Codebook Generation for Vector Quantization using Interpolations to Compress Gray Scale Images

Transcription

1 Internatonal Journal of Computer Applcatons ( ) Volume No.9, March 0 Codebook Generaton for Vector Quantzaton usng Interpolatons to Compress Gray Scale Images S.Vmala Dept. of Comp. Sc. Mother Teresa Women s Unversty Kodakanal 6 0 K.KowsalyaDev Dept. of Comp. Sc. Mother Teresa Women s Unversty Kodakanal 6 0 M.Sathya Dept. of Comp. Sc. Mother Teresa Women s Unversty Kodakanal 6 0 ABSTRACT Vector Quantzaton (VQ) s one of the Lossy Image Compresson Technques. Vector Quantzaton s performed n three phases:.codebook Generaton,.Image Encodng and.image Decodng. In ths paper, we have proposed a novel dea of ncorporatng the technque of Interpolaton as part of the estng codebook generaton technque to further reduce the bt-rate that s obtaned. Eperments were carred over standard mages lke Lena, Cameraman, Boats, Brdge, Baboon, Goldhll, and Kush. Accordng to the smulated results, the proposed algorthm acheves sgnfcant reducton n bt-rate for codebooks of varous szes such as 6,, 6, 8, 6 and. General Terms Image Processng, Compresson, Vector Quantzaton. Keywords vector quantzaton, codebook, encodng, decodng, bt-rate, nterpolaton, mage compresson. INTRODUCTION The mage compresson [] technques are broadly classfed nto two categores:.lossless technques and.lossy technques. In lossless compresson technques, the reconstructed mage wll be the eact replca of the orgnal mage. Some of the lossless compresson technques:.run Length Encodng,.Huffman Encodng,.LZW codng and.area codng []. In lossy compresson technques, the decompressed mage s not dentcal to the orgnal mage, but an appromaton of the orgnal mage []. Some of the lossy compresson technques:.transformaton Codng,.Vector Quantzaton,.Fractal Codng,.Block Truncaton Codng and. Subband Codng []. Vector Quantzaton (VQ) s a classcal quantzaton technque from sgnal processng and mage compresson [] whch allows the modelng of probablty densty functons by the dstrbuton of prototype vectors. VQ asssts to project a contnuous nput space on a dscrete output space, whle mnmzng the loss of nformaton [6]. The purpose of VQ [7] orgnally stems from encodng dscrete data vectors to compress data whch have to be transferred quckly e.g for onlne communcaton channels. The performance of the VQ s known to be asymptotcally optmum n the sense of mnmum rate dstorton as the vector dmenson ncreases [8], [9], [0]. VQ has been wdely used for sgnal compresson due to ts ecellent rate-dstorton performance. The ecellent revew on speech and mage applcatons can be found n [] []. VQ s done n three steps:.codebook Desgn,.Image Encodng and.image Decodng. The performance of the VQ depends manly on the qualty of the codebook that s generated. There are several known methods for generatng codebook. The most cted and wdely used s the Lnde Buzo Gray (LBG) [] Algorthm. It starts wth an ntal soluton, whch s teratvely mproved usng two optmalty crtera untl a local mnmum s reached []. Another herarchcal algorthm, the Parwse Nearest Neghbor (PNN) [] uses an opposte, bottom-up approach to generate the codebook. In codebook generaton, an mage s splt up nto blocks of sze pels. The blocks are converted nto vectors of dmenson K. These vectors are called tranng vectors, and the set of tranng vectors s called the tranng set of sze N vectors [6]. N s computed usng the equaton (). N = (m m) / k () where k s the dmenson of the vector and m m s the number of rows and columns of pels n the nput mage. The poston p from whch the codevectors to be selected s computed usng the equaton (). p = N /M () where N s the sze of the Tranng Set and M s the desred sze of the codebook. The codevectors at every p th poston from the tranng set are selected to form the codebook.

2 Internatonal Journal of Computer Applcatons ( ) Volume No.9, March 0 In encodng stage, the closest codevector for each tranng vector s dentfed by computng the dstance d(y, ) usng the equaton (). d 6 Y, y j j j where, = to M and d(y, ) must be mnmum for j. Each block of the nput mage s replaced wth the nde of the codevector satsfyng equaton (). The collecton of such ndces s called the Inde Map. Now the compressed mage s ether stored or transmtted n the form of Inde Map and the Codebook. In the decodng stage, whle reconstructng the mage from the compressed mage, each nde n nde map s replaced wth the correspondng codevector. The dfference between the nput mage and the reconstructed mage s the Mean Square Error (MSE) and s computed usng the equaton (). The Peak Sgnal to Nose Rato (PSNR) s the qualty of the reconstructed mage and s computed usng the equaton (). (). Kekre s Proportonate Error (KPE) Algorthm [8] Step: Computng centrod for the entre tranng set Step: Add a proportonate error to the covector. Magntude of elements of the codevector decdes he error rato. Step: Hereafter the procedure s same as that as LBG. Step: Whle addng proportonate error a safe guard s also ntroduced so that nether V nor V. Step: Go beyond the tranng vector space.. Smple Codebook Generaton (SCG) Algorthm [9] Step: Input the gven mage of sze m m pels. Step: Dvde t nto blocks of sze pels. MSE ' N I I N () Step: Generate N tranng vectors usng equaton (). Step: F the codebook sze to M. PSNR 0Log 0 MSE () Step: Compute p=n/m Step6: Select every p th tranng vector as codevector to generate the codebook. Our proposed dea s to ncorporate the nterpolaton technque whch has been adopted as part of Block Truncaton Codng [7] for mage compresson to further reduce the btrate of the compressed mage. The Organzaton of the paper s as follows: The estng codebook generaton method s eplaned n Secton, the proposed method s eplaned n Secton, the results are dscussed n secton and the Concluson s gven n Secton.. EISTING METHODS. Lnde Buzo Gray (LBG) Algorthm Step: Computng centrod for the entre tranng set Step: Add a constant error {,,,,,,,,,,,,,,,,,} to the centrod Step: Addng a constant error to and subtractng the constant error from the centrod respectvely Step: Two clusters are formed by groupng the nearest vectors of V and V usng the mnmum dstance method. Interpolaton Technque The Interpolaton s adopted n the Block Truncaton Codng (BTC) based mage compresson methods to have a better compresson rato. In ths method, the boldfaced components as n Fg. are dropped to mprove the codng effcency Fg. : Droppng pattern of bts n nterpolaton technque In decodng phase, the dropped bts are recovered by takng the arthmetc mean of the adjacent pel values as gven n equaton set (6). Step: Repeat Step untl the desred the sze of codebook s generated.

3 Internatonal Journal of Computer Applcatons ( ) Volume No.9, March 0 6, 8 for, for 9, for, for. PROPOSED METHOD. Modfed Interpolaton Technque The estng nterpolaton order s slghtly changed and the dropped elements are generated usng the equaton set (7). for for 8 for 9 for for for for. Smple codebook Generaton wth Interpolaton(SCGI) In the proposed method, both the Smple Codebook Generaton technque and the Interpolaton technque adopted n BTC are combned and ncorporated as part of SCG. The algorthm s as follows:.. Encodng Algorthm. Generate the Smple Codebook as stated earler.. Generate the Inde Map.. Drop the elements of all the codevectors of the codebook as n Fg... Store or transmt the compressed mage n the form of Codebook and Inde Map... Decodng Algorthm. Generate the dropped elements of the codevectors usng the equaton set (7).. Reconstruct the mage by replacng each nde from the Inde Map wth ts correspondng Codevector.. RESULTS AND DISCUSSION Usng the proposed (SCGI) technque, codebooks of dfferent szes 6,, 6, 8, 6 and are generated. The mages Lena, Cameraman, Boats, Brdge, Baboon, Goldhll and Kush are used for the study and are gven n Fg.. a) Lena b) Cameraman c) Boats d) Brdge e) Baboon f) Goldhll g) Kush Fg : Input Images taken for the study (6) (7)

4 Internatonal Journal of Computer Applcatons ( ) Volume No.9, March 0 TABLE. PSNR AND BITRATE OBTAINED WITH VARIOUS CODEBOOK SIZES Image Codebook Sze SCG SCGI bpp PSNR bpp PSNR Lena Cameraman Boats Brdge

5 Internatonal Journal of Computer Applcatons ( ) Volume No.9, March 0 TABLE. COMPARISON OF THE PSNR OBTAINED WITH LBG, KPE AND PROPOSED METHOD. Codebook Sze Image LBG KPE Proposed bpp PSNR bpp PSNR bpp PSNR 8 Baboon Goldhll Kush Lena Baboon Goldhll Kush Lena Baboon Goldhll Kush Lena The Results observed for dfferent codebook szes are lsted n the TABLE and TABLE. For all mages, wth the codebook of sze, the proposed method outperforms both n terms of PSNR and bpp. For Lena mage, the bpp and the PSNR obtaned wth the proposed method (SCGI) are 0. and.9 respectvely, but n SCG, the bpp and PSNR are only 0.8 and.8. For codebooks of lowers szes such as 6 and, the proposed method gves better results both n terms of bpp and PSNR. For hgher sze codebooks, the bpp s reduced sgnfcantly wth slght degradaton n PSNR. For a codebook of sze, the bpp s reduced from 0.8 to 0.. For a codebook of sze, the bpp s reduced from.6 to.06, whch s sgnfcant mprovement n codng effcency. In Table, the comparson of LBG, KPE and the proposed methods s gven wth respect to PSNR for codebooks of szes 8, 6 and. In Fg., the reconstructed mages usng the SCG and the SCGI technques are gven. Orgnal SCG (bpp:.00) Proposed (bpp: 0.7) Orgnal SCG (bpp:.00) Proposed (bpp: 0.7) Fg : Reconstructed mages of Lena and Cameraman for a codebook of sze 6 8

6 Internatonal Journal of Computer Applcatons ( ) Volume No.9, March 0. CONCLUSION In ths paper, we have proposed a codebook ceneraton technque SCGI for Vector Quantzaton usng Interpolaton. Ths method was used generate codebooks of dfferent szes 6,, 6, 8, 6 and. The methods, when tred wth standard mages, gave better bpp. The PSNR obtaned wth the proposed method s better when compared to that few estng methods such as LBG and KPE. Ths method s sutable for handheld devces. The same technque can also be etended for color mages. 6. REFERENCES [] Sonal, Dnesh,Kumar, A study of varous Image Compresson Technque, Natonal Conference on Challenges and Opportuntes n Informaton Technology, Hsar, 007. [] Davd Solomon, Data Compresson, The Complete Reference, Thrd Edton. [] Somasundaram and S.Vmala, Codebook generaton for vector quantzaton wth Edge Features, CT Internatonal Journal of Dgtal Image Processng, 00. [] Rafael C.Gonzalez, Rchard E.Woods, Dgtal Image Processng, Second Edton. [] G.Boopathty and S.Arockasamy, Implementaton of Vector Quantzaton for Image Compresson A Survey, Global Journal of Computer Scence and Technology, vol.0, Issue, pp. -8, Aprl 00. [6] K.Makhoul, S.Roucos, H.Gsh, Vector Quantzaton s speech codng, IEEE, vol. 7, n., November 00. [7] R.Gray, Vector Quantzaton, IEEE ASSP Mag., pp. -9, 989. [8] A.Gersho, Asymptotcally optmal block quantzaton, IEEE Trans. Inform. Theory, vol. IT-, pp. 7-80, July 979. [9] Y.Yamada, S.Tazak, and R.M.Gray, Asymptotc performance of block quantzers wth dfference dstorton measure, IEEE Trans. Inform. Theory, vol. IT-6, pp.6-, Jan 980. [0] T.Berger, Rate Dstorton Theory, Englewood Clffs, NJ: Prentce Hall, 97. [] A.Gersho and R.M.Gray, Vector Quantzaton and Sgnal Compresson, Norwell, MA:Kluwer, 99. [] N.M.Nasradbad nad R.A.Kng, Image Codng Usng Vector Quantzaton: A revew, IEEE Trans. Commun., vol. 9, pp , Aug 988. [] Y.Lnde, A.Buzo and R.M.Gray, An Algorthm for Vector Quantzer Desgn, IEEE Trans. Commun., vol. COM -8, no., pp. 8-9, 980. [] H.B.Kekre, Tanuja K.Sarode, An Effcent Fast Algorthm to Generate Codebook for Vector Quantzaton, IEEE, 008. [] Wllam H.Equtz, A New Vector Quantzaton Clusterng Algorthm, IEEE Trans. On Acoustcs, Speech and Sgnal Processng, vol. 7, No. 0, October 989. [6] S.Vmala, Convergence Analyss of Codebook Generaton Technques for Vector Quantzaton usng k- means Clusterng Technques, Internatonal Journal of Computer Applcatons, vol, No.8, May 0. [7] S.Vmala, P.Uma Edwn and P.Anne Raja Reega Ruth, Block Truncaton Codng usng Enhanced Interpolatons and Lookup procedures for Image Compresson, Internatonal Journal of Computer Applcatons, vol 9, No., Sep 0. [8] H.B.Kekre, Sudeep Thepade and Nkta Bhandar, Colorzaton of Greyscale Images Usng Kekre s Borthogonal Color Spaces and Kekre s Fast Codebook Generaton, Internatonal Journal of Advances n Multmeda, vol., Issue, 009. [9] Somasundaram and S.Vmala, Smple and Fast Ordered Codebook for Vector Quantzaton, Proceedng of the Natonal Conference on mage processng, Gandhgram rural Insttute, March 00. 9