# An Efficient Context-Based BPGC Scalable Image Coder Rong Zhang, Qibin Sun, and Wai-Choong Wong

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2 982 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 53, NO. 9, SEPTEMBER 2006 Scalable Lossless Coding (SLS) Standard [8]. We start this section with a brief review of the algorithm, followed by our implementation details for scalable image coding. TABLE I DESCRIPTION OF D2L CONTEXTS 06 AND EXAMPLES OF BIT PLANE CODING (FROM BIT PLANE M TO BIT PLANE 0) A. Bit-Plane Golomb Coding Consider a Laplacian distributed source probability density function given by, which has the where the magnitude of each sample is binary represented by bit planes and the sign is uniformly distributed. If the source is independent and identically Laplacian distributed (i.i.d.), the approximate probability of the bit in bit plane can be described as (1) (2) (3) where is the most significant bit plane, is the number of samples, and is the absolute sum of the samples. By calculating and, parameter can be easily obtained. divides the bit planes into two parts: lazy bit planes where bits 0 and 1 have a probability of 1/2 and can be directly output, and nonlazy bit planes (the bit plane to the bit plane), whose skew probabilities are specified by the distance to the lazy bit plane, and these bits are coded by the static arithmetic coder [7]. B. Context Modeling Although BPGC is designed for Laplacian distributed data, it is not directly practical for coding wavelet coefficients. For audio scalable coding, the good performance of BPGC is based on the constraint that the coding source is i.i.d. and the fact that the audio signal is a one-dimensional (1-D) signal. As spatial dependencies of image wavelet coefficients are quite high, the BPGC static probability model where probability is specified only by would obviously lose some coding efficiency. Bits in the wavelet coefficient bit planes are significantly affected by the neighbors. For example, it is more likely for the current bit to be 1 when most bits of the corresponding neighbor bit planes are 1. Fortunately, BPGC can be easily combined with image context modeling techniques, by which bit probabilities differ from each other according to both and neighborhood contexts. The seven contexts used in CB-BPGC are listed in Table I. Context 0 is for the lazy bit planes where raw bits are output without compression. There are also bit-plane coding examples in the table listing the corresponding context for each bit plane. For the neighborhood contexts, part of the contexts in EBCOT, which is widely used for image coding [9], is adopted [4]: nine contexts for the coefficients which are about to be significant in the current bit plane; three contexts for those already significant in previous coded bit planes. To reduce complexity, the sign bits are output directly while five contexts are Fig. 2. CB-BPGC encoding a block. used for sign coding in EBCOT. Codebooks of bit probabilities can be trained offline and presaved in both the encoder and decoder. C. CB-BPGC CB-BPGC uses the same PCRD algorithm as in EBCOT Tier 2 to pack the bitstream after block coding. Fig. 2. illustrates the block encoding process of CB-BPGC. As shown in Fig. 2, after finding parameter, there is a block classification procedure which is applied to model the coefficient local properties in a better way. Observation shows that blocks with (LOWE blocks), most of which are in the very low-entropy high-frequency subbands, have quite different and related bit probabilities compared with those blocks with (SIG blocks). Table II tabulates the different bit probabilities of SIG and LOWE blocks for the nine significant coding when. In addition, for the SIG blocks, three different classes appear with distinct bit probabilities as illustrated in Fig. 3. The three blocks have the same most significant bit plane and the same lazy bit plane, but the left one is smooth, the middle one seems more textural, and the right one contains an obvious edge. If each block is divided to smaller 8 8 subblocks (the number in the subblock area indicates the most significant bit plane in the current subblock, and and are the subblock horizontal and vertical indices), we can see that the smooth block

3 ZHANG et al.: EFFICIENT CONTEXT-BASED BPGC SCALABLE IMAGE CODER 983 TABLE II PROBABILITY COMPARISON OF SIG AND LOWE BLOCKS FOR NINE SIGNIFICANT CODING CONTEXTS WHEN D2L =3 Fig. 4. Error-resilient segment markers. Fig. 3. SIG block classification example (three SIG blocks, , m =6, L =3. Left: class 0, smooth; middle: class 1, textual; right: class 2, edge). has a smaller, the textual block has a median, and the edge block has a larger, where is the standard deviation of the array given by where is the mean value of the array. Similarly, LOWE blocks can also be divided to two classes (smooth and edge) according to. We can train the thresholds of the parameter to classify all of the blocks. Blocks with the same class share the same codebook. A memory of about 3.7 KB is used for the codebooks in CB-BPGC. After classification, CB-BPGC applies the three fractional bit-plane coding passes to these nonlazy bit planes. The static binary arithmetic coder compresses these bits with the lookup probabilities from the codebooks according to the parameters,,, and. In order to decode correctly, the parameters and are transmitted as side information in the bitstream packet header. III. ERROR RESILIENCE Similar with JPEG2000, CB-BPGC hierarchically organizes the codestreams by subbands, blocks, and bit planes for resynchronization at the packet level to prevent error propagation. Fig. 4 illustrates the error-resilient strategies used in CB-BPGC. The static arithmetic coder terminates at each fractional bit plane to stop error propagation, followed by the segment marker 1010 after the coding pass 3, which is also the end of the current bit plane, and segment marker 10 after the coding passes 1 and 2. Whenever a mistake appears in decoding these markers, an error is detected. (4) In the decoder, CB-BPGC conducts the partial decoding [6] for the following bit planes of the corrupted blocks. Case 1) Error detected in coding pass 1. No further coding passes 1 and 3 can be decoded, but coding pass 2 in the current bit plane can proceed. Case 2) Error detected in coding pass 2. No further coding pass 2 can be decoded, but coding passes 1 and 3 in the current and the following bit planes can proceed. Case 3) Error detected in coding pass 3. No further coding passes 1, 2, and 3 can be decoded. Note that the error-resilient PSNR gain reported in [6] is based on the assumption that there is an external error-detection mechanism to tell the decoder from which byte in a fractional bit plane is corrupted, which leads to more complicated partial decoding applied on the fractional bit-plane level instead of the bit-plane level, i.e., additional information outside of the decoder helps to guide the decoding of the corrupted codestream. Our test results show that, by only using the internal error-detection method in CB-BPGC, substantial PSNR improvement can be obtained when the image is transmitted through a Rayleigh channel. IV. EXPERIMENTAL RESULTS The proposed coder is implemented with the Java implementation of JPEG2000. The codebooks are trained from a large set of grayscale natural images taken by the authors. Ten typical grayscale JPEG2000 test images (such as café, fruits, and Lena) are used to evaluate the coding and error resilience performance. A. Coding Performance Table III shows the lossless compression ratio of five-level decomposition at different block sizes (64 64 and 16 16) with a reversible 5/3 filter. The numbers of bits per pixel for losslessly compressed images by JPEG2000 and the proposed CB-BPGC are listed. The positive numbers in the Perc. column are the percentages of CB-BPGC better than JPEG2000 and the negative ones are inverse. The average results show that CB-BPGC is more efficient than JPEG2000, especially for those images which seem harder to compress, e.g., baboon and café, where the adaptive coder probably fails to learn the complicated texture-like blocks well. In addition, JPEG2000 loses more efficiency in the case of smaller code block size where the number of the wavelet coefficients is small and the adaptive coder may end coding before it adapts to the context well, e.g., when the code block size is 16 16, CB-BPGC is 2.56% better on average. Fig. 5 gives an example for the bit-plane coding com- 1 [Online]. Available:

4 984 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 53, NO. 9, SEPTEMBER 2006 TABLE III LOSSLESS PERFORMANCE FOR 5/3 REVERSIBLE DWT (bpp) Fig. 6. Comparison of error resilience performance between JPEG2000 (solid lines) and CB-BPGC (dashed lines) at channel BERs of 10, 10, and Fig. 5. Lossless compression comparison of image café for all of the code blocks in levels 04 between JPEG2000 and CB-BPGC. TABLE IV AVERAGE LOSSY PSNR PERFORMANCE (db) parison results of levels 0 4 coefficients of image café. For the nonlazy bit planes, CB-BPGC removes more redundancy and therefore saves some bytes. The lazy bit-plane performance also shows that it is more efficient to output raw bits in these bit planes instead of adaptive coding them. The average scalable coding performances of the images (9/7 filter, 5 level decomposition, block size: 16 16) are given in Table IV, which shows that CB-BPGC outperforms JPEG2000 in terms of PSNR except at very low bit rates. The PSNR increase is about 0.1 db for a bi trate of 1 bpp and about 0.25 db for a bit rate of 2 bpp on average. However, at low bit rates, JPEG2000 is better. This is probably because these subband coefficients, whose coding results affect the lossy coding performance a lot at the lower bit rates, are more like Rayleigh distributed, whereas BPGC is suitable for Laplacian distribution and cannot model them well. Another reason may be that we sacrifice some coding efficiency for the sign bits by direct transmission where in low-frequency subbands sign bits are compressible. B. Error Resilience Performance Fig. 6 shows the CB-BPGC average PSNR improvements of the ten images compared to JPEG2000 (5 level 9/7 filter, block size: 64 64) for different bit rates. Both of them are simulated though a wireless Rayleigh fading channel at bit error rates (BERs) of,, and (the corresponding channel Eb_No parameters are 0.6, 1.3, and 2.1 db, respectively; a detailed description of the channel conditions can be found in [10]). Each image is simulated over the Rayleigh channel 1000 times. CB-BPGC uses the error-resilient tools described in Section III, and EBCOT is set with the entropy level properties BYPASS, RESET, CAUSAL, ERTERM, SEGMARK, and RESTART. For both bitstreams, LL subband layers are protected from error corruption, which is the most important information and often assumed to be transmitted through a more reliable channel. As shown in Fig. 6, CB-BPGC is more resilient to errors with improved PSNR for all the bit rates on averages at 0.731, 1.514, and db for BERs at,, and, respectively. It should be noted that, at higher BERs, both CB-BPGC and JPEG2000 have almost constant decoded image quality across all bit rates. This is probably because, when BER is high enough, almost all of the blocks are damaged from the most significant bit planes and, thus, the bit-rate increase cannot improve image quality [11]. Subjective results of the images woman, Lena, and peppers at a BER of and 1 bpp are shown in Fig. 7. Comparing the decoded images, we can see that CB-BPGC gains not only a better PSNR in decibels but also a substantial improvement of subjective visual effect. The improvement of CB-BPGC error-resilient performance is not only gained by partial bit-plane decoding, but also by the more efficient scalable coding. As the PCRD algorithm organizes codestreams according to the contribution of reducing distortion, i.e., in decreasing order, more efficient compression enables CB-BPGC to consume less bytes to embed the codestream while still providing the equivalent distortion reduction. Hence, when a transmission error occurs, it corrupts the less important bitstream of CB-BPGC and, thus, the PSNR result is better. Direct output of lazy bit planes also improves error resilience performance. Although errors may occur in certain lazy bit plane, we can further decode the remaining because the errors are isolated to certain coefficients instead of propagating to the others. In addition, CB-BPGC uses partial decoding to fully decode the corrupted codestream. Further improvement of error resilience

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