Dynamic Code Block Size for JPEG 2000

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1 Dynamc Code Block Sze for JPEG 2000 Png-Sng Tsa a, Yann LeCornec b a Dept. of Computer Scence, Unv. of Texas Pan Amercan, 1201 W. Unv. Dr., Ednburg, TX USA ; b Sgma Desgns, Inc., 1778 McCarthy Blvd., Mlptas, CA USA ABSTRACT Snce the standardzaton of the JPEG 2000, t has found ts way nto many dfferent applcatons such as DICOM (dgtal magng and communcaton n medcne), satellte photography, mltary survellance, dgtal cnema ntatve, professonal vdeo cameras, and so on. The unfed framework of the JPEG 2000 archtecture makes practcal hgh qualty real-tme compresson possble even n vdeo mode,.e. moton JPEG In ths paper, we present a study of the compresson mpact usng dynamc code block sze nstead of fxed code block sze as specfed n the JPEG 2000 standard. The smulaton results show that there s no sgnfcant mpact on compresson f dynamc code block szes are used. In ths study, we also unvel the advantages of usng dynamc code block szes. Keywords: mage compresson, JPEG 2000, rate-dstorton optmzaton, dynamc code block sze 1. INTRODUCTION AND BACKGROUND JPEG s an acronym for the Jont Photographc Experts Group and s well known n the photographc mage compresson communty. The group was organzed n 1986 and n the past two decades has developed one of the most wdely adopted stll color mage compresson standard, ISO /ITU T.81 1, 2. The JPEG fle (mages that employ the JPEG compresson standard) can be found n dverse applcaton areas such as the nternet webcam, dgtal camera, cellular phone wth dgtal camera, and so on. Recently, n the year 2000, the JPEG 2000 standard 3, 4, 5 was added to the famly of nternatonal standards developed by the Jont Photographc Experts Group. The JPEG 2000 standard s ntended to be the successor to JPEG n many areas of applcaton. It ams at creatng a new versatle codng system for varous types of stll mages that would provde excellent mage qualty both objectvely and subjectvely at low bt rates. It was also developed to have desrable functonaltes such as progressve transmsson, scalablty, regon of nterest codng, random access, and error reslence. In fact, most state-of-the-art technologes of stll mage compresson were ntegrated nto the JPEG 2000 standard. Even though the basc key encodng modules of JPEG 2000 such as dscrete wavelet transformaton, quantzaton, bt plane codng and bnary arthmetc codng are clearly specfed, some mplementaton was stll left to ndvdual developers. Among these remanng, rate-dstorton optmzaton plays a key role n JPEG 2000 mplementaton. In ths secton, we wll brefly gve an overvew of the JPEG 2000 standard, detal constrants for the code block sze n JPEG 2000, and revew general rate-dstorton optmzaton for JPEG Overvew of JPEG 2000 Standard Fg. 1(a) shows the basc functonal block dagram of the JPEG 2000 algorthm. For a JPEG 2000 encoder, the mage components can be dvded nto rectangular tles as shown n the dataflow dagram of Fg. 1(b). Ths operaton makes t sutable to work wth huge mages. DC level shftng s performed on these tle components followed by ether an rreversble or reversble component transformaton. The component transformaton helps mprove compresson performance. Each component of a tle s ndependently transformed by the Dscrete Wavelet Transformaton (DWT) 5, 6. In JPEG 2000, the 9/7 rreversble wavelet transformaton s used for lossy compresson and the 5/3 reversble lftng based wavelet transform s specfed for lossless compresson. Unform scalar quantzaton wth dead-zone at the orgn s appled to the samples n subbands at the wavelet doman for lossy compresson. The quantzaton step sze can be determned by the dynamc range of the samples n a subband. After quantzaton, each subband s dvded nto non- pstsa@eee.org; phone ; fax ; cs.panam.edu

2 overlappng rectangular blocks, called code blocks. Code blocks are the basc codng unt for entropy. Encodng s done ndependently and the sze of the code block s typcally or A unque feature of JPEG 2000 s regon of nterest (ROI) codng whch allows dfferent regons of an mage to be coded wth dfferent fdelty crtera. The MAXSHIFT method proposed by Chrstopoulos et al. 7, 8 s adopted by the JPEG 2000 part 1 standard. The entropy encodng n JPEG 2000 conssts of a fractonal bt plane codng (BPC) 3, 4, 9 and bnary arthmetc codng (BAC). The combnaton of BPC and BAC s also referred to as Ter 1 codng n the standard. BPC has three passes n each bt plane: Sgnfcance Propagaton Pass, Magntude Refnement Pass, and Cleanup Pass. Each pass generates context models and the correspondng bnary data. The output of BPC and BAC produces the compressed bt stream. So each codng block has an ndependent bt stream. These ndependent bt streams of all the code blocks are combned nto a sngle bt stream usng Ter 2 codng whch s based on the result of rate-dstorton optmzaton. An effcent rate-dstorton algorthm provdes possble truncaton ponts of the bt streams n an optmal way to mnmze dstorton accordng to any gven target bt rate. However, n order to obtan an optmal soluton such as the EBCOT (Embedded Block Codng wth Optmzed Truncaton) method proposed by D. Taubman 9, one wll need to buffer up all the bt streams from all code blocks. Ths s a heavy burden for any hardware based mplementaton. Ter 2 codng multplexes these ndependent bt streams that were generated n Ter 1 codng to compose the fnal compressed output bt stream. It also effcently gves header nformaton to ndcate orderng of the resultng coded blocks and correspondng codng passes. 1.2 Fxed Code Block Sze n JPEG 2000 The code block wdth and heght of the JPEG 2000 standard are lmted to the powers of two numbers between the range of 2 2 and Further restrctons are descrbed n the codng style default (COD) and/or codng style component (COC) marker segments. The JPEG 2000 Part 1 amendments ntroduce Profle-0 and Profle-1 that restrct the set of possble values for the codng parameters and optons. The purpose of those amendments s to enable low complexty mplementatons wth lmted resources. The code block sze s restrcted to or for Profle-0 and or smaller for Profle-1. The selected code block sze wll apply to all DWT sub-bands at dfferent resolutons. Fg. 2 shows an example of 2 levels of DWT decomposton. The code block 0 n the resoluton 0 (2LL sub-band), code blocks 1 3 n resoluton 1 (2HL, 2LH, and 2HH), and code blocks 4 15 n resoluton 2 (1HL, 1LH, and 1HH) are the DWT coeffcents correspondng to the mage regon proporton of the code block sze n the 2LL sub-band. The fxed code block sze wth defntons of packet, layer, resoluton, component, and precnct (see references 3 and 4 for detal defntons) provdes the flexblty of dfferent progresson bt stream orders. However, n order to keep track of all the code blocks correspondng to the same spatal locaton of an mage, one wll need to mplement a quad-tree type data structure. Such mplementaton overhead, especally for a hardware based mplementaton, s not sutable for a close-loop type encoder-decoder system. Ths motvates us to study the mpact of compresson effcency n dfferent code block szes at dfferent DWT levels. Rate Control Source Image Forward MultComponent Transformaton Forward Wavelet Transform Quantzaton Ter 1 Encoder Ter 2 Encoder Coded Image Regon of Interest (a)

3 ROI tle Subbands Subband Subband Subband Component of an mage tle Subbands Subband Subband Subband tle tle DWT + (Q) Subbands Subband Subband Subband BPC + BAC Bt Streams Subbands Subband tle Subband Subband (b) Fg. 1. (a) Block dagram of the JPEG 2000 Encoder Algorthm, (b) Encoder data flow LL 2HL HL 2LH 2HH LH 1HH Fg. 2. JPEG2000 fxed code block sze at dfferent resolutons.

4 1.3 General Rate-Dstorton Optmzaton for JPEG 2000 Smlar to the well known NP-hard bn packng or knapsack problems 10, the bt rate control problem n the JPEG 2000 standard s a challengng problem and s an open ssue for encoders. In JPEG 2000 VM3 (verfcaton model verson 3), the embedded block codng wth optmzed truncaton method 9 s adopted as the post compresson rate control mechansm. Ths s also known as the post-compresson rate-dstorton (PCRD) optmzaton. Yet t s stll requred that the entre bt streams from all code blocks be buffered up before formng the fnal compressed output fle. In general, the rate-dstorton optmzaton problem n JPEG 2000 can be summarzed as follows. Let { B } denote a set of all code blocks that represent an mage n the wavelet transformed doman. The bt rate and dstorton of each code block s measured ndependently. Snce each code block s encoded ndependently, we can assume that the relevant dstorton metrc s addtve,.e. n = n D D, where D represents overall mage dstorton and D denotes dstorton generated by the truncaton pont n of code block B. The overall bt rate ( R ) ncluded n the bt stream s gven by max n n R = R max R, where R s a gven bt rate constrant and R s the accumulated bt rate up to the truncaton pont n of code block B. Now the rate-dstorton optmzaton problem becomes the optmal selecton of the truncaton ponts n that mnmze over all dstorton. Ths well known problem can be solved usng a Lagrange multpler. Any set of truncaton ponts, { n λ }, that mnmzes λ n = ( D + λ n J λ R ) for some λ s optmal n the sense that the dstorton cannot be reduced wthout ncreasng the overall rate where D s λ max the correspondng dstorton generated by n. The value of λ must be adjusted untl the rate satsfes R R. Fndng the correct value of λ can be done usng a bsectonal search or alternatve methods It s worth notng that although possble truncaton ponts of each codng pass n JPEG 2000 could be qute large, typcally the locaton of the truncaton ponts are chosen to be at the end of codng passes for keepng mplementaton smple. Also the convexty of the rate-dstorton curve s enforced by some adjustment where needed. Other assumptons and observatons n rate-dstorton algorthms nclude that a hgher bt plane wthn a code block has a hgher ratedstorton slope than the lower bt plane. Also that the sgnfcance propagaton pass has a hgher rate-dstorton slope than the magntude refnement pass and the cleanup pass has the lowest rate-dstorton slope n the same bt plane. The rest of the paper s organzed as follows. In secton 2, we explan the proposed dynamc code block szes for JPEG 2000 and unvel ts advantages. Smulaton results of compresson mpact are shown n secton 3. Conclusons and future work s dscussed n secton 4. n λ 2. DYNAMIC CODE BLOCK SIZE FOR JPEG 2000 Instead of usng fxed code block sze as specfed n the JPEG 2000 standard, we lke to use dynamc code block szes at dfferent DWT levels. As dscussed n the prevous secton, the code block wdth and heght of the JPEG 2000 standard can be powers of two numbers wthn the range 2 2 and The wdth and heght nformaton are specfed n ether COD or COC marker segments wth the scope up to a tle of one component. In other words, all the code blocks wthn the same tle of a component need to have the same wdth and heght accordng to the JPEG 2000 standard. However, for a

5 close-loop type encoder-decoder system, we do not need to use the marker segments to pass the code block sze nformaton between encoder and decoder. As long as there s a predefned set of code block szes for dfferent DWT levels n the system, the encoder and decoder can both functon normally. Ths flexblty opens up opportuntes for dfferent ways to mplement DWT, BPC, and even bt rate control. Next, we wll summarze the advantages of usng dynamc code block sze. Then, n the followng secton, we wll study the mpact of compresson effcency f one uses dfferent code block sze at dfferent DWT levels. 2.1 Advantages of Dynamc Code Block Sze As llustrated n Fg. 3, one can select the code block szes between the adjacent DWT levels that are dfferent by a factor of 2 n both wdth and heght. Ths wll yeld the same number of code blocks n dfferent DWT subbands. Instead of usng a quad-tree type data structure, one can keep track of all the code blocks that correspond to the same spatal locaton of an mage usng a smple lnear type data structure. Ths feature s attractve for both hardware and software based mplementatons. For a typcal lne-based DWT archtecture as shown n Fg. 4, there wll be a latency of 4 lnes when usng a 9 taps flter. Therefore, n order to generate N lnes of DWT coeffcents at level 3 for formng code blocks wth a heght of N, one wll need to buffer 2 N + 4 lnes at level 2, 2 (2 N + 4) + 4 = 4N + 12 lnes at level 1, and 2 (4N + 12) + 4 = 8N + 28 lnes n the orgnal pcture. For a large value of N, a large szed memory buffer wll be requred. On the other hand, when N s too small, the code block sze becomes nsuffcent n sze and the effcency of bt plane codng s reduced. The dynamc code block sze approach wll assst n balancng the requred memory buffer for DWT and the effcency of BPC. Smple, effcent, and hardware frendly Constant Bt Rate (R) control method can be developed based on the dynamc code block sze Fg. 3. JPEG 2000 Dynamc code block sze at dfferent resolutons.

6 Fg. 4. A typcal lne-based DWT archtecture. 3. COMPRESSION IMPACT WITH DYNAMIC CODE BLOCK SIZE In order to test the mpact of usng dynamc code block szes, we tested several mages wth 4 levels of DWT decompostons. Fg. 5 shows three of those mages used n the paper. The 5/3 flters were used n all experments wth no quantzaton appled. The baselne case used the fxed code block sze for all the code blocks. We also tested a smaller code block sze of for comparson. Two cases of dynamc code block sze were evaluated. In dynamc case 1, code block szes 64 64, 32 32, 16 16, and were used for DWT level 1, level 2, level 3, and level 4 respectvely. In dynamc case 2, code block szes 64 64, 64 32, 64 16, and 64 8 were used for 4 dfferent DWT levels. Table 1 shows the compressed sze n bytes of all subbands at dfferent DWT levels for the Bke mage whch serves as the baselne case of our comparson. Table 2 shows the compresson results of all the three other cases for the same Bke mage. As we can see from Table 3, the case of usng smaller fxed code block sze ncreases the compressed sze by 1.22% and the other two cases of usng dynamc code block sze ncrease the compressed sze by 0.59% and 0.23% respectvely. Fg. 6 also shows the compressed sze comparson n terms of dfferent subbands. There s no sgnfcant dfference between the baselne case and the three other cases n terms of compresson sze. The results of the other two test mages wth sx components are ncluded n Table 3. Smlar conclusons can be obtaned; that there s no sgnfcant mpact on compressed sze when the dynamc code block sze s employed. (a) Bke (b) Brdge (c) Flower Fg. 5. Test mages used n the paper. Table 1. Baselne case: code block sze for all code blocks. Bke DWT level LL HL LH HH Total (byte) Level Level Level Level Total

7 Table 2. Test cases wth fxed code block sze, and two dynamc cases. Bke DWT level LL HL LH HH Total (byte) Level Level Level Level Dynamc Case 1 Dynamc Case 2 Total Level Level Level Level Total Level Level Level Level Total Table 3. Compressed sze Comparsons Dynamc Dynamc Case 1 Case 2 Bke % +0.59% +0.23% Brdge-R % +0.59% +0.19% Brdge-G % +0.61% +0.21% Brdge-B % +0.59% +0.20% Flower-R % +0.67% +0.25% Flower-G % +0.66% +0.26% Flower-B % +0.58% +0.21% K-bytes LL4 HL4 LH4 HH4 HL3 LH3 Sub-bands HH3 HL2 LH2 HH2 HL1 LH1 HH1 Fxed 64x64 Fxed 32x32 Dynamc 1 Dynamc 2 Fg. 6. Compressed sze comparson of Bke mage usng dfferent fxed and dynamc code block szes.

8 4. CONCLUSIONS AND FUTURE WORKS The smulaton results show that there s no sgnfcant mpact on compresson effcency f one uses dfferent code block szes at dfferent DWT levels. Even though the dynamc code block sze s not JPEG 2000 complant, t can be easly employed for a close-loop type encoder-decoder system. The flexblty of usng dynamc code block szes opens up opportuntes for dfferent ways to mplement DWT, BPC, and even bt rate control. In the future, we wll further develop bt rate control methods based on dynamc code blocks. REFERENCES 1. W. B. Pennebaker and J. L. Mtchell, JPEG: Stll Image Data Compresson Standard, Van Nostrand Renhold, New York, ISO/IEC and ITU-T Recommendaton T.81. Informaton technology dgtal compresson and codng of contnuous-tone stll mages: Requrements and gudelnes, D. Taubman and M. Marcelln, JPEG2000: Image Compresson Fundamentals, Standards and Practce. Boston: Kluwer Academc Publsher, T. Acharya and P. S. Tsa, JPEG2000 Standard for Image Compresson Concepts, Algorthms and VLSI Archtectures, Hoboken, New Jersey: John Wley & Sons, Inc., JPEG 2000 Part I: Fnal Commttee Draft (ISO/IEC FCD ), ISO/IEC JTC1/SC29/WG1 N11855, March M. Antonn, M. Barlaud, P. Matheu, and I. Daubeches, Image codng usng wavelet transform, IEEE Trans. Image Processng, vol. 1, pp , Aprl D. Nster and C. Chrstopoulos, Lossless regon of nterest wth embedded wavelet mage codng, Sgnal Processng, vol. 78, no. 1, pp. 1-17, C. Chrstopoulos, J. Askelof, and M. Larsson, Effcent regon of nterest codng technques n the upcomngjpeg2000 stll mage codng standard, n Proc. Internatonal Conference on Image Processng, ICIP 2000, vol. 2, pp D. Taubman, Hgh performance scalable mage compresson wth EBCOT, IEEE Trans. Image Processng, vol. 9, no. 7, pp , July H. Kellerer, U. Pferschy, and D. Psnger, Knapsack Problems, Sprnger, A. Ortega and K. Ramchandran, Rate-dstorton methods for mage and vdeo compresson, IEEE Sgnal Processng Magazne, vol.15, no.6, pp.23-50, November J. C. Dagher, A. Blgn, and M. W. Marcelln, Resource-Constraned Rate Control for Moton JPEG2000, IEEE Trans. Image Processng, vol. 12, no. 12, pp , Dec T. J. Flohr, M. W. Marcelln, and J. C. Rountree, Scan-based processng wth JPEG-2000, Proc. SPIE, vol. 4115, July Y. M. Yeung, O. C. Au, and A. Chang, An effcent optmal rate control scheme for JPEG2000 mage codng, n Proc. Internatonal Conference on Image Processng, ICIP 2003, vol. 3, pp W. Du, J. Sun, and Q. N, Fast and effcent rate control approach for JPEG 2000, IEEE Trans. Consumer Electroncs, vol. 50, no. 4, pp , Nov T. Masuzak, H. Tsutsu, T. Izum, T. Onoye, and Y. Nakamura, JPEG2000 adaptve rate control for embedded system, n Proc. IEEE Internatonal Symposum on Crcuts and Systems, 2002, vol. 4, pp. IV-333 IV T. Km, H. M. Km, P. S. Tsa and T. Acharya, Memory Effcent Progressve Rate-Dstorton Algorthm for JPEG 2000, IEEE Tran. Crcuts and Systems for Vdeo Technology, vol. 15, no. 1, pp , Jan

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