Shape-adaptive DCT and Its Application in Region-based Image Coding

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1 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton, pp Shape-adaptve DCT and Its Applcaton n Regon-based Image Codng Yamn Zheng, Xaoyan Wang and Chengyou Wang School of Mechancal, Electrcal and Informaton Engneerng, Shandong Unversty, Weha , P. R. Chna sduzym@vp.sna.com, swwxy @163.com, wangchengyou@sdu.edu.cn Abstract To get better and flexble performance, regon-based mage codng has been studed wdely n the last few years. In regon-based mage codng, the whole mage can be dvded nto two parts: regon-of-nterest (ROI) and background area. ROI s coded n low compresson rato, whle background area s coded n hgh compresson rato. In ths paper, shape-adaptve DCT (SA-DCT) for codng arbtrarly shaped mage segments s ntroduced. And two regon-based mage codng methods usng dscrete cosne transform (DCT) and SA- DCT are presented. The algorthm based on SA-DCT s comparable wth the one based on DCT n terms of reconstructed mages effects. Expermental results show that the algorthm based on SA-DCT performs better than the one based on DCT both n subectve effect and obectve effect. Therefore, SA-DCT s a more sutable transform for regon-based mage codng than DCT. Keywords: mage codng; dscrete cosne transform (DCT); shape-adaptve DCT (SA- DCT); regon-of-nterest (ROI); mage segmentaton 1. Introducton Conventonal mage codng algorthm whch unformly parttons an mage nto N N rectangle blocks has some problems, such as mosquto and blockng artfacts [1], especally n very low bt rate applcatons. To solve ths problem, regon-based mage codng has been studed wdely n the last few years. Regon-based mage codng conssts of three steps: mage segmentaton, contour codng and texture codng. Texture codng s manly ntroduced n ths paper. An mage s segmented nto regon-of-nterest (ROI) and background area by mage segmentaton [2]. Encoder can encode ROI and background area respectvely. Therefore decoder can decode and manpulate ROI ndependently from the background area. And regon-based mage codng can mprove mage codng qualty n low bt rate applcatons. Shape-adaptve DCT (SA-DCT) s a transformaton method for codng arbtrarly shaped mage segments, and mage denosng [1, 3]. The regon-based mage codng ncludes regonof-nterest and background area codng. In ths paper, two regon-based mage codng methods usng dscrete cosne transform (DCT) and SA-DCT are acheved. The regon-based mage codng algorthm usng SA-DCT uses DC-SA-DCT transform method [4]. The regon-based mage codng method usng DCT uses DCT-JPEG codng system framework [5]. Compared wth regon-based mage codng method usng DCT, the regon-based mage codng usng SA-DCT performs better both n subectve effect and obectve effect. The rest of ths paper s organzed as follows. Secton 2 ntroduces DCT and SA-DCT. And then n Secton 3, the regon-based mage codng s explaned. Expermental results of Book made by ths fle s ILLEGAL. ISSN: IJSIP Copyrght c 2014 SERSC

2 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton the regon-based mage codng usng DCT and SA-DCT are gven n Secton 4. Some reconstructed mages are presented. Conclusons and remarks on possble further work are gven fnally n Secton DCT and Shape-adaptve DCT 2.1. Dscrete Cosne Transform (DCT) The tradtonal two-dmensonal DCT transform s made usually by two one-dmensonal DCT transform on row and column drectons separately. Let X and C represent an mage block and DCT matrx wth sze of N N respectvely. After two-dmensonal DCT transform, transform coeffcents block Y can be denoted by Y CXC T, (1) 1, 0, 0,1,, N 1, N C (, ) (2) 2 (2 1)π cos, 1, 2,, N 1, 0,1,, N 1. N 2N T where C s the transpose matrx of C DCT-based Image Codng The smplest DCT-based mage codng process s referred to as the baselne sequental process. Fgure 1 shows the man procedures for encodng and decodng processes based on the conventonal DCT [5]. It llustrates the specal case of a sngle-component mage; for color mages, all processes operate on each mage component ndependently. In the encodng process, the nput mage data are grouped nto 8 8 blocks, and each block s transformed by the forward DCT (FDCT) nto 64 DCT coeffcents [6]. One s the DC coeffcent and the other 63 are the AC coeffcents. Each of the 64 coeffcents s then quantzed usng one of 64 correspondng values from the quantzaton table. The JPEG standard [5] suggests the lumnance and chromnance quantzaton table respectvely, where the sze of quantzaton nterval s determned by lots of subectve experments. Orgnal Reconstructed FDCT IDCT Quantzer Dequantzer Zg-zag Scan Inverse Zg-zag Scan Entropy Encoder Entropy Decoder Compressed Quantzaton Table Huffman Table Channel Book made by ths fle s ILLEGAL. Fgure 1. Smplfed Dagram of DCT-based Image Encoder and Decoder After quantzaton, the DCT coeffcents are prepared for entropy encodng. The prevous quantzed DC coeffcent s used to predct the current quantzed DC coeffcent, and the dfference s encoded. The 63 quantzed AC coeffcents undergo no such dfferental encodng, but they are converted nto a one-dmensonal zg-zag sequence. The quantzed 100 Copyrght c 2014 SERSC

3 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton coeffcents are then passed to an entropy encodng procedure whch compresses the data further. Here, Huffman encodng s used and Huffman table must be provded to the encoder. In contrast to the encoder, each step of decodng process performs essentally the nverse of ts correspondng man procedure wthn the encoder. The entropy decoder decodes the zgzag sequence of quantzed DCT coeffcents. After dequantzaton the DCT coeffcents are transformed to an 8 8 block of samples by the nverse DCT (IDCT) Shape-adaptve DCT (SA-DCT) The process of SA-DCT s composed of four steps: vertcal shft, vertcal one-dmensonal varable-length DCT, horzontal shft and horzontal one-dmensonal varable-length DCT. The SA-DCT s defned as follows [4]. Fgure 2(a) shows a boundary block of an arbtrarly shaped mage obect segmented nto foreground (black) and background (whte). To perform SA-DCT to foreground segment, frstly the poston of frst pxel of each column n the foreground and the length of each column n the foreground are obtaned. Then based on the obtaned shape nformaton, all pxels of each column n foreground segment are shfted to the uppermost poston and grouped nto column vectors x (Fgure 2(b)). Then, N pxels of each column vector x are transformed by vertcal one-dmensonal DCT nto N vertcal transform coeffcents (Fgure 2(c)). The frst coeffcent of each transform coeffcents column vector a s DC coeffcent. Based on the poston of frst coeffcent of each row and length of each row n the foreground, all transform coeffcents of each row are shfted to the left border and grouped nto row vectors b (Fgure 2(d)). M transform coeffcents of each row n the foreground segment are transformed by horzontal one-dmensonal DCT nto fnal SA-DCT coeffcents (Fgure 2(e)) [1, 2, 7]. The vertcal and horzontal one-dmensonal DCT transforms are expressed n (3) and (4). a S DCT. x, (3) N N c S DCT. b, (4) M M where DCT L ( L N or L M ) denotes the one-dmensonal DCT transform matrx wth sze of L L defned n (5) and S L ( L N or L M ) s the SA-DCT transform prefactor. The horzontal and vertcal nverse one-dmensonal DCT transforms are expressed n (6) and (7). 1 π 1/ 2, p=0, DCTL ( p, k) c0cos p( k ), c0 (5) 2 L 1, otherwse. Book made by ths fle s ILLEGAL. 2 b DCT. c, (6) Τ M MS M 2 x DCT. a, (7) T N NS N where the stars ndcate the resulted data after the SA-DCT coeffcents are quantzed and Τ dequantzed. The DCTM and DCT denote the transpose matrx of DCT M and DCT. T N N Copyrght c 2014 SERSC 101

4 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton To avod mean weghtng defect, the scalng factors S L should be nverse proportonal to L. Let SL 4/ L, however, ths verson of SA-DCT s not normalzed, whch leads to low codng effcency and nose weghtng defect [4]. To avod nose weghtng defect, the scalng factors S L should be set to 2/L. Ths knd of SA-DCT s called pseudo-orthonormal SA- DCT (PO-SA-DCT) [4]. To solve mean weghtng defect and nose weghtng defect, DC- SA-DCT transform method s optmal. The correspondng block dagram s shown n Fgure 3. x a (a) (b) (c) (d) (e) Fgure 2. Forward SA-DCT of Foreground Segment of a Boundary Block: (a) Orgnal Boundary Block, (b) The Boundary Block after the Pxels n the Foreground Segment are Shfted Uppermost Poston, (c) The Boundary Block after Vertcal One-dmensonal DCT, (d) The Boundary Block after the Foreground Segment Coeffcents are Shfted Leftmost Poston, (e) The Fnal SA-DCT Transform Coeffcents Boundary Block after Horzontal one-dmensonal DCT Before PO-SA-DCT, the encoder computes the average m of the nput foreground segment mage data. Then the average m s subtracted by the nput foreground segment mage data. The resdual data wth mean value 0 are transformed by PO-SA-DCT nto SA- DCT coeffcents. The mean value s scaled n the same way as DC values n DCT. The SA- DCT coeffcent c 1,1 s overwrtten wth the scaled mean value DC. m ˆx x ĉ Mean Calculaton DC- Extracton DC (a) b DC-Scalng PO-SA-DCT DC-Re-Scalng c b1, m c DC Correcton DC ecorr x c 1,1 DC Book made by ths fle s ILLEGAL. cˆ 0 1,1 (b) Inverse PO-SA-DCT Fgure 3. Block Dagram of DC-SA-DCT: (a) Forward Transform, (b) Inverse Transform c ˆx ĉ 102 Copyrght c 2014 SERSC

5 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton The decoder extracts the DC coeffcent from the receved coeffcents and the DC coeffcent s rescaled to mean value m. The DC coeffcent ĉ s set to zero. Each row vector c of the resulted PO-SA-DCT coeffcents s transformed by horzontal nverse onedmensonal DCT nto b. Then the corrected value e corr s obtaned by M M corr 1, 1 1 e N b N, (8) where b 1, denotes each coeffcent of frst row vector b 1 and M s the length of b 1 ; 1,1 N s the length of each column of orgnal foreground segment; e corr s subtracted by b 1, to correct the devaton. Then each row element of b s shfted to orgnal rght poston accordng to block shape nformaton and grouped nto column vector a. Each column vector a s transformed by vertcal nverse one-dmensonal DCT nto x and each element of shfted to orgnal poston towards down accordng to block shape nformaton. Fnally, m s added to shfted x, and the reconstructed block mage data are got. 3. Regon-based Image Codng x s Regon-based mage codng conssts of three steps: mage segmentaton, contour codng, and texture codng. An mage s manually splt nto the ROI and background area. Contour codng s not studed n ths paper. Texture codng ncludes ROI and background area texture codng. The ROI s coded ndependent of background area. Fgure 4 shows the smplfed dagram of encodng and decodng system based on SA-DCT. Orgnal Reconstructed DC-SA-DCT Inverse DC-SA-DCT Quantzer Quantzaton Table Dequantzer Zg-zag Scan Inverse Zg-zag Scan Entropy Encoder Huffman Table Entropy Decoder Compressed Channel Fgure 4. Smplfed Dagram of Encodng and Decodng System based on SA-DCT Background area mage data are set to zero, when the ROI mage data are encoded [8]. A mnmum rectangle ncludng regon-of-nterest s found, whose length and wdth are multples of eght. The upper-left pxel s row and column number n the rectangle are multples of eght plus one. Regon-of-nterest encodng and decodng processes based on SA-DCT are descrbed below. The pxels n mnmum rectangle ncludng regon-of-nterest are grouped nto 8 8 blocks, and the number of non-zero pxels of each block s calculated. Based on the calculated number of non-zero pxels of each block, all blocks are dvded nto three categores: Book made by ths fle s ILLEGAL. (a) The block wth 0 non-zero pxels s not transformed. Copyrght c 2014 SERSC 103

6 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton (b) The block wth 64 non-zero pxels s transformed by standard DCT. (c) The block wth non-zero pxels number s larger than 0 and smaller than 64 s transformed by DC-SA-DCT [4]. Each of the resulted coeffcents s quantzed usng the correspondng value n the quantzaton table. And then the quantzed data are entropy coded. In the decodng process, the transmtted data are entropy decoded. Then the decoded data are dequantzed. Accordng to the three dfferent categores of blocks, dfferent transforms are performed. (a) The dequantzed data of the block wth 0 non-zero pxels are not nverse transformed. (b) The dequantzed data of the block wth 64 non-zero pxels are transformed by nverse DCT. (c) The dequantzed data of other blocks are transformed by nverse DC-SA-DCT transform method. Now the reconstructed mage data of regon-of-nterest are obtaned. Regon-of-nterest mage data are set to zero, when background area mage data are encoded. The encodng and decodng processes of background area mage data are the same as the regon-of-nterest. Fnally the reconstructed regon-of-nterest and background area mage data are merged to get the reconstructed full mage. 4. Expermental Results 4.1. Regon-based Image Codng Usng MATLAB Smulaton experments are conducted usng MATLAB 7.8. In order to hghlght the advantages of regon-based mage codng usng SA-DCT, we have compared the regonbased mage codng scheme usng SA-DCT wth the one based on DCT n terms of obectve effect and subectve effect. Announcer and Lena (8bts/pxel, ) are the test gray mages. The regon-of-nterest mages of both mages wth background area mage data set to zero are shown n Fgure 5. The contour data of the regon-of-nterest are not encoded n ths paper. Expermental results are obtaned n the case of the decoder has known contour data of the regon-of-nterest of both mages. Book made by ths fle s ILLEGAL. (a) Fgure 5. Regon-of-nterest wth Background Area Set to zero: (a) Announcer, (b) Lena (b) 104 Copyrght c 2014 SERSC

7 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton In the case of SA-DCT, regon-of-nterest and background area are encoded separately accordng to the encodng process based on SA-DCT. The regon-of-nterest s encoded n low compresson rato, whle the background area s encoded n hgh compresson rato. Then the encodng bt rates of regon-of-nterest and background area are calculated ndependently. Then both areas are decoded accordng to the decodng process based on SA-DCT. The PSNRs of both areas are computed by the reconstructed ROI and background area mage data. Afterwards the reconstructed regon-of-nterest and background area mage data are merged to obtan the full mage and the PSNR of the reconstructed full mage s computed. In the case of DCT, the mnmum rectangle ncludng the regon-of-nterest wth background area mage data are set to zero s grouped nto 8 8 blocks and each block s encoded accordng to the encodng process of DCT-JPEG. The encodng bt rate of ROI s calculated. Then the full mage data wth the regon-of-nterest mage data are set to zero (.e., background area) are encoded. The encodng bt rate of the background area mage data s calculated. Afterwards the encoded regon-of-nterest mage bts are decoded to get the reconstructed regon-of-nterest mage data accordng to the decodng process of DCT-JPEG. The PSNR s computed by reconstructed regon-of-nterest mage data. Then the encoded background area mage data are decoded accordng to decodng process of DCT-JPEG. The PSNR s computed by reconstructed background area mage data. Fnally the reconstructed regon-of-nterest and background area mage data are merged to obtan the reconstructed full mage. Then the PSNR of the reconstructed full mage s computed Comparson wth DCT Regon-based mage codng usng SA-DCT s compared wth the one based on DCT n terms of PSNRs of the reconstructed mages ncludng regon-of-nterest, background area and full mage. The expermental results of the Announcer mage usng DCT and SA-DCT respectvely are shown n Table 1. Table 1. Comparson of Regon-based Image Codng usng DCT and SA- DCT Appled to Image Announcer PSNR (db) ROI Background DCT SA-DCT bt rate bt rate (bpp) Full (bpp) ROI Background ROI Background Full mage mage Book made by ths fle s ILLEGAL As shown n Table 1, the regon-of-nterest encodng bt rate and the background area encodng bt rate based on SA-DCT are the same as DCT. The regon-of-nterest s compressed wth low compresson rato, whle the background area s compressed wth hgh compresson rato. Expermental results show that the PSNRs of the reconstructed mages (regon-of-nterest, background area, and full mage) based on SA-DCT are hgher than the ones based on DCT at varous bt rates. Therefore, the regon-based mage codng algorthm usng SA-DCT s better than the one based on DCT n terms of obectve effect. Copyrght c 2014 SERSC 105

8 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton To compare the compresson performance subectvely, Fgure 6 and Fgure 7 show the reconstructed mages Announcer and Lena based on DCT and SA-DCT respectvely n the case when ROI bt rate s 0.80bpp and background bt rate s 0.50bpp. Accordng to the subectve effect, the reconstructed mages ncludng Announcer and Lena based on SA-DCT are better. The reconstructed mages ncludng Announcer and Lena based on DCT are worse than that based on SA-DCT especally n terms of the edge of the regon-of-nterest. From the expermental results, we can see that compared to the algorthm based on DCT, the regon-based mage codng algorthm usng SA-DCT mproves compresson performance n term of PSNR and vsual qualty. And the regon-based mage codng methods usng SA- DCT and usng DCT are also be appled to other test mages, smlar results can be obtaned. (a) Fgure 6. Reconstructed Announcer Images: (a) DCT, (b) SA-DCT (a) Book made by ths fle s ILLEGAL. 5. Concluson Fgure 7. Reconstructed Lena Images: (a) DCT, (b) SA-DCT In ths paper, the transform method SA-DCT for codng arbtrarly shaped mage segments s ntroduced. The regon-based mage codng process of an mage conssts of three steps: mage segmentaton, contour codng and texture codng. The texture codng ncludes ROI texture codng and background area texture codng. To reduce the total encodng bt rate and take advantage of the vson characterstcs of human eyes, the regon-of-nterest s compressed n low compresson rato and the background area s compressed n hgh (b) (b) 106 Copyrght c 2014 SERSC

9 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton compresson rato. Two regon-based mage codng methods usng DCT and SA-DCT are acheved. Compared wth regon-based mage codng method usng DCT, the regon-based mage codng algorthm usng SA-DCT s better both n terms of obectve effect and subectve effect. Therefore, SA-DCT s more sutable for regon-based mage codng than DCT. Texture codng s manly ntroduced n ths paper, whle contour codng s not consdered. So the contour codng s gong to be studed n the further work. Acknowledgements Ths work was supported by the teachng reform proect of Shandong Unversty, Weha, Chna (Grant No. B201319) and the Natonal Natural Scence Foundaton of Chna (Grant No ). The authors wsh to thank Songzhao Xe and Chunxao Zhang for ther help and valuable suggestons. References [1] T. Skora, Low complexty shape-adaptve DCT for codng of arbtrarly shaped mage segments, Sgnal Processng: Image Communcaton, vol. 7, no. 4-6, (1995), pp [2] P. Garsteck and R. Stasnsk, Influence of mage segment sze on effcency of SA DCT, Proceedngs of the 7th Nordc Sgnal Processng Symposum, Reykavk, Iceland, (2006) June 7-9, pp [3] A. Fo, K. Dabov, V. Katkovnk and K. Egazaran, Shape-adaptve DCT for denosng and mage reconstructon, Proceedngs of SPIE - Image Processng: Algorthms and Systems, Neural Networks, and Machne Learnng, San Jose, CA, USA, vol. 6064, (2006) January 16-18, pp. 0N1-0N12. [4] P. Kauff and K. Schueuer, Shape-adaptve DCT wth block-based DC separaton and DC correcton, IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol. 8, no. 3, (1998), pp [5] ISO/IEC, Informaton Technology-Dgtal Compresson and Codng of Contnuous-tone Stll Images-Part 1: Requrements and Gudelnes, ISO/IEC , (1994). [6] G. K. Wallace, The JPEG stll pcture compresson standard, IEEE Transactons on Consumer Electroncs, vol. 38, no. 1, (1992), pp [7] T. Skora and B. Maka, Shape-adaptve DCT for generc codng of vdeo, IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol. 5, no. 1, (1995), pp [8] K. Belloulata, R. Stasnsk and J. Konrad, Regon-based mage compresson usng fractals and shapeadaptve DCT, Proceedngs of the IEEE Internatonal Conference on Image Processng, Kobe, Japan, vol. 2, (1999) October 24-28, pp Authors Yamn Zheng was born n X an n She receved her B.E. degree from X'an Jaotong Unversty, Chna, n 1982 and her M.E. degree n crcut, sgnal and systems from Behang Unversty, Chna, n Now she s an assocate professor n the School of Mechancal, Electrcal and Informaton Engneerng, Shandong Unversty, Weha, Chna. Her current research nterest ncludes electronc technology, computer technology and ts applcatons. Book made by ths fle s ILLEGAL. Xaoyan Wang was born n Shandong provnce, Chna n She receved her B.S. degree n electronc nformaton scence and technology from Shandong Unversty, Weha, Chna, n Now she s pursung her M.E. degree n crcuts and systems n Shandong Unversty, Weha, Chna. Her research nterests concentrate on mage and vdeo processng. Copyrght c 2014 SERSC 107

10 Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton Chengyou Wang was born n Shandong provnce, Chna n He receved hs B.E. degree n electronc nformaton scence and technology from Yanta Unversty, Chna, n 2004 and hs M.E. and Ph.D. degree n sgnal and nformaton processng from Tann Unversty, Chna, n 2007 and 2010 respectvely. Now he s a lecturer n the School of Mechancal, Electrcal and Informaton Engneerng, Shandong Unversty, Weha, Chna. Hs current research nterests nclude dgtal mage and vdeo processng, wavelet analyss and ts applcatons, and smart grd technology. Book made by ths fle s ILLEGAL. 108 Copyrght c 2014 SERSC