times less than that for MPEG-like coder in encoding. A new fast interframe discrete cosine transform coding is proposed to compensate the computational burden of the interframe transform coding. This proposed fast algorithm uses the distribution of the 3D-DCT trans- form coefficients, then only low frequency coefficients are calculated in temporal DCT based on the frame dif- ference. This proposed algorithm can reduce by, about 25%-32% and 60%-78% computational complexity of traditional 3D-DCT in encoding and decoding respec- t8ively without significant quality degradation of the re- constructed image sequences. The computational bur- den is even much lower than that required for MPEG- like coder, especially in decoding. Like the MPEG, the proposed algorithm has an asymmetric property with decoding being much faster than encoding. Thus, this approach is certainly an efficient technique for asym- metric applications which require frequent use of the decoding process, but for which the encoding process is performed once and for all at the production of the program. This proposed algorithm can still be fur- ther improved for combining with some fast DCT algo- rithms[6,7] which reduce the operations for calculating t’he low-frequency DCT components, a fruitful direc- tion for further investigation. 8. REFERENCES J .  A.Roese and W. K. 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Wang, “Pruning the fast discrete cosine transform”, IEEE Transactions on Communications, vol-39, May 1991, pp.640-643. gust 1976,pp.172-179. 452 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on June 30,2010 at 08:06:06 UTC from IEEE Xplore.  Restrictions apply. 

Fast interframe transform coding based on characteristics of transform coefficients and frame difference

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