Image Compression based on Quadtree and Polynomial

Transcription

1 Interntionl Journl of Computer Applitions ( Imge Compression sed on Qudtree nd Polynomil Ghdh Al-Khfj Ph.D Dept. of Computer Siene, Bghdd University, College of Siene. ABSTRACT In this pper, n effiient imge ompression sheme is introdued, it is sed on prtitioning the imge into loks of vrile sizes ording to its lolly hnging imge hrteristis nd then using the polynomil pproximtion to deompose imge signl with less ompressed informtion required ompred to trditionl preditive oding tehniques, finlly Huffmn oding utilized to improve ompression performne rte. The test results indite tht the suggested method n led to promising performne due to simpliity nd effiieny in terms of overoming the limittions of preditive oding nd fixed lok size. Generl Terms Qudtree prtitioning of vrile lok sizes with polynomil pproximtion for lossy imge ompression. Keywords Imge ompression, ompression tehniques, qudtree nd polynomil representtion. 1. INTRODUCTION Imge ompression tehniques generlly fll into two tegories: lossless nd lossy depending on the redundny type exploited, where lossless lso lled informtion preserving or error free tehniques, in whih the imge ompressed without losing informtion tht rerrnge or reorder the imge ontent, nd re sed on the utiliztion of sttistil redundny lone suh s Huffmn oding, Arithmeti oding nd Lempel-Ziv lgorithm, while lossy whih remove ontent from the imge, whih degrdes the ompressed imge qulity, nd re sed on the utiliztion of psyho-visul redundny, either solely or omined with sttistil redundny suh s suh s vetor quntiztion, frtl, trnsform oding nd JPEG, reviews of lossless nd lossy tehniques n e found in [1]-[8]. In generl, lossy tehniques work on segment sed tht sudivide the imge into non-overlpping segments (loks of fixed sizes or vrile sizes. Typilly the fixed prtitioning method is dopted due to its simpliity nd populrity, ut this is t the expense of effiieny, nd omes with greter storge ost, euse the loks re prtitioned sed on the size of the region, regrdless of the ontent, whether tht region or lok is uniform or non-uniform [9]. The vrile lok prtitioning methods utilized y numer of reserhers [10]-[19], to overome the fixed prtitioning method drwk using prtitioning tehniques suh s qudtree, HV (horizontl-vertil nd tringulr, in whih the results re promising ut still under development, nd not yet reognized to e used y stndrd tehniques due to omplexity or diffiulty of hoosing the uniformity mesure nd time required. Nowdys, there s inrese trend of utilizing the polynomil pproximtion representtion [0]-[1] due to its simpliity, symmetry of enoder nd deoder nd high ompression rtes n provide where no need to extr informtion to e used like seed vlues ompred to the trditionl preditive oding method []-[3]. In this pper, lossy qudtree vrile lok prtitioning method long with the polynomil pproximtion is introdued to remove the redundny etween neighoring pixels ording to its lol dependeny tht effiiently improve the qulity nd the ompression rte. The rest of the pper orgnized s follows, setion ontins omprehensive lrifition of the proposed system; the results of the proposed system, is given in setion 3.. THE PROPOSED SYSTEM The min tken onerns in the proposed system re: Get the enefit of hierrhil prtitioning representtion where loks of vrile sizes produed tht effiiently improve the ompression rtes nd qulity. Sine in this pper the liner polynomil representtion is dopted to remove the sptil redundny, the oeffiients re fixed within the sudivided lok-y-lok imge, so three oeffiients ( 0, 1, re required to represent eh lok. Therefore, the performne vry ording to the loks nture, in other words the performne inrese when pplied to lrge smooth regions nd redued when pplied to edge regions. The entropy oding using Huffmn tehniques used effiiently in order to minimize the it required. The implementtion of the proposed system is explined in the following steps, the lyout of the enoder is illustrted in Figure 1: Step 1: Lod the input unompressed imge I of size N N Step : Prtition the imge I into non-overlpped loks of vrile sizes n m using qudtree prtitioning sheme y heking the uniformity of the tested lok, tht strt with prtitioning (dividing the imge into loks whose size is equl to the mximum lok size, if the lok is not uniform then the prtitioning repeted on its four qudrnts in hierrhil mnner until rehing the minimum lok size where the uniformity ondition is stisfied. The uniformity riteri sed impliitly on utilizing the men nd stndrd devition of qud region, where for non-uniform region it exeeds ertin Stndrd Devition Threshold Vlue nd their men intensity, is limited etween Minimum Men Threshold Vlue nd Mximum Men Threshold Vlue. After tht the onstruted qudtree will onsists of prtitions whose size vlue will e etween minimum nd mximum lok size. Algorithm 1 summrizes the qudtree prtitioning steps. 31

2 Interntionl Journl of Computer Applitions ( Step 3: Perform the polynomil representtion to the vrile loks sizes tht resultnt of step ording to equtions (1,,3 [0]. n 1m1 1 0 I( j (1 n m n1m1 I( j ( j x ( n1m1 ( j x n1m1 I( j ( i y (3 n1m1 ( i y Where I(j is the originl imge lok of size n m nd x n (4 y m (5 Step 4: Apply uniform slr quntiztion to quntize the polynomil pproximtion oeffiients, where eh oeffiient is quntized using different quntiztion step. 0 0Q round( 0D 0Q QS0...( 6 QS 1 1Q round( QS 0 1 D Q QS 1... (7 Q round( D Q QS...( 8 QS Where 0 Q, 1Q, Q re the polynomil quntized vlues, QS 0, QS 1, QS re the quntiztion steps of the polynomil oeffiients, nd 0 D, 1D, D re polynomil dequntized vlues. Step 5: Determine the predited or pproximted imge vlue I ~ using the dequntized polynomil oeffiients for eh enoded lok representtion: ~ I D D( j x 1 D( i y (9 0 1 Step 6: Find the residul or predition error s differene etween the originl I nd the predited one I ~. ~ R( j I( j I ( j (10 Step 7: Perform slr uniform quntiztion to quntize the residul prt, where residul vlue is divided y the quntiztion step. The quntiztion step vlues ffeted the imge qulity nd the ompression rte. Step 8: Apply Huffmn oding tehniques to remove the rest of redundny tht emedded etween the quntized vlues of the residul nd the polynomil oeffiients. To reonstrut the deompressed imge ll the ove mentioned steps re reversed s shown in Figure. 3. EXPERIMENTS AND RESULTS For testing the proposed system performne; it is pplied on numer of well-known stndrd imges (see Figure 3 for n overview, ll imges of 56 gry levels (8its/pixel of size The tests hve een performed using vrile lok sizes of different Minimum &Mximum lok sizes nd ompre it with fixed lok size {4 4}, the quntiztion levels utilized ws seleted to e etween 4 nd 64 levels, using to 6 its on oth the residul imge nd the pproximtion representtion oeffiients ( 0, 1,. The prtitioned imges for fixed nd qudtree shemes re shown in Figures 4, 5, 6 nd 7 respetively. The ompression rtio, whih is the rtio of the originl imge size to the ompressed size long with the normlized root men squre error (NRMSE etween the originl imge I nd the deoded imge Î ws dopted s fidelity or degrdtion mesure s in eqution (11, where the rnge of the vlues is etween 0 nd 1. A vlue ner zero indites high imge qulity, i.e. the deoded imge losely resemles the originl, nd vie vers. NRMSE ( I, Iˆ N 1N 1 [ Iˆ( x, y I( x, y] x0 y0 N 1N 1 I( x, y x0 y (11 Certinly, the qulity of the deoded imge is improves s the numer of quntiztion levels of oth the pproximtion representtion oeffiients nd residul imge inrese. The min disdvntge of inresing the quntiztion levels, however, lies in inresing the size of the ompressed informtion. It is trde-off etween the desired qulity nd the onsumption of ytes; the higher the qulity required, the lrger the numer of quntiztion levels tht must e used. The results shown in Tle 1 nd Figure 8 illustrtes tht the 4 4 fixed lok size, ompred to qudtree of nerly sme numer of loks s fixed lok se, of the three tested imges. The results show tht for qudtree higher qulity produed due to utilizing smll loks of finer detils, ut with less ompression rte where the using of igger lok sizes impliitly mening derese in modelling fidelity s the lok gets igger where the size of residul vries ording to the lok size (i.e., residul size inrese due to insuffiient model flexiility. Also the result demonstrtes tht the ompression rtes is diretly ffeted y the residul size (residul urden not the size of polynomil pproximtion oeffiients, in other words even with less oeffiient prmeters required in qudtree the residul represents the exhusted ytes. Tle, shown the high qulity results for the three tested imges, using qudtree prtitioning method of different lok sizes. The results lerly show tht the qulity improves with the inrese of the numer of prtitioned loks, nd vie vers. The deoded imges with different qulity sttus re shown in Figures 9,10 nd 11 respetively. Lstly, the results showed tht the qulity of the deoded imge dose not suffers from the loking effets nd edge degrdtion s the lok gets igger, whih differs from other ompression tehniques, tht ssumed tht s the lok got smller, higher qulity would e hieved. The min reson of the improving of imge qulity in the polynomil pproximtion oding tehniques using igger lok sizes due to dominting residul imge. 4. ACKNOWLEDGMENTS Our thnks to the experts who hve ontriuted towrds development of the templte. 3

3 Interntionl Journl of Computer Applitions ( Imge I Uniformity I ~ Test -- Polynomil Coding R Quntiztion Entropy Coding Compresse d dt Fig 1. Enoder struture of the proposed system. Compressed dt Entropy Deoding Dequntiztion Add Residul to Polynomil prt Fig. Deoder struture of the proposed system. Reonstruted Imge Î Algorithm 1. Qudtree prtitioning lgorithm. 1. Input imge I of size N N. Selet the Minimum nd Mximum Blok Size 3. Test the Uniformity riteri If (region <= Minimum Blok Size then uniform Else if (region > Mximum Blok Size then nonuniform Else If (region > Stndrd Devition Threshold Vlue nd (region > Minimum Men Threshold Vlue nd region < Mximum Men Threshold Vlue then nonuniform Else uniform Fig 3. Overview of the tested imges ( Len imge, ( Living room imge nd ( Pper imge, ll imges of size 56 56, gry sle imges. Fig 4. Fixed Prtitioning of lok size 4 4 on the tested imges of sizes ( Len imge, ( Living room imge nd ( Pper imge, numer of loks 4096 in ll imges. 33

4 Interntionl Journl of Computer Applitions ( Fig 5(-. Qudtree prtitioning pplied on Len imge with different numer of loks. Fig 6(-. Qudtree prtitioning pplied on Living room imge with different numer of loks. Fig 7(-. Qudtree prtitioning pplied on Pper with different numer of loks. Fig 8. Compression rtio versus the normlized men squre error of the tested imges ( Len (Living room (d Pper using fixed lok nd qudtree tehniques. 34

5 Interntionl Journl of Computer Applitions ( Tle 1. Comprison etween fixed nd qudtree tehniques on the tested imges. Tested imges Qunt oeff. & Res Qudtree {Minimum Blok Size=, Mximum Blok Size=16, Stndrd Devition Threshold Vlue=10, Minimum Men Threshold Vlue =0 nd Mximum Men Threshold Vlue =110 } Fixed lok 4 4 No. Bloks=4096 N. Bloks CR NRMSE CR NRMSE Len 4 levels livingroom 4 levels Pper 4 levels Tested imges Qudtree prtitioning Qunt oeff. =4 & Res=3 levels N. CR NRMSE Bloks Len livingroom Pper Tle. Compression performne of the proposed system on the tested imges of high qulity. No. Bloks=10188 CR=3.361 NRMSE= No. Bloks=36 CR=5.41 NRMSE= Fig 9. Deompressed Len imge with different qulity vlues using Qunt. (oeff. =4 & Res.=16 levels. 35

6 Interntionl Journl of Computer Applitions ( No. Bloks=905 CR=3.616 NRMSE= No. Bloks=668 CR=4.867 NRMSE=0.036 Fig 10. Deompressed Living room imge with different qulity vlues using Qunt.(oeff. =4 & Res.=16 levels. No. Bloks=93 CR=3.373 NRMSE=0.087 No. Bloks=3018 CR=5.781 NRMSE= Fig11: Deompressed Pper imge with different qulity vlues using Qunt (oeff. =4 & Res.=16 levels. 36

7 Interntionl Journl of Computer Applitions ( REFERENCES [1] Furht, B A Survey of Multimedi Compression Tehniques nd Stndrds. Rel-Time Imging, 1, [] Singh, S. K. nd Kumr, S Mthemtil Trnsforms nd Imge Compression: A Review. Mejo Interntionl Journl of Siene nd Tehnology, 4(0, [3] Shin, D A Review of Imge Compression nd Comprison of its Algorithms. Interntionl Journl on Eletronis & Communition Tehnology (IJECT. (1, -6. [4] Anith, S D Imge Compression Tehnique-A Survey. Interntionl Journl of Sientifi & Engineering Reserh, (7, 1-6. [5] Sridev S., Vijykuymr, V.R. nd Anuj, R. 01. A Survey on Vrious Compression Methods for Medil Imges. Interntionl Journl of Intelligent Systems nd Applitions, 3, [6] Vrindvnm, J., Chndrn, S. nd Mhnt G. K. 01. A Survey of Imge Compression Methods. Proeedings on Interntionl Conferene nd Workshop on Emerging Trends in Tehnology [7] Asolkr, P. S., Zope, P. H. nd Surlkr S. R Review of Dt Compression nd Different Tehniques of Dt Compression. Interntionl Journl of Engineering Reserh & Tehnology (IJERT, (1, 1-8. [8] Amrut, S.G. nd Snjy L.N A Review on Lossy to Lossless Imge Coding. Interntionl Journl of Computer Applitions (IJCA, 67(17, [9] Fisher, Y Frtl Imge Compression: Theory nd Applition. Springier Verlge, New York. [10] Visey, D. nd Gersho, A Vrile Blok-Size Imge Coding.. Proeedings of the IEEE interntionl onferene on Aoustis, Speeh, nd Signl Proessing, [11] Wu, P. nd Zheng, B A New Imge Compression Method Bsed on HV Frtl nd DCT. Communition Tehnology Proeedings, Interntionl Conferene on ICCT '98. 1, 1-4. [1] Guoru J., Yuzhuo, Z., Shiqing, Y. nd Bo, Y Fst Frtl Imge Compression Bsed on HV Prtition. Prt of the SPIE Conferene on Multimedi Storge nd Arhiving Systems. 3846, [13] Jmil, H.S Frtl Imge Compression, Ph.D. Thesis, College of Siene, University of Bghdd. [14] Ghd, K. T Adptive Frtl Imge Compression. M.S. Thesis, Ntionl Computer Center/Higher Edution Institute of Computer nd Informtion. [15] Golhin, F. nd Pliwl, K.K Qudtree-sed lssifition in sund imge oding. Digitl Signl Proessing, 13, [16] Rjkumr, W. S., Kulkrn M.V., Dhore, M.L., Ml S. N Frtl Imge Compression Performne Synthesis Through HV Prtitioning. Advned Computing nd Communitions, ADCOM Interntionl Conferene on [17] Ghd, K.T. nd Luy, K. A Merge Opertion Effet On Imge Compression Using Frtl Tehnique. Journl of Bghdd for Siene, 4, [18] Keissrin1, F A New Qudtree-sed Imge Compression Tehnique using Pttern Mthing Algorithm. Interntionl Conferene on Computtionl & Experimentl Engineering nd Sienes (ICCES, 1(4, [19] Chng, C-L., Mkr, M., Sm S.T. nd Girod, B Diretion-Adptive Prtitioned Blok Trnsform for Color Imge Coding. IEEE Trnstions on Imge Proessing, 19(7, [0] George, L. E. nd Sultn, B Imge Compression Bsed on Wvelet, Polynomil nd Qudtree. Journl of Applied Computer Siene & Mthemtis, 11(5, 15-0 [1] Ghdh, Al-K. nd George, L. E..013.Fst Lossless Compression of Medil Imges sed on Polynomil. Interntionl Journl of Computer Applitions, 70(15,8-3. [] Mrgos, P. A., Shfer, R. W. nd Mersereu, R. M Two-Dimensionl Liner Preditive nd Its Applition to Adptive Coding of Imges. Proeedings of the IEEE interntionl onferene on Aoustis, Speeh nd Signl Proessing, [3] Musmnn, H. G., Pirsh, P. nd Grllert, H Advnes in Piture Coding. Proeedings of the IEEE, 73(4, [4] Ds, M. nd Loh, N. K New Studies on Adptive Coding of Imges using Multiplitive Autoregressive Models. 10th IEEE Region Conferene on Communition, [5] Burgett, S. nd Ds, M Preditive Imge Coding using Multiresolution Multiplitive Autoregressive Models. Proeedings of the IEEE, 140(, [6] Blrm, N. nd Mour, J. M. F Nonusl Preditive Imge Code. IEEE Trnstions on Imge Proessing, 5(8, [7] Su, C.K., Hsin, H.C. nd Lin, S.F Wvelet Tree Clssifition nd Hyrid Coding for Imge Compression. IEE Proeedings on Vision, Imge nd Signl Proessing, 15(6, [8] Ino, Y., Silv, d. And Cruz, F.S A Fst nd Effiient Hyrid FrtlWvelet Imge Coder. IEEE Trnstions on Imge Proessing, 15(1, [9] Xu, J., Wu, F. nd Zhng, W Intr-Preditive Trnsforms for Blok-Bsed Imge Coding. IEEE Trnstions on Signl Proessing, 57(8, [30] Gry, R. M A Survey of Liner Preditive Coding: Prt I of Liner Preditive Coding nd the Internet Protool. Foundtions nd Trends in Signl Proessing, 3(3, [31] Rehn, V. J. nd Kumr, M. K. J Hyrid Approhes to Imge Coding: A Review. Interntionl Journl of Advned Computer Siene nd Applitions (IJACSA, (7, [3] Groh, M. nd Grg, A. 01. Imge Compression Algorithm. Interntionl Journl of Engineering Reserh nd Applitions (IJERA, (, IJCA TM : 37