Speeding- Up Fractal Image Compression Using Entropy Technique

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1 Avalable Ole at Iteratoal Joural of Computer Scece ad Moble Computg A Mothly Joural of Computer Scece ad Iformato Techology ISSN X IMPACT FACTOR: IJCSMC, Vol. 5, Issue. 4, Aprl 2016, pg Speedg- Up Fractal Image Compresso Usg Etropy Techque Hader A. Muhs 1, Dr. Hazeem B. Taher 2 ¹Computer Scece & Th-Qar Uversty/ Faculty of Educato for Pure Scece, Iraq ²Computer Scece & Th-Qar Uversty/ Faculty of Educato for Pure Scece, Iraq 1 allhader@yahoo.com; 2 haze_comp792004@yahoo.com Abstract Fractal mage ecodg s attractve due to ts potetal hgh compresso rato, fast decompresso ad mult-resoluto propertes [1]. Fractal mage compresso explores the self-smlarty property of a atural mage ad utlzes the parttoed terated fucto system (PIFS) to ecode t. It s tme-cosumg the ecodg process ad such drawback reders t mpractcal for real tme applcatos [2]. I ths paper, a ew method s proposed to reduce the ecodg tme based o usg etropy o doma blocks The etropy have bee used to speed up the Iterated Fucto System (IFS) matchg stage. Durg the match, every rage block s checkg all doma blocks ad choose the least error ad ths process eeds more tme, ad ths s the ma dsadvatage Fractal Image Compresso. The proposed method, compute the etropy for each doma block the compares each etropy of doma block wth threshold (selected threshold through experece), f the etropy of the doma block less tha threshold, matchg process coducted, ths way, each rage block o match wth all doma blocks. The results of the tests coducted o Lea (512x512) pxel, resoluto 8 bts/pxel, where the mage s parttog to blocks of sze (4x4, 8 x8ad 16x16) pxel, Where was the tme before addg the proposed method(4x4 pxel ecodg tme sec wth approprate PSNR ( dB) ad ecodg tme after addg the proposed method ( sec wth approprate PSNR ( dB) ),8x8 pxel ecodg tme sec wth approprate PSNR ( dB) ad ecodg tme after addg the proposed method( sec ) wth approprate PSNR ( db), 16x16 pxel sec wth approprate PSNR ( dB) ad ecodg tme after addg the proposed method( sec ) wth approprate PSNR ( ). Keywords Compresso, Image Compresso, Fractal Image Compresso, etropy, Speed up Fractal 1. INTRODUCTION Dgtal Image compresso s the process of reducg the amout of data eeded to represet a dgtal mage. Ths s doe by removg the redudat data (.e. the data whch s more tha eeded), Image compresso s a applcato of data compresso that ecodes the orgal mage wth few bts. The objectve of mage compresso s to reduce the redudacy of the mage ad to store or trasmt data a effcet form[4].fractal mage compresso s wdely used mage processg applcatos, such as mage sgature, texture segmetato, feature extracto, mage retreval, ad mult-resoluto medcal mage processg [3]. The sgfcat advatages of the fractal compresso are fast mage recostructo ad hgh compresso rato. Aother advatage of fractal mage compresso s ts multresoluto property,.e. a mage ca be decoded at hgher or lower resolutos tha the orgal, ad t s possble to zoom- o the sectos of the mage[5]. The ma reaso s that the smlarty matchg computato betwee rage ad doma blocks s complex. I respose to ths problem, a effectve 2016, IJCSMC All Rghts Reserved 518

2 method s that the mage blocks are compute etropy for doma block ad check t wth threshold before matchg, so as to speed up the ecodg process[6]. 2. Tradtoal PIFS Ecoder The basc dea of PIFS s parttog the mage to o overlappg rage blocks by fxed, quadtree ad HV(Horzotal- Vertcal) parttog [7].Doma pool geerato module s resposble for geeratg doma array (H d x W d ), whch s quarter the sze of the orgal mage array (H xw),(.e.,h d = H/2 ad W d = W/2).the data of doma array s take from the rage array ; there are may ways to choose the data from the rage array to fll the doma array.for each four eghborg pxels rage array,oly oe value of these pxels s stored doma array. I ths work the average of every four eghborg pxels the rage s used to fll the correspodg posto the doma [8]. After geerato the rage ad doma pools, the matchg process mples for each rage block, wth all doma blocks (D) are lsted doma pool, the best matchg betwee doma ad rage blocks whch are satsfed the mmum the dstorto error R [9 ] R b s(s a 2 a b 2 o a ) o(o 2 b ) (1) The IFS coeffcets of the equato (1),(.e. scale "S' ad the offset "O" ),s determed by usg : s. a a b 1 b a a ( 2) (3) Where: a : s the pxels values of the doma block. b : s the pxels values of the rage block. : s the umber of pxels each block (.e. the block sze ). 1 the S = 0, ad o b If a ( a ) There s a smple formula for R, but t s best to use ths oe as we ll see later. The rms error s equal to R [ 10]. The quatzato of IFS coeffcets s doe by assgg umber of bts for both, scale ad offset,to store ther quatzato dces. The quatzed scale ad offset values have bee computed by usg the followg equatos[11]. Q s = {.(4) 2016, IJCSMC All Rghts Reserved 519

3 s = roud ( ).....(5) S q = s Q s.. (6) Where S max s the hghest permssble value of scale coeffcets. S m s the lowest permssble value of scale coeffcets. b s s the umber of allocated bts to represet the quatzato dex of the scale coeffcets. Q s s the quatzato step of the scale coeffcets. I s s the quatzato dex of the scale coeffcets. s the quatzed value of the scale coeffcets. S q Q o = {.(7) I o = roud ( )...(8) O q = o Q o......(9) Where O max s the hghest permssble value of offset coeffcets. O m s the lowest permssble value of offset coeffcets. b o s the umber of allocated bts to represet the quatzato dex of the offset coeffcets. Q o s the quatzato step of the offset coeffcets. I o s the quatzato dex of the offset coeffcets. Oq s the quatzato value of the offset coeffcets. The quatzed values of scale (S) ad offset (O) parameters should be used calculate the sum of square error R by usg equato (1). After computato of the IFS parameters ad the sum of error R for ay matchg stace betwee the rage ad each doma block lsted the doma pool,the the value of R s compared wth the mmum regstered error (R m ). If R < (R m ) the S opt = s ; O opt = o ; R m = R Ed f [7] At decodg stage, the approxmatos could be performed several tmes,startg wth ay radom mage,tll reachg the fxed pot[6]. 3. Usage of Etropy Modfed PIFS Ecoder I the mprove PIFS codg stage, the rage ad doma pools geerated frst, The most computatoally tesve part of the FIC process s the search step. Oe way to decrease ecodg tme s to decrease the umber of comparsos betwee rage ad doma blocks. The proposed method based o etropy values to reduce the doma pool of matchg process betwee the rage ad doma block by usg the value of etropy of doma blocks. Each rage block s compared oly wth doma blocks f the etropy of doma block less tha threshold, the executo the matchg process. The etropy of the doma block s gve by [12]: H(D)= - = P log P..(10) where P s the probablty of doma block, s the block sze 2016, IJCSMC All Rghts Reserved 520

4 The ma steps of the proposed method ca be summarzed as: Step1: Load the mage. Step 2:choose mmum error. Step3: Choose the threshold. Step4: Parttog the mage to fxed blocks sze wth o-overlap (R1 R-1 ). Step5: Geerate the doma mage from the orgal mage by averagg method. Step 6: Parttog the doma to fxed blocks sze wth overlappg blocks (D1 D-1 ). Step7: For each ew doma block compute the etropy by usg equato (10). Step8: Compare etropy of the doma block wth threshold.. If the etropy of doma less tha threshold.. Compute the coeffcets S,O usg equato (2,3).. Quatzato S, O usg equatos (4,5,6,7,8,9). v. Compute RMS by usg equato (1), f RMS less tha, the store the IFS code; else go to the ext doma block. 4. Test Results The proposed method have bee tested by usg grayscale lea mage (512x512 pxels ) ad Barbara mage (512x512 pxels )TABLE(1) ad TABLE(2) show the ecodg tme ad PSNR before addg The proposed method ; the test results show TABLE (3) ad TABLE (4) shows that the tradtoal system s the slower PIFS ecodg ad speed up wth proposed method(etropy),the advatage of the proposed method s reduce ecodg tme but the Dsadvatage of etropy method, s the choce of threshold for each partto of the mage, as show the TABLES below : TABLE(1) test results Lea (512x512) pxel before the proposed method (etropy ) (Tradtoal FIC) Lea (512x512) pxels BLOCKSIZE PSNR ET 4x x x TABLE(2) test results Barbara (512x512) pxel before the proposed method (etropy techque ) (tradtoal FIC) Barbara (512x512) pxels BLOCKSIZE PSNR ET 4x x x , IJCSMC All Rghts Reserved 521

5 TABLE(3) test results Lea (512x512) pxel wth proposed method (etropy techque ), Lea (512x512) pxels THRESHOLD BLOCKSIZE PSNR ET x x x (a) (b) Fg 1 : (a) show orgal Image (512x512), (b) Lea(512x512) wth proposed method (etropy) PSNR= , ET= , Blocksze= 4x4 TABLE(4) test results Barbara (512x512) pxel wth proposed method (etropy Techque), block sze 4x4 pxel Barbara (512x512) pxels THRESHOLD BLOCKSIZE PSNR ET x x x , IJCSMC All Rghts Reserved 522

6 (a) Fg 2 : (a) show orgal Image (512x512), (b) Barbara mage (512x512) wth proposed method (etropy Techque ) PSNR= , ET= , Blocksze= 4x4 (b) Fg (3) The effect of block sze o PSNR Fg (4) The effect of block sze o Ecodg tme 2016, IJCSMC All Rghts Reserved 523

7 5. Coclusos The etropy s very useful to speed-up ecodg,frst compute the etropy of doma blocks ad the compare wth threshold, ths proposed method leads to decrease tme of ecodg from ( )sec to ( )sec ad crease PSNR from ( db to db) wth partto mage to 4x4 pxel. The dsadvatage of The proposed method s for each parttog must have threshold dffers from aother parttog. Refereces [1] Vahdat.G., Afaradeh.E., Yaghoub.M.," Improvemet Speed of Fractal Image Compresso through Gray Level Dfferece ad Normal Varace",Iteratoal Coferece of Soft Computg ad Patter Recogto,2009. [2] Chh Teg.W, Jyh-Horg.J, Jer-Guag.H," Spatal correlato geetc algorthm for fractal mage compresso", Avalable ole at [3] Salara.M, Naderejad.E, Nam. H," A ew modfed fast fractal mage compresso Algorthm", The Imagg Scece Joural Vol [4] We.W-Y," A Itroducto to Image Compresso",Graduate Isttute of Commucato Egeerg Natoal Tawa Uversty, Tape, Tawa, ROC. [5] L Hsu. S., Chag. Y., Jeg. J.," A Study of Fractal Image Compresso wth Coeffcet Quatzato",Departmet of Iformato Egeerg I-Shou Uversty, Ta-Hsu Hsag, Kaohsug Couty, The 24th Workshop o Combatoral Mathematcs ad Computato Theory, [6] George. L. E, Mas. N. A.," Speedg Up Fractal Image Compresso Usg DCT Descrptors", Joural of Iformato ad Computg Scece,2011. [7] Al-Hlo. E., "Speedg-up Fractal Colored Image Compresso Usg Momets Features", /08 $ IEEE. [8] Taha M.H.,"Parttog Developmet for Fractal Image Compresso",M.Sc.Thess,Scece college,al-mustasryah Uversty, December [9] Husse A.A.,"Fractal Image Compresso wth Fastg Approaches",M.Sc.thess,Collegs of Scece,Saddam Uversty,2003. [10] Fsher Y.,"Fratal Image Compresso :Theory ad Applcato",Sprger Verlage,New York,1994. [11] George,L.,"IFS Codg for Zero-Mea Image Blocks",Iraq Joral of Scece,Vol.47,No.1,2006. [12] Suad. Jamla,H." Fractal Image Compresso Based O Etropy Techque", Computer scece, college of scece/al- Mustesryh Uversty, Iraq, IOSR Joural of VLSI ad Sgal Processg (IOSR-JVSP) Volume 2, Issue 1 (Mar. Apr. 2013). 2016, IJCSMC All Rghts Reserved 524