Rate-Complexity Scalable Multi-view Image Coding with Adaptive Disparity-Compensated Wavelet Lifting

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1 SSN , England, UK Journal of nformaton and Computng Scence Vol. 4, No. 3, 9, pp. -3 Rate-Complext Scalable Mult-vew mage Codng wth Adaptve Dspart-Compensated Wavelet ftng Pongsak asang, Chang-su Km and Wuttpong Kumwlasak Electroncs and Telecommuncaton Department, Facult of Engneerng, Kng Mongkut s Unverst of Technolog, Thonbur, Thaland Electrcal Engneerng Department, Facult of Engneerng, Korea Unverst, Korea (Receved Januar, 9, accepted Aprl, 9 Abstract. Ths paper presents a novel algorthm for rate-complext scalable mult-vew mage codng usng an adaptve dspart-compensated (DC wavelet lftng scheme. Frst, mage regons of mult-vew mages are prortzed b countng matchng ponts. The proposed algorthm selects ether Haar, 5/3, or our proposed multple pcture reference DC wavelet lftng adaptvel. The selecton crteron s based on the bt budget constrant, the complext budget constrant, and the prortes of mage regons. Then, the low-pass and hgh-pass subbands, obtaned from the DC wavelet lftng, are further decomposed b a spatal wavelet transform. The resultng wavelet coeffcents are entrop encoded wth the SPHT codec. Expermental results show that the proposed algorthm provdes an effcent adaptve framework for mult-vew mage codng. Kewords: Mult-vew mage codng, rate-complext scalablt, wavelet lftng, dspart-compensaton, mage feature matchng.. ntroducton Recentl, mult-vew mage codng has been extensvel researched due to ts broad varet of applcatons, ncludng vrtual tours on the nternet, three-dmensonal navgaton, presentaton, and medcal dagnoss [-5]. Snce a set of mult-vew mage conssts of several ordnar mages, t requres a huge amount of data for storage and transmsson. A tpcal mult-vew mage, however, contans consderable redundances among mage vews, snce the represent the same scene from dfferent vewponts. The objectve of mult-vew mage codng s to acheve hgh compresson rato, reducng these redundances, whle mantanng hgh mage qualt. Varous algorthms have been proposed to encode mult-vew mage data. Magnor et al. [] proposed a mult-vew mage codng algorthm based on texture codng and model-aded predcton. 3-D scene geometr s utlzed for ther algorthm. Tong and Gra [] examned the DC predctve codng for mult-vew mages, whch emplos a block-based correspondence matchng scheme. n [3, 6], the lght feld was taken nto account for mult-vew mage codng. n [, 3, 5], geometrc structures n mult-vew mages, such as depth map, eppolar geometr, 3-D voxel model, were used for mult-vew mage codng. Also, there have been several attempts to utlze the wavelet transform n vdeo codng and mult-vew mage codng [3, 6, 9, ], especall after the success of the moton compensaton wth wavelet lftng, whch guarantees the nvertblt at the snthess sde [6]. The man advantages of wavelet compresson are ts scalablt and hgh energ compacton [6, ]. For mult-vew mage codng, Grod et al. [3, 6] used the 4-D Haar and 5/3 wavelet lftng schemes to perform the dspart compensaton (DC for lght feld compresson. Anantrasrcha et al. [9, ] emploed the hbrd of Haar and 5/3 wavelet lftng n the block-based DC. n ther work, the selecton of DC mode s based on the mnmum sum of absolute dfferences (SAD crteron. However, the restrcted reference mage vews onl to adjacent vews. n other words, ther structure does not allow the usage of several vews or combnaton of them for DC. Moreover, ther work does not explot the features, used n 3-D scene reconstructon, when performng the mult-vew mage codng. n general, when encodng mult-vew mage contents, onl the rate (or bt budget constrant s used as the encodng constrant. However, n practce, dfferent encoders ma have dfferent encodng capabltes. An encoder wth low computatonal capablt cannot choose a complex algorthm to encode mult-vew Publshed b World Academc Press, World Academc Unon

2 Pongsak asang, et al: Rate-Complext Scalable Mult-vew mage Codng mages n a lmted tme. n contrast, an encoder wth hgh capablt has more degrees of freedom n choosng a complex codng algorthm to acheve better reconstructed mult-vew mage qualt. To be useful n practce, a mult-vew mage encoder should be flexble enough to adjust ts complext adaptvel. n ths work, we propose a novel algorthm for rate-complext scalable mult-vew mage codng usng an adaptve DC wavelet lftng scheme. Fg. shows the overall archtecture of the proposed algorthm. The proposed algorthm combnes an mage regon prortzaton scheme wth an adaptve DC wavelet lftng technque to flexbl adjust both the bt rate and the encodng complext. Frst, mage regons are prortzed. The prortes of mage regons are derved from a feature matchng method. n ths paper, the Harrs corner detector [9] s used to fnd the matchng ponts. mage regons wth hgher denstes of matchng ponts are assgned hgher prortes n the DC wavelet lftng. Fg. : The archtecture of the proposed mult-vew mage codng algorthm. Then, for each regon, we select the mode of DC wavelet lftng among three modes: Haar, 5/3, or the proposed multple pcture reference modes. The mode s selected to acheve the mnmum dstorton gven the constrant on the target bt rate, the encodng complext, and the regon prort. After the DC wavelet lftng s appled to reduce the redundanc among vews, the dscrete wavelet transform s appled to decompose low-pass and hgh-pass subbands, respectvel. Fnall, the wavelet coeffcents are entrop coded wth the SPHT codec to generate the btstream. Dspart vectors and DC modes are also entrop encoded b the arthmetc codng and sent to the decoder. The remander of the paper s organzed as follows. Secton explans the mage prortzaton va mage feature matchng, and Secton 3 descrbes the DC wavelet lftng modes. Secton 4 brefl dscusses the entrop codec. Secton 5 proposes a mode selecton scheme, whch supports rate-complext scalablt. Secton 6 provdes expermental results. Fnall, the conclusons are drawn n Secton 7.. mage Regon Prortzaton va mage Feature Matchng n general, mult-vew mages taken from real lfe scenes wth multple cameras contan a huge amount of redundant nformaton. We attempt to prortze mage regons so that a regon wth less redundanc has a hgher prort and s encoded wth a more precse predcton scheme. On the other hand, a regon wth more redundanc s assgned a lower prort, snce t can be effectvel encoded even wth a smple predcton scheme. We determne the prortes b countng the number of nterestng ponts. nterestng ponts n an mage vew can be matched to nterestng ponts n the other vews. Notce that the regons, whch have dense matchng ponts, can be used to compute a depth map n 3-D reconstructon [9]. To fnd nterestng ponts, the Harrs corner detector s emploed [9]. t detects the local varaton of ntenst n both x and drectons. et ( x, denote the ntenst of the pxel at poston ( x,. Also, let x and denote the partal dervatves of (x, wth respectve to x and, respectvel. The local JC emal for contrbuton: edtor@jc.org.uk

3 Journal of nformaton and Computng Scence, Vol. 4 (9 No. 3, pp -3 3 structure matrx s defned as x x x wg, ( where w G s a Gaussan flter. The above equaton can be wrtten n another form as x x x, ( where x w G x and w, whch are the Gaussan smoothed versons of the partal G der vatves of the local ntenst. The local structure matrx n ( s smmetrc. Thus, t can b e dagonalsed b a matrx transformaton. The resultng dagonal matrx has two non-negatve egenvalues and. f both egenvalues are large, the ntenst has strong varaton n two orthogonal drectons, whch ndcates that ( x, s probabl a corner pxel. Therefore, we compute M k( det( k( trace(, (3 where k s a small number. n ths work, k s set to.4 as suggested n [9]. f M s larger than a threshold, the pxel at ( x, s declared as an nterestng pont. The threshold s set to 4. Matchng ponts are determned as follows. Frst, gven an nterestng pont a t x, n the reference vew (the frst vew, we buld up a wndow of 55 pxels around the center x,. Then, n each of ( ( the other vews, we buld up a wndow of the same sze wth center ( x,, whch s the poston of the nterestng pont nearest to x,. We compute the sum of squared dfferences (SSD between the ( correspondng pxels wthn the wndows. Then, we move the center of the second wndow to the other nterestng ponts wthn the search radus of pxels. The center of the wndow eldng the mnmum SSD s selected as the matchng pont of (x,. We later use these matchng ponts to select the mode of DC wavelet lftng adaptvel. 3. Multple Pcture Reference Dspart Compensated Wavelet ftng ftng schemes can be used to construct dscrete wavelet transforms []. The subband decomposton nto hgh-pass and low-pass components s acheved wth a sequence of predcton and update steps n the lftng structure. Suppose that we have N mage vews. We dvde ths group of mage vews nto even vews, X, and odd vews, X, whch are smlar and hghl correlated n general. n the context of mult-vew mage codng, the dspart estmaton and compensaton can be effectvel ntegrated nto the predcton and update steps. Fgs. and 3 show the frst level decompostons of the Haar and 5/3 DC wavelet lftng, respectvel. The Haar DC wavelet lftng s performed b usng onl a sngle adjacent vew as a reference vew, whereas the 5/3 DC wavelet lftng uses two adjacent vews. Specfcall, the Haar lftng uses mage vew or mage vew to reduce the redundanc n mage vew, whle the 5/3 lftng uses both of them. On the other hand, our proposed lftng mode enables us to use more than two reference JC emal for subscrpton: publshng@wau.org.uk

4 4 Pongsak asang, et al: Rate-Complext Scalable Mult-vew mage Codng X X X a, b, b, H H a, X Fg. : The frst level decomposton of the Haar DC wavelet lftng. X b, b, X X a, a, H H a, a, X X b, b 3, b, b 3, X X 3 a,3 a 4,3 H H a,3 a 4,3 X 3 X 4 b 3,4 b 3,4 X 4 Fg. 3: The frst level decomposton of the 5/3 DC wavelet lftng. mage vews. To predct mage vew wth the new lftng mode, we use mage vews,, 3, 3, 5, 5,. n other words, an even vew s predcted from odd vews, and an odd vew s predcted from even vews. n ths wa, t s guaranteed that all mage vews can be recovered at the snthess sde of the wavelet lftng. X b 3, b, b N, b 3, b b N,, X X a 4, a, a, a N, H H a 4, a, a, a N, X X b, b 3, b N, b, b 3, X X 3 a,3 a 4,3 a,3 a N,3 H H a,3 a 4,3 a,3 a N,3 X 3 X 4 b 3,4 b,4 b 3,4 b,4 X 4 Fg. 4: The unfed structure of DC wavelet lftng for mult-vew mage codng. Fg. 4 shows the unfed structure of DC wavelet lftng for mult-vew mage codng, whch ncludes the Harr, 5/3, and our proposed lftng modes as specal cases. n the unfed structure, the number of reference JC emal for contrbuton: edtor@jc.org.uk

5 Journal of nformaton and Computng Scence, Vol. 4 (9 No. 3, pp -3 5 vews can be flexbl chosen to obtan the best predcton. t also does not restrct reference vews to adjacent mage vews onl. n other words, non-adjacent vews can be used as references as well. Suppose that a N /N / N / mult-vew mage conssts of N / even vews and N / odd vews. Then, there are possble choces for selectng reference mage vews for DC. The -th low-pass ( and hgh-pass ( components can be wrtten as and H X a DC( X, dˆ, a DC( X, dˆ, a DC( X, dˆ, a DC( X, dˆ 4, 4 4 a DC( X, dˆ 4, 4 4 a ˆ 6,DC( Xj, d 6 X b DC( H, dˆ, b DC( H, dˆ, b DC( H, dˆ 3, 3 b DC( H, dˆ 3, 3 b DC( H, dˆ 5, 3 l b ˆ 5,DC( H, d Table : Scalng factors n the predcton and update steps n dfferent lftng modes. ( denotes the number of reference mage vews. N r ftng modes mn, a b mn, Haar mode 5/3 mode 4 Proposed mode N r N r where dˆn m denotes the set of dspart vectors from mage vew n to mage vew m. DC( X ˆ m, dn m s the dspart compensated mage of X n, whch s obtaned from the reference vew X n usng dˆn m. The scalng factors a mn, and b mn, are used n the predcton and update steps, respectvel. All the subscrpts, denotng vew ndces, are restrcted between and N-, where N s the number of mage vews. Note that, for the Haar and 5/3 wavelet lftng schemes, a mn, s set to and.5, and b mn, s set to.5 and.5, respectvel. For our proposed lftng mode, we adopt the weghtng scheme n [8]. Specfcall, a mn, s set to the nverse of the number of reference vews, and b mn, s set to a mn, /. Table summarzes the scalng factors n the lftng modes. Fg. 5 llustrates the reference mage vews used n DC wth Haar, 5/3, and our proposed lftng modes, when a number of vews n a set of mult-vew mage are equal to fve. H (4 (5 JC emal for subscrpton: publshng@wau.org.uk

6 6 Pongsak asang, et al: Rate-Complext Scalable Mult-vew mage Codng The complext of DC wavelet lftng s determned b the block matchng process. Suppose that the search range of each block s equal to R R pxels, the block sze s N N pxels, and the mage sze s M M pxels. The complext, when we use onl a sngle reference vew, requres (R M operatons to perform block matchng process. Therefore, f we use k reference vews, the total complext per block s equal to k(r M operatons. n ths work, we treat ( R M operatons as one complext unt. Therefore, we requre k complext unts when we use k reference vews. Dfferent DC wavelet lftng modes requre dfferent levels of complext. A mult-vew mage encoder can choose the mode based on ts computatonal capablt. For example, f the encoder has low processng power, t should choose smple DC wavelet lftng modes, whch requre a small number of complext unts. On the other hand, f the encoder s powerful, t can choose more complex DC lftng modes. 4. Entrop Codng of Moton Vectors, Modes, and Resdue Error The DC wavelet lftng decomposes multple mage vews nto low pass subbands and hgh pass subbands, reducng the nter-vew redundanc. Each subband, however, stll contans spatal redundances, and thus t s decomposed further b the b-orthogonal dscrete wavelet transform (DWT, as shown n Fg. 6. The DWT coeffcents are then compressed usng the SPHT coder [], whch s based on the set parttonng n herarchcal trees and encodes the coeffcents n the bt-plane order from most sgnfcant bts to least sgnfcant bts. n general, the low pass subband mages from the DC wavelet lftng contan more mportant nformaton to human vsual sstem than the hgh pass subband mages. Therefore, we assgn more bts to encode the DWT coeffcents for a low pass subband mage than those for a hgh pass subband mage. f the total bt budget allocated to a low pass subband s equal to, the total bt budget allocated to a hgh pass subband wll be equal to B budget, H Bbudget, B budget,, where. The output btstream of the SPHT codec s transmtted to the decoder. At the decoder sde, the SPHT decoder obtans the low pass and the hgh pass subband mages, whch are, n turn, used to reconstruct the mult-vew mage at the snthess sde of the DC wavelet lftng. There are two parameters that should be also transmtted from the encoder to the decoder: dspart vectors and DC lftng modes. n ths work, we encode dspart vector dfferences (DVD and DC lftng modes usng arthmetc codng. The dspart vector of the current block s predcted from the medan of the dspart vectors of the left block, the top block, and the top rght block. Then, we compute DVD, whch s the dfference between the dspart vector of the current block and the predcted one. We represent DVDs and DC lftng modes b code numbers, as shown n Table and Table 3, respectvel. The code numbers are then encoded usng the arthmetc coder n [] to obtan a bt stream. At the decoder, dspart vectors and DC lftng modes are decoded and then used to reconstruct the mult-vew mages. Table 3: The DC lftng modes and the correspondng code Table : The code numbers for DVDs. numbers. Haar_left and Haar_rght denote the Haar mode when the left sde mage and the rght sde mage are used as the reference, respectvel. DVDs Code numbers ftng modes 5/3 mode Haar_left mode Haar_rght mode Proposed mode Code numbers 3 JC emal for contrbuton: edtor@jc.org.uk

7 Journal of nformaton and Computng Scence, Vol. 4 (9 No. 3, pp -3 7 (a Haar mode (b 5/3 mode (c Proposed mode Fg. 5: llustraton of the reference mage vews n the Haar, 5/3 and our proposed lftng modes, when a number of mage vews are equal to fve. Fg. 6: After the DC wavelet lftng, the low pass and hgh pass subbands stll contan spatal redundances. Thus, each subband mage s decomposed further b the spatal DWT. 5. Mode Selecton wth Scalable Rate and Complext 5.. Problem Formulaton The DC wavelet lftng modes determne the rate and the qualt of reconstructed mult-vew mages, and the complext of a DC mode s proportonal to a number of reference frames n the compensaton procedure. The mode should be selected to maxmze the qualt of reconstructed mages, subject to both the rate and complext constrants. et D M, B denote the dstorton of the th dspart compensated block, when t s compensated wth mode Proposed}, and the bt rate ( M at bt rate B B. The mode M s selected from {Haar_left, Haar_rght, 5/3, ncludes the bts for encodng the mode, dspart vectors, and resdue errors. Also, let C( M denote the complext to encode block wth mode M. Notce that the complextes of Haar, 5/3, and the proposed modes are,, and N/ complext unts, where N s the number of multple vews. Our objectve s to obtan the hghest mage qualt subject to both the rate and complext constrants. t can be formall stated as Problem: For block, search for the DC mode M and the bt rate B that mnmze the dstorton JC emal for subscrpton: publshng@wau.org.uk

8 8 subject to the constrants and Pongsak asang, et al: Rate-Complext Scalable Mult-vew mage Codng D M, B (6 ( B B, (7 budget C ( M C, (8 budget where Bbudget and C budget are the bt budget and the complext budget, and and are the prort factors of block for the bt budget and the complext budget, respectvel. The prort factors can be determned based on the number of matchng ponts wthn the block. Ths constraned optmzaton problem can be solved b mnmzng the agrangan cost functon, gven b (, D ( M, B B C ( M, (9 bts comp bt comp where bt s the agrangan multpler for the bt budget, and s the agrangan multpler for the complext budget. 5.. Problem Soluton To fnd out the exact soluton that mnmzes (9, we need the relatonshp between the bt budget, the complext, and the dstorton. However, the accurate estmaton of the relatonshp requres a huge amount of computatons. Ths s because we need consder all possble modes and bt rates. Therefore, n ths work, we nstead obtan an approxmate soluton b constructng unversal ratedstorton and complext-dstorton curves from a tranng set of mult-vew mages. These traned ratedstorton and complext- dstorton curves approxmate the rate-dstorton and complext-dstorton characterstcs of ncomng mult-vew mages. These traned curves are shown n Fgs. 7 and 8, whch were obtaned from three sets of mult-vew mages: Hotel, Marker, and Tedd. comp Fg. 7: The complext-dstorton plot of dfferent DC wavelet lftng modes. Fg. 8: The rate-dstorton curves of dfferent DC wavelet lftng modes. Usng these traned curves, we select the DC wavelet lftng mode and the bt rate n two steps. Frst, gven the complext budget, we select the mode achevng the lowest average dstorton from the complext-dstorton curve. Then, wth the selected mode, we choose the rate-dstorton curve to determne the target bt rate. For example, suppose that there are totall fve vews n a set of mult-vew mages. f the complext budget of a block s equal to 3 unts, the proposed adaptve DC mode s selected, snce t provdes the lowest average dstorton wthn the budget. Then, the rate-dstorton curve correspondng to the proposed adaptve DC mode s selected. Fnall, gven the bt budget constrant, the optmal bt rate s obtaned from the rate-dstorton curve. JC emal for contrbuton: edtor@jc.org.uk

9 Journal of nformaton and Computng Scence, Vol. 4 (9 No. 3, pp -3 9 Fg. 9: The example of rate-dstorton curves for dfferent DC wavelet lftng modes. n ths example, the optmal bt rate, correspondng to a agrangan multpler bt, s found. The detaled algorthm can be stated as follows. Algorthm: (Rate-Complext Optmzed Mode Selecton to Acheve the Hghest Pcture Qualt Step : Gven the total bt budget and complext budget for an entre frame, dstrbute them to all blocks b consderng the prort factors and. Step : For each block n the frame, peform Step.: Gven the complext budget, select the mode, provdng the mnmum average dstorton, from the traned complext-dstorton plot. et M denote the selected mode. Step.: Choose the traned rate-dstorton curve of the mode * * M. Use the b-secton algorthm n [3], * to search for the optmal bt rate correspondng to a agrangan multpler bt. et B denote the optmal bt rate. Fg. 9 llustrates the process of determnng the optmal bt rate, assumng the selected mode n Step. s M3. Step.3: Encode the block usng * M and. * B Please acknowledge collaborators or anone who has helped wth the paper at the end of the text. 6. Expermental Results To evaluate the performance of the proposed rate-complext scalable algorthm, we experment on both snthetc and real mult-vew mages. The snthetc sequence s the hotel mage. The real sequences are the marker and tedd mages. These mages consst of fve vews and have the sze of 5ⅹ5 pxels. The performance of the proposed algorthm s evaluated n terms of DC predcton effcenc and PSNR. We compare the PSNR performances of the proposed algorthm under dfferent rate and complext budgets. Note that we use the block sze of 4x4 pxels and the nteger-pel search accurac for all DC modes. The rato of the bt allocaton n low and hgh subbands s equal to 3 to. n other words, defned n Secton 4 s set to.6. As mentoned n Sectons and 5, the regons wth hgh denst of matchng ponts are gven hgher prortes. Fg. shows the computed matchng ponts of the hotel mage. Fg. (c depcts the matchng ponts obtaned from Fg. (a and Fg. (b. We dvde mage blocks to two classes: the class correspondng to hgh denst matchng ponts and the class correspondng to low denst matchng ponts. n the followng tests, the complext prort factor for blocks wth hgh matchng pont denstes s set to be twce hgher than the other blocks wth low denstes. The bt prort factor s set to be the same for all blocks. To be more specfc, s equal to and for blocks wth hgh and low matchng pont denstes, respectvel. s set to be for all blocks. Fgs. and show the hgh pass subbands of the hotel and the tedd mages, respectvel. The represent resdue errors after the DC predcton. The normalzed resdue energ s defned as the squared sum of resdue pxel errors, dvded b the number of pxels. We see that resdue errors are reduced, when we JC emal for subscrpton: publshng@wau.org.uk

10 Pongsak asang, et al: Rate-Complext Scalable Mult-vew mage Codng allow a hgher complext encoder to explot more complex DC wavelet lftng modes. Fg. 3 compares the subjectve qualt of the tedd sequence under dfferent complext budgets. We can conclude from these expermental results that, f the encoder ncreases ts complext, the better performance can be acheved. Fgs. 4, 5, and 6 show the average PSNRs over all mage vews for the hotel, tedd and marker mages, respectvel, n terms of bts per pxel (bpp under dfferent complext budgets. The complext budgets for scenaro to scenaro 5 are 6384, 4576, 3768, 496, and 495 unts per mage, respectvel, whch correspond to the average complext budgets of. unt,.5 unts, unts,.5 unts, and 3. unts per block. Scenaro has the lowest complext budget,. unt per block, n whch the onl possble DC mode s the Haar mode [9,]. On the other hand, n scenaros ~5, the mode for a block can be selected from the Haar, 5/3, and the proposed modes, dependng on the gven complext budget. t s observed that the better performance can be acheved when the encoder uses bgger complext and rate budgets. Note that, at low bt rates, the performance gans are not sgnfcant even though we ncrease the complext budgets. Ths s because the addtonal bts for more dspart vectors n the advanced modes become a heaver burden at low bt rates. Fgs. 4, 5, and 6 ndcate that the proposed algorthm can support dfferent bt budgets and complext budgets effcentl and adaptvel. Note that bt rates n Fgs. 4, 5, and 6 nclude all the bts for encodng wavelet coeffcents, dspart vectors, and lftng modes. (a (b (c Fg. : (a nterestng ponts from the frst vew (76 ponts. (b nterestng ponts from the second vew (73 ponts. (c Matchng ponts between the frst and the second vews (488 ponts. (a (b (c Fg. : A hgh pass subband of the hotel mage: (a Haar mode (normalzed energ = 9.79, complext = unt per block, (b 5/3 mode (normalzed energ =.34, complext = unts per block, and (c the proposed adaptve wavelet lftng (normalzed energ = 5.95, complext = 3 unts per block. JC emal for contrbuton: edtor@jc.org.uk

11 Journal of nformaton and Computng Scence, Vol. 4 (9 No. 3, pp -3 (a (b (c Fg. : A hgh pass subband of the Tedd mage. (a Haar mode (normalzed energ = 7.98, complext = unt per block, (b 5/3 mode (normalzed energ = 3.9, complext = unts per block and (c the proposed adaptve wavelet wavelet lftng (normalzed energ = 7.94, complext = 3 unts per block. (a (b (c Fg. 3:Reconstructed tedd mages at the bt rate of. bpp. (a Haar mode (complext = unt per block, (b 5/3 mode (complext = unts per block, (c the proposed adaptve wavelet lftng (complext = 3 unts per block, and (d the orgnal mage. (d JC emal for subscrpton: publshng@wau.org.uk

12 Pongsak asang, et al: Rate-Complext Scalable Mult-vew mage Codng PSNR (db Scenaro Scenaro Scenaro 3 Scenaro 4 Scenaro bts/pxel (bpp Fg. 4: The PSNR performances on the hotel mage. n scenaros ~5, the average complext budgets are.,.5,.,.5, and 3. unts per block, respectvel PSNR (db Scenaro 6 Scenaro Scenaro 3 5 Scenaro 4 Scenaro bts/pxel (bpp (a PSNR (db Scenaro Scenaro 34 Scenaro 3 Scenaro 4 Scenaro bts/pxel (bpp (b Fg. 5: The PSNR performances on the tedd mage(fg a and marker mage(fg b. n scenaros ~5, the average complext budgets are.,.5,.,.5, and 3. unts per block, respectvel. 7. Conclusons We proposed a rate-complext scalable framework usng adaptve DC wavelet lftng technque for mult-vew mage codng. The proposed algorthm smartl selects a proper DC mode among the Haar, 5/3, or our proposed wavelet lftng for each block subject to the complext budget and bt budget constrants. The hgher PSNR performance can be acheved b ncreasng the complext, the bt rate, or both. Therefore, ths prototpe scheme s ver scalable, whch can be appled n varous applcatons. The smulaton results on test mages demonstrated that the proposed algorthm can support the rate-complext scalablt effcentl. 8. References [] M. Magnor, P. Ramanathan, and B. Grod. Mult-vew codng for mage-based renderng usng 3-D scene geometr, EEE Trans. Crcuts Sst. Vdeo Technol.. 3, 3(: 9-6. [] X. Tong and R. M. Gra. Codng of mult-vew mages for mmersve vewng. n Proc. CASSP., 4: JC emal for contrbuton: edtor@jc.org.uk

13 Journal of nformaton and Computng Scence, Vol. 4 (9 No. 3, pp -3 3 [3] B. Grod, C.. Chang, P. Ramanathan, and X. Zhu. ght feld compresson usng dspart-compensated lftng. n Proc. CASSP 3. 3, 4: [4] M. Ferl and B. Grod. Codng of mult-vew mage sequences wth vdeo sensors. n Proc. CP. 6, pp [5] M. Ferl, A. Mavlankar, and B. Grod. Moton and dspart compensated codng for mult-vew vdeo, EEE Trans. Crcut Sst. Vdeo Technol.. 7, 7(: [6] C.-. Chang, X. Zhu, P. Ramanathan, and B. Grod. ght feld compresson usng dspart-compensated lftng and shape adaptaton, EEE Trans. mage Proc.. 6, 5(4: [7] A. Smolc and P. Kauff. nteractve 3-D vdeo representaton and codng technologes. Proc. EEE. 5, 93(: 98-. [8] R. S. Wang and Y. Wang. Mult-vew vdeo sequence analss, compresson, and vrtual vewpont snthess. EEE Trans. Crcut Sst. Vdeo Technol.., (4: [9] N. Anantrastcha, C. N. Canagarajah, and D. R. Bull. ftng-based mult-vew mage codng. n Proc. SCAS. 5, 3: [] N. Anantrastcha, C. N. Canagarajah, and D. R. Bull. Mult-vew mage codng wth wavelet lftng and n-band dspart compensaton. n Proc. CP. 5, 3: [] X. San, H. Ca, J.-G. ou, and J.. Mult-vew mage codng based on geometrc predcton. EEE Trans. Crcut Sst. Vdeo Technol.. 7, 7(: [] Y. Morvan, D. Farn, and H. N. Peter. ncorporatng depth-mage based vew-predcton nto H.64 for multvewmage codng. n Proc. CP. 7, : 5-8. [3] J. u, H. Ca, J.-G. ou, and J.. An eppolar geometr-based fast dspart estmaton algorthm for mult-vew mage and vdeo codng. EEE Trans. Crcut Sst. Vdeo Technol.. 7, 7(6: [4] F. Yang, Q. Da, and G. Dng. Mult-vew mage codng based on mult-termnal source codng. n Proc. CASSP. 7, : [5] Y. Gao and H. Radha. Mult-vew mage codng usng 3-D voxel models. n Proc. CP. 5, : [6] A. Secker and D. Taubman. Moton-compensated hghl scalable vdeo compresson usng an adaptve 3D wavelet transform based on lftng. n Proc. CP., : 9-3. [7]. uo, J., S., Z. Zhuang, and Y. Q. Zhang. Moton compensated lftng wavelet and ts applcaton n vdeo codng. n Proc. CME., pp [8] N. Mehrseresht and D. Taubman. Adaptvel weghted update steps n moton compensated lftng based scalable vdeo compresson. n Proc. CP.3, 3: [9] C. J. Harrs and M. Stephens. A combned corner and edge detector. n AVC 4th Proc.. 988, pp [] W. Swelden. The lftng scheme: A constructon of second generaton wavelets. SAM Journal of Mathematcal Analss. 998, 9(: pp [] A. Sad and W. A. Pearlman. A new, fast, and effcent mage codec based on set parttonng n herarchcal trees. EEE Trans. Crcuts Sst. Vdeo Technol.. 996, 6(3: [] A. Moffat, R. M. Neal, and. H. Wtten. Arthmetc codng revsted. ACM Trans. nformaton Sstems. 998, 6(3: [3] A. Ortega. Optmzaton Technques for Adaptve Quantzaton of mage and Vdeo under Dela Constrants. Ph.D. thess, Dept. Electrcal Engneerng, Columba Unverst, New York, NY, 994. JC emal for subscrpton: publshng@wau.org.uk