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1 Exploiting interframe redundancies in the lossless compression of 3D medical images Steven Van Assche 1, Dirk De Rycke 2, Wilfried Philips 3 and Ignace Lemahieu 4 1,4 University of Gent, Department of Electronics and Information Systems (ELIS), Sint-Pietersnieuwstraat 41, B-90 Gent, Belgium 2,3 University of Gent, Department for Telecommunication and Information Processing (TELIN), Sint-Pietersnieuwstraat 41, B-90 Gent, Belgium 1,4 {svassche,il}@elis.rug.ac.be 2,3 {ddr,philips}@telin.rug.ac.be Abstract Recent advances in digital technology have caused a huge increase in the use of 3D medical image data. In order to cope with large storage and transmission requirements, data compression is necessary. Although lossy techniques achieve higher compression ratios than lossless techniques, the latter are sometimes required, e.g., in medical environments. There exist a lot of lossless image compressors, but most of them do not exploit interframe correlations. In this paper, an evaluation is made of different approaches in removing interframe redundancies. It is shown that linear predictive techniques are not able to provide any compression improvement. Non-linear techniques, such as context-modeling do yield better results. This is mainly due to the special nature of 3D medical image data (i.e., large interslice distances, a lot of noise, etc.). In this paper, a new technique is proposed based on the 2D lossless image compressor JPEG-LS (which will be part of the new JPEG-20 lossless image compression standard). A context-modeling scheme is developed which catches the interframe redundancies, and is integrated into JPEG-LS statistical modeling chain. The results show that typically 0.5 to 1 bit per pixel (10-20%) is gained. Keywords interframe modeling, lossless medical image compression I. INTRODUCTION RECENT years, there has been a considerable increase in the volume of medical image data generated in hospitals. As most of these images have to be kept and archived, hospitals must deal with high storage requirements. Another important issue is the transmission of the image data, through both high-bandwidth channels (e.g., LANs) and low-bandwidth channels (e.g., modem-links). Data compression is required to alleviate these problems. Because of the high quality requirements in medicine, mostly only lossless compression is accepted. Although higher compression ratios can be achieved by lossy compressors (JPEG [1,2], Wavelet-techniques [3], etc.), radiologist are very reluctant to use them as they might introduce compression artefacts, which could complicate diagnosis. In this paper, lossless compression of three-dimensional medical images is considered. As the largest part of the three-dimensional medical image data originates from Magnetic Resonance Imaging (MRI) and Computerized Tomography (CT), we will focus on these types of images. MRI- and CT-images are volume images, in which all three dimensions are spatial. There exist many lossless image compressors (LJPEG [1], CALIC [4, 5], BTPC [6, 7], JPEG-LS [8, 9], etc.), but most of them do not take the third dimension into account. In this case, the frames of an image must be compressed independently of each other. However, it is clear that the third dimension introduces some interframe redundancy, which could be exploited to attain higher compression. We have to mention one technique which does use interframe information, namely Interframe CALIC [5]. It implements a highly non-linear prediction, followed by context-modeling. Unfortunately, we do not have an implementation of this technique at our disposal, and no results for medical images are published. The compression scheme of Interframe CALIC is quite complex, as a result of which its processing speed is rather low. Considerably higher speeds can be obtained by more simple linear predictive techniques [10]. In this paper, we will first investigate the suitability of three-dimensional (interframe) linear prediction for medical images. It has already been found that three-dimensional linear prediction mostly does not yield any compression improvement compared to two-dimensional prediction [11, 12]. This finding will be demonstrated and it will be shown that a nonlinear approach should be used to exploit interframe redundancies. We investigated the combination of simple in- ISBN: c STW, :078

2 Steven Van Assche et al. 522 Fig. 1. An MRI-sequence Fig. 2. Interframe correlation in the MRI-sequence traframe prediction and interframe context-modeling. Due to the scheme s simplicity, we are also guaranteed high processing speeds. A second scheme, based on JPEG-LS, is slightly more complicated. It exploits interframe redundancies the same way as the first scheme, and attains stateof-the-art compression ratios. this finding can be the major source of improvement in an interframe approach. Previous frames can be used by an edge-detector for the current frame, allowing a more efficient coding of the edges. Considering the low overall correlation between successive frames, it can be expected that simple linear interframe prediction will not yield a better decorrelation than intraframe prediction. Techniques which exploit the edgeinformation from previous frames will not bother about the flat image regions (where almost no coding gain can be obtained), but will be able to code the edges better. In this case, the coding gain can be significant, as will be shown later. II. I NTERFRAME CORRELATIONS In figure 1 an MRI-sequence is shown and in figure 2 the local correlations are visualized. A frame in figure 2 shows the local correlations between its corresponding frame in the original sequence and the corresponding frame s previous frame. For each pixel, the local correlation is computed based on its eight closest neigbours in the current and previous frame (considering the raster-scan coding order, just as Interframe CALIC does). Higher intensities correspond with higher (absolute values of the) correlation. It can be seen that local interframe correlations are rather low in flat image regions (in which pixel intensities do not differ much) and that they are high at edges. In flat image regions, noise has a large influence on the local correlations. It is known that noise is very little correlated between successive frames, which is the main reason for the small correlation in the flat image regions. At edges, noise is less important and correlations tend to be larger (if the edges are not too much displaced between successive frames). From these results, some interesting conclusions can be drawn. Firstly, interframe redundancies are low in flat image regions. This is no real drawback as flat image regions can be coded very effectively using an intraframe approach. Secondly, the location (and sharpness) of edges can be predicted very well from the previous frame. As intraframe-only techniques have great difficulties coding edges efficiently (because the prediction errors are large), III. O PTIMAL LINEAR PREDICTION n, where 1 h H, An image consists of pixels P 1 w W and 1 n N, and where H is the height and W is the width of a frame and N is the number of frames in the image. Prediction is based on a pixel s closest neigbours in the current frame and the previous frames. Since the decoder must be able to reconstruct the prediction, only pixels can be used which are already coded and known to the decoder. We will refer to these past pixels as the coding history. When processing an image frameby-frame, and within a frame in raster-scan order, the coding history consists of all pixels in the previous frames and all pixels in the current frame which lie above the current pixel or to the left of the current pixel on the same line. The coding history is depicted in figure 3. It is obvious that not all pixels from the coding history are equally suitable for prediction. Only the pixels in a small neigbourhood from the current pixel can effectively contribute to the pixel s prediction. In this paper, we will focus on simple linear predictors. Such a predictor is used in Lossless JPEG (LJPEG) [1], the current lossless compression standard for gray-scale STW/SAFE99

3 Exploiting interframe redundancies in the lossless compression of 3D medical images 523 y x z Frame n-2 11 Frame n Frame n ? Fig. 3. The already coded pixels form the coding history images. In fact, the LJPEG-standard defines seven simple linear predictors, of which we will only consider the seventh. With P n denoting the current pixel, its prediction is (Ph 1,w n + P 1 n )/2, where x denotes the largest integer not greater than x. This simple linear intraframe predictor will be the reference predictor when evaluating the interframe predictor. In order to be able to evaluate the full potential of linear prediction, an optimal predictor will be constructed. Given the pixels used in the prediction, optimal predictioncoefficients can be computed for a particular image. Although this is not feasible in practical compression schemes (because it is very time-consuming), the performance of the optimal predictors will give an idea of the obtainable coding gain. If no coding gain is obtained using the optimal predictors, non-optimal predictors will very probably not do better. The optimal linear predictor is K P n = a k P k, k=1 where K is the number of pixels involved in the prediction. The pixels P k (1 k K) are part of the coding history of the pixel to be predicted P n. The predictioncoefficients a k will be computed based on the correlations between the pixels P k in the image. Because minimization of the compressed code-length cannot easily be done, the coefficients will be optimized such that the variance of the prediction error is minimal. The prediction errors will not be entropy-coded. Rather, the remaining entropy after (predictive) decorrelation is computed. These entropy figures will be very close to the actual code-lengths obtainable by state-of-the-art arithmetic coders [13 15]. IV. JPEG-LS JPEG-LS combines simplicity with the powerful compression potential of context-modeling. The JPEG-LS modeler/predictor processes the images in raster scan mode and has 2 basic modes of operation: regular mode and run mode. The latter is entered in smooth regions, where the limitations of its entropy coder (a Golomb-Rice coder) would force it to write at least one bit per pixel. However, coding runs of pixels as super-symbols allows the average number of bits per coded pixel to be less than 1. As far as lossless compression is concerned, most pixels are compressed using the regular mode; therefore, we will concentrate on this mode here. In a first step, the current pixel is predicted using the following non-linear predictor that takes the gray values P 1 n, P h 1,w n and Ph 1,w 1 n of three neighbouring pixels as inputs, see table I. Even though this predictor is very simple, it deals appropriately with at least the most basic type of edges, i.e., horizontal and vertical ones. This predictor is called the fixed predictor. The context modeler of JPEG-LS not only provides information to the statistical coder but is also used to improve the prediction in a level 2 step, which is called adaptive correction. The context modeler computes local gradient information and then uses this information to classify the current pixel into one of a number of classes. It also keeps an estimate of the mean prediction error within each class and subsequently adjusts the prediction error to obtain an unbiased estimate. It was experimentally observed that the resulting level 2 prediction errors can be reliably modeled with a twosided geometric distribution (TSGD), which has only 2 parameters (the rate of decay and the mean value). This means that instead of estimating complete probability tables P(symbol context) (for use in an arithmetic coder) for every possible symbol, the context modeler can simply estimate the 2 parameters of the TSGD. This has two important advantages: firstly, less memory is required to store 2 parameters than to store a probability table and secondly, the 2 parameters of the TSGD can be estimated much more reliably than a general probability table, especially in the early stages of coding when only a few pixels have been encoded. This improves the compression ratio. V. INTERFRAME CONTEXT-MODELING In the non-linear approach, prediction is purely intraframe (using the simple LJPEG-predictor or the more complicated two-step JPEG-LS predictor, see fig. 4). Interframe redundancies are exploited by interframe context- IEEE/ProRISC99

4 524 Steven Van Assche et al. min(p P n 1 n,pn h 1,w ) if P h 1,w 1 n max(p 1 n,pn h 1,w ) = max(p 1 n,pn h 1,w ) if P h 1,w 1 n min(p 1 n,pn h 1,w ) P 1 n + P h 1,w n P h 1,w 1 n otherwise TABLE I PREDICTOR USED IN JPEG-LS modeling. The context for the current pixel is formed by the magnitude of the prediction error for the corresponding pixel in the previous frame. Note that this prediction error comes from the intraframe prediction step in the previous frame. In the following, we will refer to it as the reference frame prediction error. The contexts hold counts of intraframe prediction error/reference frame prediction error pairs. In practical compression schemes, these counts drive an entropycoder. As mentioned above, we will do no actual coding, but we will only compute the remaining entropy. The main asset of context-modeling lies in its ability to separate statistics. In our case, intraframe prediction errors are coded conditioned on the corresponding reference frame prediction errors. If there exists a good correlation between the reference frame prediction errors and the intraframe prediction errors, context-modeling will provide conditional statistics which are very well suited for5 entropy-coding. In our case, the context-modeling step serves as edgedetector: the magnitude of the reference frame prediction errors indicate the presence and sharpness of edges. As found in section II, there exists a strong correlation between edges in successive frames. Therefore, we expect the interframe context-modeling step to be very beneficial for coding because the intraframe prediction error statistics from flat and edgy image regions will be separated. In flat image regions (small reference frame prediction errors), intraframe prediction is adequate and intraframe prediction errors are very small. The statistics will not be distorted by the generally much larger prediction errors coming from edgy image regions. On the other hand, statistics in edgy image regions will also be more reliable: large intraframe prediction errors will be more probable than small errors, which is certainly not the case in the flat image regions. When forming the context, reference frame prediction errors are grouped into bins depending on their magnitude. The bins are chosen larger for large reference frame prediction errors in order to make it possible for the contextmodeling step to gather sufficient counts and build reliable Image Size of a frame Number of frames MRI T MRI T MRI PD CT Technique LJPEG LJPEG-3D/opt TABLE II IMAGES USED IN THE EVALUATION Predictor (Ph 1,w n + P 1 n )/2 a 1 Ph 1,w n + a 2P 1 n + a 3P n 1 TABLE III EVALUATED LINEAR PREDICTORS statistics. This is necessary because large intraframe prediction errors are far less frequent than small errors. VI. EXPERIMENTAL RESULTS We will evaluate the different techniques on four threedimensional medical images: three MRI-images and one CT-image. These images originate from the Visible Human Project (VHP) [16], in this case the female corpus. Their sizes are shown in table II. All four images have 12 bits per pixel (bpp). A. Optimal linear prediction The linear predictive techniques which will be evaluated are shown in table III. It is supposed that pixel P n is to be predicted. LJPEG is the reference predictor. LJPEG- 3D/opt uses a current pixel s three closest pixels in the prediction: the pixels from the LJPEG-prediction and its corresponding pixel in the previous frame. This is the most straightforward interframe extension of the LJPEGstandard predictor. Note that, as the correlation between frames in medical images drops off rapidly for more distant frames, only one previous frame is used in the interframe prediction. STW/SAFE99

5 Exploiting interframe redundancies in the lossless compression of 3D medical images 525 Current Frame INTRA-FRAME CONTEXT MODEL Determine Intra-frame Context INTER-INTRA CONTEXT MODEL Predict + Error Feedback Reference frame residuals Real Pixel Value - Residual INTRA INTER Entropy coding using selected statistics Coded bits Quantize MOST INFORMATION RETRIEVAL ACTIONS ARE SHOWN INFORMATION UPDATES ARE NOT Fig. 4. Overview of the 3D JPEG-LS scheme Image Original LJPEG LJPEG-3D/opt MRI T MRI T MRI PD CT TABLE IV RESULTS FOR THE LINEAR PREDICTORS Image MRI T1 MRI T2 MRI PD CT Optimal predictor 0.21Ph 1,w n +0.75P 1 n 0.27Ph 1,w n +0.68P 1 n 0.22Ph 1,w n +0.75P 1 n 0.46Ph 1,w n +0.21P 1 n +0.03P n P n P n P n 1 TABLE V OPTIMAL COEFFICIENTS FOR LJPEG-3D/OPT The results for the linear predictors from table III, are shown in table IV. The figures given are remaining entropies after predictive decorrelation, expressed in bit per pixel. It can be seen that the interframe predictors do not yield any noteworthy compression improvement. interframe redundancies in medical images can thus clearly not be exploited by linear prediction. In table V, the optimal coefficients are shown for the LJPEG-3D/opt predictor. For the MRI images, the interframe pixel (P n 1 ) makes only a very minor contribution to the prediction. From this, it can easily be understood that the linear interframe prediction does not work. It is remarkable that for the CT image, the reference frame pixel does add to the prediction. This is probably due to the fact that CT images mostly contain far less noise than MRI im- ages. Nevertheless, the additional decorrelating potential of the interframe pixel is not sufficient to provide a clearly better linear prediction. B. Interframe context-modeling In table VI, the results are shown for the techniques using interframe context-modeling. As can be seen, the non-linear approach does yield a compression improvement. Compressed bitrates drop by about 5 to 10%. As the implemented context-modeling is very simple, higher gains can be expected from more complex non-linear approaches. In fig. 5, a comparison is shown of JPEG- LS/CM, JPEG-LS and CALIC on the CT image. In this figure, every frame is compressed using its previous frame as reference frame. For most frames, JPEG-LS/CM per- IEEE/ProRISC99

6 526 Steven Van Assche et al. Image Original LJPEG LJPEG/CM JPEG-LS JPEG-LS/CM MRI T MRI T MRI PD CT TABLE VI RESULTS FOR THE INTERFRAME CONTEXT-MODELING APPROACH bit per pixel JPEG-LS (3D) JPEG-LS (2D) Calic (2D) frame number Fig. 5. Comparison of JPEG-LS/CM with CALIC and JPEG- LS on the CT image from the VHP (female) data set forms better than the intraframe techniques, but for some others, its performance is worse. It is not clear why this happens. VII. CONCLUSION In this paper the suitability of three-dimensional predictive techniques for lossless compression of medical images is investigated. It is shown that linear interframe prediction does not provide a better decorrelation than twodimensional intraframe prediction. It is demonstrated that the use of a non-linear interframe decorrelator (in this case context-modeling) does yield higher compression. With a simple technique, a decrease in compressed bitrate of about 10% could be noted. ACKNOWLEDGMENTS This work was financially supported the Flemish Institute for the Advancement of Scientific-Technological Research in Industry (IWT) through the projects Tele-Vision (IWT ) and Samset (IWT ). REFERENCES [1] The International Telegraph and Telephone Consultative Committee (CCITT), Eds., Digital Compression and Coding of Continuous-Tone Still Images, Recommendation T.81, [2] G.K. Wallace, The JPEG still picture compression standard, Communications of the ACM, vol. 34, no. 4, pp , Apr [3] Stephane G. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp , July [4] X. Wu, N. Memon, and K. Sayood, A context-based, adaptive lossless/nearly-lossless coding scheme for continuous-tone images, Proposal for the initial ISO/JPEG evaluation, juli [5] Xiaolin Wu, Wai-kin Choi, and Nasir Memon, Lossless interframe image compression via context modeling, in Proceedings of the Data Compression Conference, J. A. Storer and M. Cohn, Eds., Snowbird, Utah, USA, Mar. 1998, IEEE Computer Society, pp [6] John A. Robinson, Efficient general-purpose image compression with binary tree predictive coding, IEEE Transactions on Image Processing, vol. 6, no. 4, pp , Apr [7] John A. Robinson, Binary tree predictive coding, john/btpc.html, [8] JPEG-LS source code, v.2.1, [9] M. Weinberger, G. Seroussi, and G. Sapiro, The LOCO-I lossless image compression algorithm: Principles and standardization into JPEG-LS, Tech. Rep. HPL , HP Computer Systems Laboratory, Nov. 1998, [10] K. Denecker, S. Van Assche, W. Philips, and I. Lemahieu, State of the art concerning lossless medical image coding, in Proceedings of the PRORISC IEEE Benelux Workshop on Circuits, Systems and Signal Processing, J.-P. Veen, Ed., Mierlo, NL, Nov. 1997, STW Technology Foundation, pp [11] P. Roos and M.A. Viergever, Reversible 3-d decorrelation of medical images, IEEE Transactions on Medical Imaging, vol. 12, no. 3, pp , Sept [12] S. Van Assche, K. Denecker, W. Philips, and I. Lemahieu, Lossless compression of three-dimensional medical images, in Proceedings of the PRORISC IEEE Benelux Workshop on Circuits, Systems and Signal Processing, J.-P. Veen, Ed., Mierlo, NL, Nov. 1998, STW Technology Foundation, pp [13] Paul G. Howard and Jeffrey Scott Vitter, Arithmetic coding for data compression, Proceedings of the IEEE, vol. 82, no. 6, pp , June [14] Jr. Glen G. Langdon and Jorma Rissanen, Compression of blackwhite images with arithmetic coding, IEEE Transactions on Communications, vol. COM-29, no. 6, pp , June [15] W. B. Pennebaker, J. L. Mitchell, Jr. G. G. Langdon, and R. B. Arps, An overview of the basic principles of the Q-coder adap- STW/SAFE99

7 Exploiting interframe redundancies in the lossless compression of 3D medical images 527 tive binary arithmetic coder, IBM Journal of Research and Development, vol. 32, no. 6, pp , Nov [16] National Library of Medicine, Visible Human Project, data.html. [17] D. De Rycke and W. Philips, Lossless non-linear predictive coding of video data through context matching, in The 5th International Conference on Information Systems Analysis and Synthesis (ISAS 99), M. Torres, B. Sanchez, and D.G. Langlois, Eds., Aug. 1999, pp , Orlando. IEEE/ProRISC99

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