Motion Compensated Lossy-to-Lossless Compression of 4-D Medical Images Using Integer Wavelet Transforms

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1 132 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 9, NO. 1, MARCH 2005 Motion Compensated Lossy-to-Lossless Compression of 4-D Medical Images Using Integer Wavelet Transforms Ashraf A. Kassim, Member, IEEE, Pingkun Yan, Student Member, IEEE, Wei Siong Lee, and Kuntal Sengupta Abstract This paper proposes a method for progressive lossy-to-lossless compression of four-dimensional (4-D) medical images (sequences of volumetric images over time) by using a combination of three-dimensional (3-D) integer wavelet transform (IWT) and 3-D motion compensation. A 3-D extension of the set-partitioning in hierarchical trees (SPIHT) algorithm is employed for coding the wavelet coefficients. To effectively exploit the redundancy between consecutive 3-D images, the concepts of key and residual frames from video coding is used. A fast 3-D cube matching algorithm is employed to do motion estimation. The key and the residual volumes are then coded using 3-D IWT and the modified 3-D SPIHT. The experimental results presented in this paper show that our proposed compression scheme achieves better lossy and lossless compression performance on 4-D medical images when compared with JPEG-2000 and volumetric compression based on 3-D SPIHT. Index Terms Cube matching algorithm, four-dimensional (4-D) medical image, integer wavelet transform (IWT), lossy-tolossless compression, motion compensation, three-dimensional (3-D) set-partitioning in hierarchical trees (SPIHT). I. INTRODUCTION MEDICAL IMAGES have become essential information resources in diagnostic processes. There is a gradual shift away from the inefficient and costly process of moving image hard copies between practitioners toward digital imaging for viewing and storing medical images. This paper focuses on four-dimensional (4-D) medical images which are obtained by medical imaging techniques like magnetic resonance (MR), computerized tomography (CT), positron emission tomography, and ultrasound. They describe the temporal evolution of a dynamic phenomenon as a sequence of three-dimensional (3-D) volumetric images. Volumetric images are essentially two-dimensional (2-D) image slices that represent cross sections of a subject. A precise representation of a 3-D model requires a large number of slices and, therefore, a good amount of memory. This problem of memory storage is further exacerbated when dealing with 4-D data sets. Typically, even a few seconds of volumetric cardiac image sequences can occupy a few hundred mega-bytes of storage space. Also, with the Manuscript received October 9, 2003; revised March 12, 2004 and July 28, The authors are with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore , Singapore ( eleashra@nus.edu.sg). Digital Object Identifier /TITB increasing popularity of telemedicine, large amounts of data need to be transmitted over channels with limited bandwidth. Hence, there is a need for compressing such 4-D data sets. Compression techniques can be classified broadly into lossless and lossy techniques. Lossless techniques allow exact reconstruction of the original image, whereas lossy techniques achieve higher compression ratios. Although lossy compression is sometimes acceptable in medical image compression, lossless compression is preferred [1] [3]. Since lossless compression does not degrade the image, it does not hinder accurate diagnosis. While lossy compression techniques may lead to errors in diagnosis, as they can introduce artifacts. Furthermore, there exist several legal and regulatory issues that favor lossless compression in medical applications. Wavelet-based medical image compression algorithms [1] [8] operate on 2-D [2], [8], or on 3-D data [1], [3], [4], [6]. Since 4-D image data can be represented as multiple 3-D volumes, it is possible to code these 3-D volumetric images independently. However, such 3-D methods do not exploit the dependencies that exist among pixel values in different volumes. Four-dimensional medical data is normally temporally smooth and a better approach is to consider the whole set of volumetric images as a single 4-D data set. Several methods that utilize dependencies in all four dimensions have been proposed [5], [7]. These methods use the 4-D discrete wavelet transform (DWT) in a lossy compression scheme. In this paper, we propose a progressive lossy-to-lossless compression algorithm that exploits the dependencies in the time dimension by using 3-D motion compensation. A lossy-to-lossless compression scheme can offer better image quality with increasing bit rate until the original image is recovered [1], [9]. A problem associated with existing 4-D wavelet transform-based compression methods is that all 3-D volume images need to be decoded even if only one of them is to be viewed. Meneg-az et al. [10] proposed a solution for this problem in 3-D with a new compression scheme, which encodes volumetric images by using the 3-D wavelet transform but decodes 2-D slices independently. In this paper, instead of extending 3-D wavelet coding to 4-D, we use 3-D motion estimation to decorrelate data in the time dimension. In our method, consecutive 3-D volumetric images are divided into 3-D key and 3-D intermediate frames (i.e., volumetric images), which is similar to video coding algorithms [11]. The 3-D key frames are used as the reference to predict the intermediate frames and the prediction errors are represented in the 3-D residual frames. Our proposed fast 3-D cube matching algorithm exploits the redundancy that exists in 4-D data sets /$ IEEE

2 KASSIM et al.: MOTION COMPENSATED LOSSY-TO-LOSSLESS COMPRESSION OF 4-D MEDICAL IMAGES USING IWTs 133 Fig. 1. Our proposed scheme for coding 4-D medical images. for efficient compression and simplified computations. The resulting 3-D key and residual frames are decomposed into subbands by using the reversible integer wavelet transform (IWT) [12]. A modified 3-D version of the set-partitioning in hierarchical trees (3-D SPIHT) [14], [15] coding scheme is used to encode the subband coefficients. The SPIHT algorithm is an efficient technique for coding 2-D wavelet coefficients [16] among others such as the embedded zerotree wavelet (EZW) [17]. The extension of the SPIHT algorithm for coding 3-D IWT coefficients is also straightforward, especially when all three dimensions are spatial. The paper is organized as follows. Section II presents the new 3-D motion compensation algorithm and the proposed compression scheme. Its performance in lossless and lossy modes is discussed in Section III. In Section IV, we present our conclusions. II. CODING 4-D MEDICAL IMAGES In our work, we apply video compression concepts for coding 4-D medical images, which consist of sequences of 3-D image frames. To code a group of 3-D frames, the first frame is selected as the 3-D key frame and the remaining intermediate frames are predicted using 3-D motion estimation. Details about the motion estimation process are given in Section II-A. Subtracting the 3-D predicted frame from the corresponding intermediate frame results in the 3-D residual frame. Thus, as illustrated in Fig. 1, a group of 3-D image frames are processed at the encoder to produce a single 3-D key frame, motion vectors, and 3-D residual frames that need to be coded. The key and residual frames are coded using 3-D IWT and 3-D SPIHT. The resulting bit stream is arithmetic coded. The motion vectors are coded by entropy coding and transmitted separately. At the decoder end, assuming that the key and residual frames are received correctly, the intermediate frames are reconstructed one after another. The key frame and the associated motion vectors are used to reconstruct the first predicted frame, which is then added to the first residual frame to reconstruct the first intermediate frame. The reconstructed first intermediate frame is then used together with its associated motion vectors and the second residual frame to reconstruct the second intermediate frame and the process continues until all the intermediate frames are reconstructed. A. Motion Estimation Process and Residual Frames Our 3-D cube matching algorithm is an extension of the 2-D block matching proposed in [20] and [21], which has been extensively used in video compression. It is used in the motion compensation process to exploit the redundancy between 3-D frames. In 3-D cube matching, the current frame is divided into subcubes and each subcube is matched inside a 3-D search window in the 3-D reference frame as shown in Fig. 2. Here, the first frame is used as the key frame and motion estimation is carried out on subsequent intermediate frames. The motion vector is essentially the difference between the position of the subcube in current frame and the position of the matched subcube in the reference frame. The matched subcube is defined as the one that has the

3 134 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 9, NO. 1, MARCH 2005 Fig. 2. Illustration of 3-D cube matching for motion estimation. minimum mean square error (MSE) with the current subcube. The MSE is calculated as follows: Fig. 3. Block diagram of the three-step 3-D cube matching algorithm. where and refer to the subcubes in the reference frame and the current frame (to be compared), respectively. The MSE is minimized to obtain the estimates of motion vector. The 3-D predicted frame can be constructed by filling its subcube at position with the subcube at position in the 3-D reference frame, where is the corresponding motion vector. The 3-D residual frame is the difference between the 3-D predicted frame and the actual 3-D intermediate frame (see Fig. 1). If the full search method is used, the entire search window consisting of points need to be checked. To reduce the computation complexity of the search process, a fast cube matching algorithm is proposed, which is essentially an extension of the fast 2-D center-biased search algorithm [20], [21]. Fig. 3 illustrates our three-step fast 3-D cube matching algorithm based on a D search window, which is as follows. 1) In the first step, MSEs are calculated using (1) at 53 points, which are composed of the center point, 26 points at from, and other 26 ones at. Here, the points at away from are defined as where and are either zero or. In this step, the checked points are not uniformly distributed but centered about. For medical image sequences, the motion fields are usually gentle, smooth, and vary slowly [7]. As a consequence, the global minimum distribution is normally center-biased. Selection of the 26 points at is based on the assumption that the error surface is monotonic in a small neighborhood around the global minimum [20], [21]. In a D search window, these points are halfway between the center and the borders (or corners). The point with minimum MSE is (1) found from these 53 points and the algorithm proceeds to Step 2. A halfway-stop technique [20] is used to facilitate the identification and estimation of the motions of these cubes as follows. a) If the minimum MSE in the first step occurs at the center of the search cube, the search is stopped. (This is called the first-step stop.) b) If the point with minimum MSE in the first step is one of the 26 points at from the center, the global minimum is assumed to be near or at this point. Hence, in the second step, only the 26 points at from will be checked before the search is stopped. However, some of these 26 points have been checked in the first step, as shown in Fig. 4. Therefore, the number of points to be checked is less than 26. In Fig. 4(a), a total of 18 points have already been checked including the point with minimum MSE and so only 9 more points (in black) will be checked. In Fig. 4(b), 15 points will be checked, while 19 points are to be checked in Fig. 4(c). (This is called the second-step stop.) c) If the point with minimum MSE in the first step is one of the 26 points at, the point is marked as and the algorithm proceeds to step 3. 2) In the third step, the MSEs of the 26 points at from the new center point are compared. The search is then performed on the 26 neighbor points of the one with minimum MSE and stopped. In practice, the search is usually performed within an area of size , and so. For such a choice, the full search will check 3375 points, while our fast 3-D cube matching algorithm only checks 105 points in the worst case, thus leading to a speed-up of more than 32. B. Coding the Key and Residual Frames As explained earlier, a group of 3-D frames are processed to produce a single 3-D key frame, motion vectors, and 3-D residual frames. The motion vectors are coded using the Huffman encoder. The 3-D key and residual frames are first separately transformed using the 3-D IWT and then coded using the 3-D SPIHT scheme [14], [15]. The decoding and reconstruction

4 KASSIM et al.: MOTION COMPENSATED LOSSY-TO-LOSSLESS COMPRESSION OF 4-D MEDICAL IMAGES USING IWTs 135 Fig. 4. Point with minimum MSE at different positions: (a) when it is at a center of one side, 17 points out of 26 have been searched and only 9 more points will be checked; (b) when it is located at a mid-point of one edge, 11 points have been searched and only 15 points will be checked; (c) when it is at a corner, 7 points have been searched and 19 more points will be checked. Fig. 5. Reordered bit stream for progressive transmission. process is simply the reverse of the encoding process. The original 3-D frames can be reconstructed perfectly (i.e., lossless reconstruction) using the entire bit-stream. Progressive lossy-to-lossless decoding, where the quality of the reconstructed 3-D frames improves as more bits are decoded, can be easily achieved by reordering the bit-stream (as shown in Fig. 5) and correct decoding of the motion vectors. The coded bit stream of the key frame is normally larger than that of a residual frame. Hence, there are two segments of the key frame bit stream and one segment from each residual frame in a group, as shown in Fig. 5. With this arrangement, the bit streams of 3-D key frame and 3-D residual frames can be decoded simultaneously. Hence, both the 3-D key frames and the 3-D residual frames can be reconstructed progressively. To reconstruct the th frame in a group, the key frame and the preceding residual frames must be decoded and the predicted frames derived from motion vector information. Each predicted frame is constructed by replacing its subcube at position with the subcube at position offset by the motion vector in the reference frame. The residual data is then added to the predicted frames to yield the desired coded frame. III. EXPERIMENTAL RESULTS We used 4-D data sequences (A and B) in our two experiments. Sequence A is a 16-bits/voxel real sequence of cardiac CT volumes obtained using the dynamic spatial reconstructor [22] in a canine experiment. Sequence B is a set of 8-bits/voxel MRI images showing an enhanced human kidney cortex, spleen, and liver obtained for a urography study. Sequence A consists of 15 frames of voxels and Sequence B has 33 frames of voxels. In the first experiment, a sequence of volumetric images are treated as key frames and coded independently by 3-D SPIHT [15]. We call this the all key frames method which is essentially pure volumetric compression. The second experiment involves our proposed 4-D motion compensation scheme, which uses key and predicted frames to reduce interframe redundancy. Each key frame is interleaved with two motion predicted frames. The resulting residual frames are transformed and coded using 3-D SPIHT. A. Lossless Performance Table I summarizes the lossless coding performance results using various IWT filters. In our experiments, every three frames are grouped together to form a group of frames (GOF) and a three-level dyadic wavelet decomposition is applied. The experiments show that our motion compensated 4-D compression scheme results in a much lower coding bit rate (by more than 25%) than the all key frames method. As the two algorithms use same wavelet filters and coding strategy in the lossless compression mode, the 3-D motion compensation strategy is clearly responsible for the lower coding bit rate. The compression ratio of our scheme in Table I for lossless compression can be further increased if a larger GOF is used. Table I also shows that there is no single transform filter that performs best for both data sets. Different filters perform differently for each data set. However, the wavelet transform filters with fewer vanishing moments perform better than those

5 136 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 9, NO. 1, MARCH 2005 TABLE I LOSSLESS PERFORMANCE OF DIFFERENT INTEGER WAVELET FILTERS. (DATA IS GIVEN IN BITS PER VOXEL) with more vanishing moments, which is consistent with the previous 3-D results in [1] and [3]. This is because of the degradation in the approximation power of the wavelet basis due to the rounding operations in each lifting step while implementing IWT through the lifting scheme, which is aggravated with the increasing of the filter length, as shown in [23]. A C++ implementation of our algorithm on a Pentium 2.4-GHz personal computer takes about 8 s for lossless encoding decoding each 3-D frame of Sequence A and 2 s for Sequence B. B. Progressive Performance We also evaluated the lossy performance of our algorithm in 2-D as medical images are usually viewed slice by slice. Fig. 6 shows plots of the peak signal-to-noise ratio (PSNR) versus slice number. Our algorithm is compared against the all key frames method and JPEG-2000, the DWT-based 2-D image compression standard, in the lossy mode with the coding bit rate set at 1 bit/voxel. Fig. 6 clearly shows that our proposed motion compensated compression scheme performs better than JPEG-2000 and the all key frames method. Our 4-D compression scheme exploits the redundancy in all four dimensions unlike the JPEG-2000 which operates in 2-D. The PSNR gain is not achieved by using the IWT as the rounding operations of IWT degrades the performance on lossy image compression [23]. In Fig. 6(a), the PSNR fluctuations between adjacent slices are noticeable in the motion compensated 4-D medical image compression scheme but no such effects are produced by JPEG The PSNR fluctuations in our scheme are caused by the 3-D wavelet transform coding as explained by Menegaz [24] and Signoroni et al. [25], while the small PSNR changes with JPEG-2000 are due to content differences between slices. This phenomenon is not obvious in Fig. 6(b) because the number of slices within each frame is much smaller. Although the fluctuations may not be desired, they do not degrade the performance of our algorithm as the PSNR values in each slice are still much higher than that of JPEG Fig. 7 shows the reconstructed slices of Sequence A based on the all key frames method and our motion compensated 4-D compression scheme using (1, 1) and (2, 2) filters with the Fig. 6. Lossy coding results using our 4-D compression scheme with wavelet filter (2, 2) (a) on eighth frame of Set A and (b) on thirrd frame of Set B at 1 bit/voxel. PSNR results using all key frames method and JPEG-2000 on 2-D slices are also included for comparison. (a) Lossy performance on data Set A. (b) Lossy performance on data Set B. coding bit rate set at 0.5 bit/voxel. Due to its short length, the (1, 1) wavelet filter which is also known as the Haar wavelet, produces block artifacts at high compression [see Fig. 7(b)]. While some slight blurring is observed when the (2, 2) filter is used. Taking into account the experimental results in Table I and Fig. 6, the wavelet filter (2, 2) is recommended as the default wavelet filter for our motion compensated lossy-to-lossless 4-D medical image compression scheme because it works well in both lossless and lossy modes. In addition, as shown in Fig. 7(c) and (e), the artifacts become less perceivable when the motion compensated 4-D compression scheme is applied. Fig. 8 illustrates the reconstructed visual quality of data Set B using the two methods decoded at 0.1 bit/voxel with 3-level IWT, respectively. It is evident that our compression scheme produces better quality decoded images. With the 3-D motion compensation, the redundancy between frames is exploited, resulting in lower bit-rates for the predicted frames. Hence, our

6 KASSIM et al.: MOTION COMPENSATED LOSSY-TO-LOSSLESS COMPRESSION OF 4-D MEDICAL IMAGES USING IWTs 137 Fig. 7. (a) Original 90th slice of the eighth volume of Sequence A (cardiac data). Decoded results when encoded with (1, 1) filter at 0.5 bit/voxel using (b) the all key frames method and (c) our 4-D compression method, respecively. Decoded results when encoded with (2, 2) filter at 0.5 bit/voxel (d) using all key frames method and (e) our 4-D compression method, respecively. (a) and (b) PSNR 32.6 db; (c) PSNR 34.0 db; (d) PSNR 36.3 db; (e) PSNR 36.8 db. algorithm enables higher quality images to be reconstructed at the same bit-rate compared with those using the all key frames method. It is well known that PSNR is not an adequate quality measure of compressed images, especially for medical applications. Lossy compression is usually not acceptable for diagnostic purposes. Our proposed compression scheme is progressively lossy-to-lossless, which offers the flexibility of using any truncated version of the embedded bit stream to decode a lossy version for preview and utilizing the entire bit stream to generate the lossless version whenever needed. Doctors may use the lossy mode in applications like telemedicine for fast searching and browsing of 4-D medical data and the lossless mode for diagnosis. IV. CONCLUSION In this paper, we have proposed a coding system for lossy-tolossless compression of 4-D medical images using the motion compensated 3-D IWT and a modified version of 3-D SPIHT. Encouraging experimental results on real 4-D medical data sets were obtained by combining these techniques. In the lossless mode, the coding bit rates were reduced by more than 25% when Fig. 8. (a) Original fourth slice of the second volume of Sequence B (4-D MR urography study). Decoded results using all key frames at 0.1 bit/voxel with (b) (3, 1) filter and (d) (2, 2) filters, respectively. Decoded results using one key frame and two intermediate frames at 0.1 bit/voxel with (c) (3, 1) filter and (e) (2, 2) filters, respectively. (a) and (b) PSNR 29.4 db; (c) PSNR 30.5 db; (d) PSNR 31.9 db; (e) PSNR 33.1 db. compared with the purely volumetric image compression approach. The enhanced performance comes from successfully exploiting redundancies in all four dimensions. The scheme could possibly be improved by generalizing it to support object-based coding [9]. ACKNOWLEDGMENT The authors thank Dr. C. Riedel of the Mayo Clinic for providing 4-D cardiac data and Assoc. Prof. S.-C. Wang and Dr. B. Shuter of the National University Hospital in Singapore for providing the 4-D MR urography study. They also thank the anonymous reviewers for their valuable comments. REFERENCES [1] Z. Xiong, X. Wu, S. Cheng, and J. Hua, Lossy-to-lossless compression of medical volumetric data using three-dimensional integer wavelet transforms, IEEE Trans. Med. Imag., vol. 22, no. 3, pp , Mar

7 138 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 9, NO. 1, MARCH 2005 [2] W.-J. Hwang, C.-F. Chine, and K.-J. Li, Scalable medical data compression and transmission using wavelet transform for telemedicine applications, IEEE Trans. Inform. Technol. Biomed., vol. 7, no. 1, pp , Mar [3] A. Bilgin, G. Zweig, and M. W. Marcellin, Three-dimensional image compression with integer wavelet transforms, Appl. Opt.: Inform. Proc., vol. 39, pp , Apr [4] J. Wang and K. Huang, Medical image compression by using threedimensional wavelet transformation, IEEE Trans. Med. Imag., vol. 15, no. 8, pp , Aug [5] I. Peter and W. Straßer, The wavelet stream Progressive transmission of compressed light field data, in Proc. IEEE Visualization, San Francisco, CA, Oct. 1999, pp [6] Y. Kim and W. A. Pearlman, Lossless volumetric medical image compression, Proc. SPIE, vol. 3808, pp , [7] L. Zeng, C. P. Jansen, S. Marsch, M. Unser, and P. R. Hunziker, Fourdimensional wavelet compression of arbitrarily sized echocardiographic data, IEEE Trans. Med. Imag., vol. 21, no. 9, pp , Sep [8] E. Chiu, J. Vaisey, and M. S. Atkins, Wavelet-based space-frequency compression of ultrasound images, IEEE Trans. Inform. Technol. Biomed., vol. 5, no. 4, pp , Dec [9] G. Menegaz and J.-P. Thiran, Lossy to lossless object-based coding of 3D MRI data, IEEE Trans. Image Process., vol. 11, no. 9, pp , Sep [10], Three-dimensional encoding/two-dimensional decoding of medical data, IEEE Trans. Med. Imag., vol. 22, no. 3, pp , Mar [11] T. Sikora, MPEG digital video-coding standards, IEEE Signal Process. Mag., vol. 14, no. 5, pp , Sep [12] A. R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo, Wavelet transforms that map integers to integers, J. Appl. Comput. Harmon. Anal., vol. 5, pp , [13] A. Said and W. A. Pearlman, A new, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Technol., vol. 6, no. 3, pp , Jun [14] A. A. Kassim, E. H. Tan, and W. S. Lee, 3-D color set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Technol., submitted for publication. [15] B.-J. Kim, Z. Xiong, and W. A. Pearlman, Low bit-rate scalable video coding with 3-D set partitioning in hierarchical trees (3-D SPIHT), IEEE Trans. Circuits Syst. Video Technol., vol. 10, no. 8, pp , Dec [16] A. A. Kassim and W. S. Lee, Embedded color image coding using SPIHT with partially linked spatial orientation trees, IEEE Trans. Circuits Syst. Video Technol., vol. 13, no. 2, pp , Feb [17] J. M. Shapiro, Embedded image coding using zerotrees of wavelets, IEEE Trans. Signal Process., vol. 41, no. 12, pp , Dec [18] S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp , Jul [19] I. Daubechies and W. Sweldens, Factoring wavelet and subband transforms into lifting steps, J. Fourier Anal. Applicat., vol. 4, pp , [20] R. Li, B. Zeng, and M. L. Liou, A new three-step search algorithm for block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 4, no. 4, pp , Aug [21] J. Y. Tham, S. Ranganath, M. Ranganath, and A. A. Kassim, A novel unrestricted center-biased diamond search for block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 8, no. 4, pp , Aug [22] E. L. Ritman, R. A. Robb, and L. D. Harris, Imaging Physiologic Functions: Experience with the Dynamic Spatial Reconstructor. New York: Praeger, [23] J. Reichel, G. Menegaz, M. Nadenau, and M. Kunt, Integer wavelet transform for embedded lossy to lossless image compression, IEEE Trans. Image Process., vol. 10, no. 3, pp , Mar [24] G. Menegaz, Model-based coding of multi-dimensional data with applications to medical imaging, Ph.D. dissertation, Signal Processing Lab. (LTS), Swiss Federal Inst. Technol. (EPFL), Lausanne, Switzerland, [25] A. Signoroni and R. Leonardi, Modeling and reduction of PSNR fluctuations in 3D wavelet coding, in Proc. ICIP 2001, Thessaloniki, Greece, Oct. 2001, pp Ashraf A. Kassim (M 81) received the B.Eng. (first class honors) and the M.Eng. degrees in electrical engineering from the National University of Singapore (NUS), in 1985 and 1987, respectively, and the Ph.D. degree in electrical and computer engineering from Carnegie Mellon University, Pittsburgh, PA, in From 1986 to 1988, he worked on machine vision systems at Texas Instruments. Since 1993, he has been with the Electrical and Computer Engineering Department, National University of Singapore, Singapore, where he is currently an Associate Professor and Deputy Head of Department. His research interests include image analysis, machine vision, video/image processing, and compression. Pingkun Yan (S 04) received the B.Eng. degree in electronics engineering from the University of Science and Technology of China (USTC) in He is currently working toward the Ph.D. degree in electrical and computer engineering at National University of Singapore (NUS). His research interests include biomedical information technology, image processing and compression, computer vision, and medical image analysis. Wei Siong Lee received the B.Eng. (first class honors) in electrical engineering from the National University of Singapore (NUS) in He is currently working toward the Ph.D. degree at the Embedded Video Laboratory of NUS. From 2001 to 2003, he worked on the scalable video under the Singapore Advanced Research and Education Network national project. He is currently a Research Engineer at the Embedded Video Laboratory of the National University of Singapore. His research interests include image/video compression, enhancement, and visualization. Kuntal Sengupta received the B.Tech. degree from IIT Kanpur, India, in 1990, and the M.S. and Ph.D. degrees from Ohio State University, Columbus, in 1993 and 1996, respectively. From 1996 to 1998, he worked as a Researcher at the Advanced Telecommunications Research (ATR) Laboratories in Kyoto, Japan. From 1998 to 2002, he was an Assistant Professor in the Electrical and Computer Engineering Department, National University of Singapore, Singapore. Presently, he is a Senior Algorithm Scientist with AuthenTec. His present research interests are in biometrics, HCI, video analysis, and multimodal fusion. Dr. Sengupta received the Siemens Best Paper Award at IEEE CVPR 1993.

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