Adaptive bit-reduced mean absolute difference criterion for block-matching algorithm and its VLSI design

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1 Adaptive bit-reduced mean absolute difference criterion for block-matching algorithm and its VLSI design Hwang-Seok Oh, MEMBER SPIE Korea Advanced Institute of Science and Technology Department of Computer Science Kusong-dong, Yousong-gu Taejon, , Korea Yunju Baek Ansung ational University Department of Computer Engineering 67 Seokjeong-ri, Ansung-up, Ansung-gun Kyunggido, , Korea Heung-Kyu Lee Korea Advanced Institute of Science and Technology Department of Computer Science Kusong-dong, Yousong-gu Taejon, , Korea Abstract. An adaptive bit-reduced mean absolute difference (ABRMAD) is presented as a criterion for the block-matching algorithm (BMA) to reduce the complexity of the very large scale integration (VLSI) implementation and to improve the processing time. The ABRMAD uses the lower pixel resolution of the significant bits instead of full-resolution pixel values to estimate the motion vector (MV) by examining the pixels in a block. Simulation results show that the 4-bit ABRMAD has competitive mean square error (MSE) results and a half less hardware complexity than the mean absolute difference (MAD) criterion. It has also better characteristics in terms of both MSE performance and hardware complexity than the MiniMax criterion and has better MSE performance than difference pixel counting (DPC), binary block matching with edge map (BBME), and bit-plane matching (BPM) with the same number of bits Society of Photo-Optical Instrumentation Engineers. [S (98) ] Subject terms: block-matching algorithm; motion estimation; very large scale integration. Paper received Mar. 6, 1998; revised manuscript received Aug. 10, 1998; accepted for publication Aug. 14, Introduction Motion estimation ME techniques have an important role in video coding due to their capability to reduce the temporal redundancies residing between successive frames. Most of the ME techniques developed so far are blockmatching algorithms BMAs that estimate a motion vector MV on a block-by-block basis. In BMAs, the current frame is partitioned into nonoverlapping equal-sized rectangular blocks and all pixels in one block are assumed to have the same motion displacement. The MV for each block is estimated by searching for its highest correlation with an associated block within the search area in the reference frame. A general search algorithm is the full-search BMA FSBMA, which obtains the optimal result by searching exhaustively for the best matching block within a search window. Many video coding standards such as H.261 Ref. 1, H.263 Ref. 2, and Motion Picture Experts Group MPEG -1,2 Ref. 3 have adopted the ME technique. The enormous amount of computational demand for the ME, especially FSBMA, prevents the software implementation from running in a timely fashion in real-time video coding systems. Therefore, the very large scale integration VLSI implementation of the ME is indispensable for such systems. Owing to the regularity and simplicity of matching operations, the FSBMA is suitable for VLSI implementation, 4 6 and thus it is the most widely used for the ME. Three factors determine the performance of a BMA: 1 search method, 2 search range, and 3 block-matching criteria. Many search methods have been investigated in the literature Among them, the full-search method provides an optimal solution and has low control overhead. The block-matching criterion adopted in a search method affects the accuracy of the estimation. Since the matching is a main operation of the VLSI architecture for the BMA, a hardware-efficient matching criterion is essential. Thus several block-matching criteria to reduce hardware requirements have been investigated In this paper, we focus on the block-matching criterion to propose a new scheme to reduce the hardware requirement and speed up the VLSI implementation with acceptable video performance. As the estimation in the BMA was accomplished with block-by-block comparison, which is performed pixel by pixel, the basic operation of the BMA is a pixel comparison. Since the pixel comparison is a bitwise operation, if the number of bits is reduced, the corresponding hardware requirement can be reduced. Taking this point into consideration, we propose a more hardware-efficient blockmatching criterion, called adaptive bit-reduced mean absolute difference ABRMAD. The rest of the paper is organized as follows. In Sec. 2, various well-known block-matching ME criteria and some lower bit resolution criteria are briefly discussed before presenting the ABRMAD criterion. In Sec. 3, we present a new criterion ABRMAD for the BMA and its features. In Sec. 4, the performance of the ABRMAD is evaluated and compared with other methods such as mean absolute difference MAD, MiniMax, difference pixel counting DPC, binary block-matching with edge map BBME, and bit Opt. Eng. 37(12) (December 1998) /98/$ Society of Photo-Optical Instrumentation Engineers

2 plane matching BPM. Finally, the hardware characteristics synthesized using VLSI design tools are presented in Sec Criteria for Block-Matching ME Many BMA criteria have been presented to find the best matching block among the candidate blocks in the search area. The normalized cross-correlation function 7 CCF, mean-square difference 8 MSD, and MAD Ref. 9 are well-known criteria. Because the CCF and MSD require the multiplication, both are too complex and their hardware realization seems far from being feasible. Thus the MAD criterion is widely used for ME and it has been implemented with VLSI. But the hardware implementation of the MAD with full resolution of pixels is still computationally expensive. Therefore, new matching criteria, such as DPC Ref. 12, BBME Ref. 13, and BPM Ref. 14, have been presented with lower pixel resolution to reduce the hardware complexity of the MAD. In this section, we briefly describe the MAD and several criteria that use lower resolution pixel data. Assume that R(i, j) is pixel intensity at the (i, j) position of the current block in the current frame, and S(i u, j v) is pixel intensity at the (i, j) location of the candidate block in the reference frame, shifted by the u pixels and v lines within the search area. For the best match, the displacement (u,v), called the MV, represents the estimate of the displacement in horizontal and vertical directions, respectively. In the following criteria, the size of block is and the position (u,v) lies within the search area. 2.1 MAD In the MAD criterion, 9 the MV is determined by the smallest MAD(u,v) for all possible displacements (u,v) within the search area. MAD u,v 1 2 i 1 R i, j S i u, j v. The MAD is the most widely used matching criterion due to its lower computational complexity. 2.2 Minimized Maximum Error (MiniMax) In this recently developed method, 11 the smallest MiniMax(u,v) within the search area is chosen for the best match. MiniMax u,v R i, j S i u, j v max. Chen et al. 11 reported that the MiniMax criterion requires 15% less hardware than the conventional MAD criterion while it maintains an acceptable video performance. 2.3 DPC The DPC criterion 12 is defined as the number of pixels whose 2-bit requantized values are matched. It can be described as follows: 1 2 DPC u,v i 1 AD XOR R k i, j S k i u, j v, where R k (i, j) and S k (i u, j v) are the requantized values of R(i, j) and S(i u, j v), respectively. The requantized pixel resolution is lower than the original resolution; thus the DPC can require less hardware than the MAD. The requantized value P k (i, j) is obtained as if p i, j t 10 if t p i, j 0 P k i, j if 0 p i, j t 00 if p i, j t, where p(i, j) is pixel intensity at position (i, j). For each block, the value t used in Eq. 4 can be derived using t 3 2M i 1 p i,j m, where m denotes the mean of the block. 2.4 BPM In this method, 13 the current and the reference frames are transformed into binary-valued pixel frames. For two binary blocks, the matching criterion, called the BPM, is as follows: BPM u,v 1 2 i XOR Rˆ i, j Ŝ i u, j v, 6 where Rˆ (i, j) and Ŝ(i u, j v) denote pixel values after the transformation to 1-bit frames. The MV is defined by the (u,v) for which BPM(u,v) is minimum. To transform the current and reference frames, they apply the convolution kernel K to the original frame F to obtain the filtered version G. The pixels of the binary frame Fˆ are given by Fˆ i, j 1 if F i,j G i,j 7 0 otherwise. They use the convolution kernel K, for example, given by j 1 if i, j 1,4,8,12,16 K i, otherwise. 2.5 BBME The BBME estimates 14 the MV using the binary edge map to reduce the complexity of hardware implementation. For the comparison of the current block R and a candidate block S, the binary edge maps of blocks Rˆ and Ŝ are com- Optical Engineering, Vol. 37 o. 12, December

3 Fig. 1 Example of selected bits for pixel comparison using (a) MAD, (b) RBMAD with 4 bits, and (c) ABRMAD with 4 bits. pared. The edge maps of the current frame and the reference frame are obtained using preprocessing. This method can reduce the complexity of hardware because of using 1 bit/pixel for pixel comparison. The matching criterion is as follow: BBME u,v i 1 XOR Rˆ i, j,ŝ i u, j v. The MV is the displacement that is pointed to by the smallest BBME(u,v). 2.6 Reduced Bit Mean Absolute Difference In reduced-bit mean absolute difference 15 RBMA, for any n-bit pixel value A, let A p:q be p q 1 bits A p A q in the binary representation of A A n 1 2 n 1 A A 1 2 A 0, where n 1 p q 0. The RBMAD criterion is described as follows: RBMAD k u,v i 1 R i, j n 1:n k S i u, j v n 1:n k, 9 10 where k is a given factor that should be n k 0. Similar to MAD, the MV is determined by the smallest RBMAD k (u,v) for all possible displacements (u,v) within the search area. Since the RBMAD uses only the upper k bits of pixels, the RBMAD is equivalent to the MAD when k n. This criterion can reduce hardware complexity depending on k but causes the significant degradation of video quality. 3 ABRMAD Criterion The RBMAD criterion is very effective to reduce the hardware complexity and to improve the processing speed. But the degradation of video quality is a critical problem. The video quality of the RBMAD applied for video sequences that contain large dark area, that is, pixels have effective values at close to the least significant bit LSB, is degraded seriously. To overcome the problem of performance degradation, if only effective bits are compared by examining the pixels of the block, the significant degradation of video quality can be remedied. Taking this point into consideration, an efficient matching criterion, ABRMAD, is proposed. In the ABRMAD, for any n-bit pixel A, selected k bits are represented as A m:m k 1 similar to the RBMAD. But the most significant bit position m is obtained by examining the current block in contrast to the RBMAD, where m is set to the most significant bit MSB of the pixel i.e., m n 1. The ABRMAD criterion is described as follow: ABRMAD m,k u,v i 1 R i, j m:m k 1 S i u, j v m:m k 1, 11 where k(n k 0) represents how many bits are used and m is the effective MSB position in the range n 1 m 0. Similar to the RBMAD, the MV is determined by the smallest ABRMAD m,k (u,v) for all possible displacements (u,v). The effective MSB position m is obtained by looking at the current block. For pixels in the block, the nonzero MSB position of the pixel that has the largest intensity is set to m. In case of k 1 m, the k bits from the m to the m k 1 bit positions are used. In the other case (k 1 m), the k bits from the k 1 to the 0 bit positions are used. The number of bit bit width k is predetermined by considering the required quality and hardware complexity. An example for pixel comparisons of the criteria MAD, RBMAD with 4 bits, and ABRMAD with 4 bits is shown in Fig. 1, where the largest pixel value of the current block is 45( ), n 8, and k 4. Thus the effective MSB position m is set to 5. Therefore, the 4-bit pixel values positioned from 5 down to 2, instead of 8-bit pixel values, are compared in the ABRMAD. In the other criterion, 3274 Optical Engineering, Vol. 37 o. 12, December 1998

4 MAD, all n bits are used to compare the pixels and 4 MSB bits are used in the RBMAD. If k n, the ABRMAD is the same as the MAD and the RBMAD. The choice of the most effective bit position m can be affected by the noise, so the performance of the ABRMAD can be degraded by a large value of the noise pixel. To overcome this circumstance, a smoothed version of the ABRMAD SABRMAD is also presented. In this scheme, the effective MSB m is determined by examining the smoothed current block, which is obtained by averaging the neighboring pixels. When the ABRMAD is implemented in VLSI, we have the two following advantages: 1. Reductions in VLSI area. In the ABRMAD, pixel comparison is a k-bit subtracter, which is implemented 16 by a k-bit adder in VLSI. The comparison requires O(k) bit hardware with a trivial ripple carry adder. In this case, if k is reduced to 50%, the comparison hardware is reduced to 50%. However, if the comparison is implemented with a fast method, e.g., a carry look-ahead adder, the hardware reduction becomes larger. 2. Speedup in VLSI operation. The main operation of the ME is the pixel comparison to calculate the sum of absolute differences of the pixels. The comparator, in general, is composed of a subtracter, an absolute function, and an accumulator. If the n-bit subtracter is constructed with a bit-serial adder, such as the ripple carry adder, the comparison becomes a bitserial operation. Thus, if k is reduced, the hardware runs faster. If one uses a fast method such as a carry look-ahead adder, the speedup would not be significantly high in comparison with that achieved using the ripple carry adder. Table 1 Average MSE performance of each matching criterion. Test Video Sequences Matching criterion Miss America Carphone Foreman Claire MAD (8 bits) MiniMax (8 bits) DPC (2 bits) BBME (1 bit) BPM (1 bit) RBMAD ABRMAD SABRMAD 1 bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits Optical Engineering, Vol. 37 o. 12, December

5 Table 2 Average PSR and bit rate of each criterion for BMA implemented on the H.263 standard with fixed quantizer QP 8. Test Video Sequences Miss America Carphone Foreman Claire Matching Criterion PSR Bit Rate PSR Bit Rate PSR Bit Rate PSR Bit Rate MAD (8 bits) MiniMax (8 bits) DPC (2 bits) BBME (1 bit) BPM (1 bit) RBMAD ABRMAD SABRMAD 1 bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits Experimental Results Four quarter common intermediate format QCIF, , 30 frames/s video sequences, called Miss America, Carphone, Foreman, and Claire were used to investigate the performance of the ABRMAD criterion. Two video sequences, Miss America and Claire, contain a speaker with the slow movements that are typical in low-bit-rate video applications such as videophones and videoconferencing. The sequences Carphone and Foreman have a little moderate motion field, which is caused by the movements of the objects and the effects of the video camera. The experimental results are compared with those of existing ME criteria such as MAD, MiniMax, RBMAD, BPM, DPC, and BBME. The mean square error MSE per pixel is used for a performance measure of the ME criteria. Also, the peak SR PSR and bit rate are compared to show the performance of the criterion implemented on H.263. The MV for a block size is estimated within the 16 allowable displacement. The average performance of each matching criterion is summarized in Table 1. The ME for the pure matching criteria is performed within only luminance components. The numbers of bits, used for ME, of DPC, BBME, and BPM are 2, 1, and 1 bit s, respectively. The motioncompensated frame is used as a reference frame. The MSE performances of RBMAD, ABRMAD, and SABRMAD are described according to how many bits are used to compare the pixels in a block. The three matching criteria RBMAD, ABRMAD, and SABRMAD, which use 8 bits, are the same as the MAD. The MSE performances of the ABRMAD with small numbers of bits, such as 5 or 4 bits, are similar to or slightly worse than those of the MAD, but they are better than those of the RBMAD with the same number of 3276 Optical Engineering, Vol. 37 o. 12, December 1998

6 Table 3 Average PSR and bit rate of each criterion for BMA implemented on the H.263 standard with fixed quantizer QP 16. Test Video Sequences Miss America Carphone Foreman Claire Matching Criterion PSR Bit Rate PSR Bit Rate PSR Bit Rate PSR Bit Rate MAD (8 bits) MiniMax (8 bits) DPC (2 bits) EDGE (1 bit) BPM (1 bit) RBMAD ABRMAD SABRMAD 1 bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits bits and MiniMax. In particular, from the results of the video sequences Miss America and Claire, the MSE performances of the ABRMAD with a small number of bits are very similar to those of MAD. Also, the results show that the ABRMAD with the same number of bits has a better MSE performance than the SABRMAD, which performs preprocessing, smoothing using of the averaging of the 3 3 adjacent pixels, to be robust to a noise signal that has a large pixel value. The results also show that the MSE performances of the ABRMAD with 1 or 2 bits are better than those of the DPC, BBME, and BPM. In video sequences with low motion fields, the performance gains are not great, but in the sequences Carphone and Foreman, the MSE performance of the ABRMAD with 1 bit is much better than the performance of BBME and BPM. Also, the ABRMAD with 2 bits has good MSE performance comparing with DPC. The pure MSE performance of the proposed ABRMAD shows that it is a good ME criterion for low-complexity hardware. The proposed method is also implemented on the H.263 standard to show the interactive behaviors of the ME strategies. The results are obtained using the Telenor TM software coder 17 on the test video sequences, with a fixed quantizer, with no advanced mode and with the search range of 15 pixels. In the simulation, we set the quantizer QP to 8, 16, 24 and compare the PSR and the bit rate per second in kilobits per second of each method, since the decoded video quality is greatly dependent on the bit-rate regulation scheme. The simulation results are summarized in Tables 2, 3, and 4. From the tables, we can see that the PSR of each criterion is very similar, but the bit rate varies according to the accuracy of the ME and the coding efficiency of the other parts of the H.263 standard. Generally, the bit rate is low when the criteria with full pixel resolution are used. In Optical Engineering, Vol. 37 o. 12, December

7 Table 4 Average PSR and bit rate of each criterion for BMA implemented on the H.263 standard with fixed quantizer QP 24. Test Video Sequences Miss America Carphone Foreman Claire Matching Criterion PSR Bit Rate PSR Bit Rate PSR Bit Rate PSR Bit Rate MAD (8 bits) MiniMax (8 bits) DPC (2 bits) BBME (1 bit) BPM (1 bit) RBMAD ABRMAD SABRMAD 1 bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits bit bits bits bits bits bits bits bits the RBMAD, ABRMAD, and SABRMAD criteria, the bit rate is decreasing as they use more number of bits. In the Miss America sequence, an exception is observed, which is caused by other parts of the H.263 standard such as coding mode decision, half-pixel ME, and entropy coding. The results show that the bit rates of the ABRMAD, RBMAD, and SABRMAD are very similar when the same number of bits is used. Compared with the other criteria, such as DPC, BBME, BPM, and MiniMax, the bit rate generated from ABRMAD with 1 or 2 bits is lower in some video sequences and higher in others. Because the results from the H.263 software coder are greatly dependent on the other parts of the H.263 standard, the quality of the ME criterion that estimates the MV is slightly inaccurate and is compensated by other parts. From the simulation, all of the matching criteria that use lower pixel resolutions can be used for the BMA without significant degradation of quality. 5 VLSI Design The VLSI synthesis for the conventional MAD and the proposed ABRMAD were implemented by Compass VLSI design automation tools using the architecture described in Ref. 4. They are described and tested with the high-level hardware description language, Verilog, and its simulator. Then, the layout for the synthesis was automatically generated by the application-specific integrated circuit ASIC compilers. Similarly, the timing aspect of the synthesis was tested using a critical path analyzer in the tools. The VLSI design for the ABRMAD consists of a comparator to detect the effective MSB, two bit selectors, and processing elements PEs to estimate the MV, as shown in 3278 Optical Engineering, Vol. 37 o. 12, December 1998

8 Fig. 2 Block diagram for the VLSI ABRMAD architecture. Fig. 2. The comparator determines the largest pixel value and sets the effective MSB position. Two bit selectors pass k bits of pixels from the effective MSB position m to m k 1 in the current block and the search area. The PE architecture compares the current block with the candidate block and generates the MV. The VLSI structure described in Ref. 4 was used for the PE architecture, as shown in Fig. 3, which is for an 8 8 current block. Each PE element calculates the sum of absolute differences of the corresponding pixels between the current block and a candidate block. In the figure, the index CB denotes sequences of current block data, SWL and SWR denote sequences of reference frame data from different portions of the search area. The pixels in the left half portion and the right half portion of the search area are passed through the SWL and SWR, respectively. The pixels in the current block are passed through from PE0 to PE7 at each cycle time. The pixels in the search area are broadcast to all PEs. The detailed data-flow diagram and its features are described in Ref. 4. Each PE element consists of an accumulator to accumulate of sum of the absolute differences, an absolute difference component composed of a subtracter, and an absolute function to calculate the difference of the two pixels. The PE architecture can be easily scaled to perform the ME with a large number of blocks. The structure for the ABRMAD is similar to that of the RBMAD except for a single comparator, as shown in Fig. 2. The overhead for the ABRMAD compared with that of the RBMAD is so minor that it can be ignored. But, as shown in Table 1, the MSE performance gain is very high. With the same video quality as MiniMax, the ABRMAD can be implemented with significantly less VLSI complexity. With 0.8- m complementary metal-oxide semiconductor CMOS standard cell technology, the characteristics of the synthesized VLSI design are shown in Table 5. The table shows that the fewer bits we use, the smaller the hardware cost and the faster the speed we can achieve. Examining Tables 1 and 5, we can observe the trade-off between video quality and hardware cost in the ABRMAD. As an example, consider the case of the 4-bit ABRMAD. With negligible degradation of video performance, we can implement the ME with 57% smaller hardware area and 34% faster speed than that using MAD criterion. Thus, if Fig. 3 VLSI architecture for full-search BMA (Ref. 4). Optical Engineering, Vol. 37 o. 12, December

9 Table 5 Performance of the VLSI implementation. Criterion Area (mil 2 ) Area ABRMAD Area MAD (%) Speed per Cycle (ns) Speed ABRMAD Speed MAD (%) MAD bit ABRMAD bit ABRMAD bit ABRMAD bit ABRMAD bit ABRMAD bit ABRMAD bit ABRMAD cost-effective real-time applications are required, the presented criterion is very suitable for the VLSI implementation of the ME. 6 Conclusion A new ME criterion called ABRMAD that is very suitable for an efficient VLSI implementation without a significant degradation of video quality was presented. Two main advantages of the proposed ABRMAD criterion are 1 much VLSI area is saved and 2 operational speed is increased. To show the hardware efficiency of the proposed scheme, we synthesized the ME using the ABRMAD criterion and compared it with the statistics of the conventional MAD criterion. Through intensive simulation tests, we also showed that the ABRMAD has competent video performance, like the MAD. As a result, the new scheme can be adopted in VLSI implementation of real-time video applications. Acknowledgments The financial support from the Korea Telecom in part in 1998 is gratefully acknowledged. References 1. M. Liou, Overview of the P 64 kbit/s video coding standard, Commun. ACM 34 4, R. Schaphorst, ITU-T Recommendation H.263, Video coding for low bitrate communication, ITU-T Report SG15 WP15/1 ov D. L. Gall, MPEG: a video compression standard for multimedia application, Commun. ACM 34 4, K. Yang, M. Sun, and L. Wu, A family of VLSI designs for the motion compensation block-matching algorithm, IEEE Trans. Circ. Syst , T. Komarek and P. Pirsch, Array architecture for block-matching algorithms, IEEE Trans. Circ. Syst , L. D. Vos and M. Stegherr, Parameterizable VLSI architectures for the full-search block-matching algorithm, IEEE Trans. Circ. Syst , H. G. Musmann, P. Pirsch, and H. Grallert, Advances in picture coding, Proc. IEEE 73 4, J. R. Jain and A. K. Jain, Displacement measurement and its application in interframe image coding, IEEE Trans. Commun , T. Koga, K. linuma, A. Hirano, Y. Iijima, and T. Ishiguro, Motioncompensated interframe coding for video conferencing, in Proc. at. Telecomm. Conf., pp. G5.3.1 G5.3.5, ew Orleans, LA R. Srinivasan and K. R. Rao, Predictive coding based on efficient motion estimation, IEEE Trans. Commun. 33 8, M.-J. Chen, L.-G. Chen, T.-D. Chiueh, and Y.-P. Lee, A new blockmatching criterion for motion estimation and its implementation, IEEE Trans. Circ. Syst. Video Technol. 5 3, S. Lee, J. M. Kim and S.-I. Chae, ew motion estimation using low-resolution quantization for MPEG2 video encoding, in Proc. IEEE Workshop on Signal Processing, pp M. M. Mizuki, U. Y. Desai, I. Masaki, and A. Chandrakasan, A binary block-matching architecture with reduced power consumption and silicon area requirement, in Proc. IEEE ICASSIP, pp B. atarajan, V. Bhaskaran, and K. Konstantinides, Low-complexity block-based motion estimation via one-bit transforms, IEEE Trans. Circ. Syst. Video Technol. 7 4, Y. Baek, H.-S. Oh, and H.-K. Lee, ew block-matching criterion for efficient VLSI implementation of motion estimation, Electro. Lett , K. Hwang, Computer Arithmetic: Principles, Architectures, and Design, John Wiley & Sons, ew York Telenor H.263 Software, Telenor Research at Brukere/DVC/H263 software/. 18. H. Gharavi and M. Mills, Block matching motion estimation algorithm new results, IEEE Trans. Circ. Syst. 37 5, Hwang-Seok Oh received his BS degree in computer science from Kyungpook ational University, Korea, in 1992 and his MS degree in computer science from the Korea Advanced Institute of Science and Technology (KAIST) in He is currently a PhD candidate in the department of computer science at the KAIST. He is a member of IEEE, ACM, and SPIE. His research interests include video coding, multimedia systems, and very large scale integration architectures for signal processing. Yunju Baek received his BS degree in computer science from the Korea Institute of Technology in 1990 and his MS and PhD degrees in computer science from the Korea Advanced Institute of Science and Technology (KAIST) in 1992 and 1997, respectively. From 1997 to 1998 he was the research staff for Handi Software Inc. and in 1998 he became an assistant professor with the Ansung ational University. His research interests include verylarge scale integration architecture, computer architecture, parallel processing, and multimedia system architecture Optical Engineering, Vol. 37 o. 12, December 1998

10 Heung-Kyu Lee received his BS degree in electronics engineering from the Seoul ational University, Korea, in 1978 and his MS and PhD degrees in computer science from the Korea Advanced Institute of Science and Technology (KAIST) in 1981 and 1984, respectively. From 1984 to 1985 he was a postdoc at the University of Michigan, Ann Arbor. In 1986 he became a professor with KAIST, where since 1990 he has been a research staff member at the Satellite Research Center. He is a member of IEEE and ACM. His major interests are very large scale integration and parallel processing, fault-tolerant and real-time computing, and multimedia systems. Optical Engineering, Vol. 37 o. 12, December

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