A Complexity-Based Approach in Image Compression using Neural Networks

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1 Internatonal Journal of Sgnal Proceng 5; Sprng 009 A Complexty-Baed Approach n Image Compreon ung eural etwork Had Ve, Manour Jamzad Abtract In th paper we preent an adaptve method for mage compreon that baed on complexty level of the mage. The bac compreor/de-compreor tructure of th method a multlayer perceptron artfcal neural network. In adaptve approach dfferent Back-Propagaton artfcal neural network are ued a compreor and de-compreor and th done by dvdng the mage nto block, computng the complexty of each block and then electng one network for each block accordng to t complexty value. Three complexty meaure method, called Entropy, Actvty and Pattern-baed are ued to determne the level of complexty n mage block and ther ablty n complexty etmaton are evaluated and compared. In tranng and evaluaton, each mage block agned to a network baed on t complexty value. Bet-SR another alternatve n electng compreor network for mage block n evoluton phae whch chooe one of the traned network uch that reult bet SR n compreng the nput mage block. In our evaluaton, bet reult are obtaned when overlappng the block allowed and choong the network n compreor baed on the Bet-SR. In th cae, the reult demontrate uperorty of th method comparng wth prevou mlar work and JPEG tandard codng. Keyword Adaptve mage compreon, Image complexty, Mult-layer perceptron neural network, JPEG Standard, PSR. I I. ITRODUCTIO MAGE data compreon contnue to be an mportant ubect n many area uch a communcaton, data torage, and computaton. The extng tradtonal technque manly are baed on reducng redundance n codng, nterpxel and pycho vual repreentaton []. In addton, new oft computng technologe uch a neural network are beng developed for mage compreon. Parallelm, learnng capablte, noe uppreon, tranform extracton, and optmzed approxmaton are ome man reaon that encourage reearcher to ue artfcal neural network a an mage compreon approach. Although there are no gnfcant work on neural network that can take over the extng technology but there are ome admble attempt. Reearch actvte on neural network for mage compreon do ext n many type of network uch a - Mult-Layer Perceptron (MLP) [-3], Hopfeld [4], Self-Organzng Map Manucrpt receved February 05, 007. Had Ve wth Computer Engneerng Department of Sharf Unverty of Technology, Tehran, Iran, (phone: ; fax: ; e-mal: ve@ce.harf.edu). Manour Jamzad wth Computer Engneerng Department of Sharf Unverty of Technology, Tehran, Iran, (e-mal: amzad@harf.edu) 8 (SOM), Learnng Vector Quantzaton (LVQ) [5,6], and Prncpal Component Analy (PCA) [7]. Among thee method, the MLP network whch uually ue backpropagaton tranng algorthm provde mple and effectve tructure. It ha been more condered n comparon wth other artfcal neural network (A) tructure. The compreon of mage by Back-Propagaton eural etwork (BP) nvetgated by many reearcher. One of the frt tre n ung th approach wa done n [3], n whch the author propoed a three layer BP for compreng mage. In ther method orgnal mage dvded nto block and fed to nput neuron, compreed block are found at the output of the hdden layer and the de-compreed block are retored n the neuron of output layer. Th mplementaton wa done on the CUBE parallel computer and the mulaton reult howed that th network could acheve a poor mage qualty even for traned mage n 4: compreon rato [3]. A n [] ponted out, none of the reult n ung ngle network are o good a the reult that could be acheved by takng average of mage block and ung ther value a the ndcator of block!. Becaue of thee poor reult acheved by ung one mple BP, everal author tred to mprove the performance of th neural network-baed compreon technque. One of thee effort wa herarchcal neural network [3] whch extended BP by addng two more hdden layer to t. Th extenon wll explot the correlaton between block n an mage n addton to the correlaton between pxel among a block. Th method had ome mprovement n SR of recontructed mage, but th mprovement not o conderable. Adaptve method ue another approach to compre/decompre (CODEC) the mage block. In th approach varou network are ued for compre/decompre dfferent mage block regardng to the complexty of block. It provde bet reult n compreon wth neural network. In [6,7] t uggeted to cluter mage block nto ome clae baed on a complexty meaure called actvty. They have ued four BP wth dfferent compreon rate for each cla. Th yelded gnfcant mprovement over bac BP. Another adaptve approach whch propoed the ue of complexty meaure wth block orentaton by x BP ha gven better vual qualty []. An extenon of th approach gven n [8] n whch block are clafed nto nne predefned orentaton for reducng edge degradaton. In th method dfferent network were ued for compreng the block n each cla. The BP were ued for compreng mage block, after that each pxel n a block wa ubtracted from the mean value of the block. Th method gve ome

2 good reult although accommodate extra overhead n tranmttng the average value. In th paper we have ued the bac neural network-baed algorthm for compreng mage. Then an adaptve approach for compreon preented. We have propoed method for computng the complexty of mage block that are baed on the concept of Entropy, Actvty, and Pattern traectory n block. Th adaptve approach utlze varou BP wth dfferent compreon rato that are ued to compre/decompre mage block dependng on the level of complexty n the block. In practce, we have ued the complexty crteron to elect the approprate network for compreng ncomng mage block. Alo Bet-SR method ued to elect the network that gve the bet SR for that mage block. In addton, overlappng of mage block ued n order to elmnate the che-board effect n de-compreed mage. Our expermental reult howed that compoton of overlappng block and choong the network wth Bet-SR yeld mprovement n PSR and vual qualty of recontructed mage compared to tandard and conventonal JPEG codng. Th paper organzed a follow. In ecton II we dcu mult-layer perceptron neural network and t adaptve approach that drectly developed for mage compreon. Secton III decrbe the complexty meaurement method ued n th paper. In ecton IV, the expermental reult of our mplementaton are dcued and fnally n ecton V we conclude th reearch and gve a ummary on t. II. MULTI-LAYER EURAL ETWORKS FOR IMAGE COMPRESSIO Mult-Layer neural network wth back-propagaton algorthm can drectly be appled to mage compreon. The mplet neural network tructure for th purpoe llutrated n Fg.. Th network ha three layer, nput, hdden and output layer. Both the nput and output layer are fully connected to the hdden layer and have the ame number of neuron,. Compreon can be acheved by allowng the value of the number of neuron at the hdden layer, K, to be le than that of neuron at both nput and output layer ( K ). A n mot compreon method, the nput mage dvded apart nto block, for example wth 8 8, 4 4 or 6 6 pxel. Thee block ze determne the number of neuron n the nput/output layer whch convert to a column vector and fed to the nput layer of network; one neuron per pxel. Wth th bac MLP neural network, compreon conducted n tranng and applcaton phae a follow. Internatonal Journal of Sgnal Proceng 5; Sprng 009 Fg. Bac mage compreon tructure ung neural network a narrow channel. Tranng ample of block are converted nto vector and then normalzed from ther gray-level range nto [0, ]. In accordance wth the tructure of neural network hown n Fgure, the operaton for adutng weght for compreng and de-compreng can be decrbed a the followng equaton. H Xˆ n n = = = = K n V X, h = f ( H ); K () n Wh, Xˆ = g( Xˆ ) ; () In the above equaton, f and g are the actvaton functon whch can be lnear or nonlnear. V and W repreent the weght of compreor and de-compreor, repectvely. The extracted K tranform matrx n compreor and K n de-compreor of lnear neural network are n drecton of PCA tranform. Th tranform provde optmum oluton for lnear narrow channel type of mage compreon and mnmze the mean quare error between orgnal and recontructed mage. In addton, t map nput ample nto a new pace where all ample n the new pace are decorrelated; th fact led better compreon. But unfortunately th a data-dependent tranform and t can only provde good compreon for traned mage. Ung lnear and nonlnear actvaton functon n th network reult lnear and non-lnear PCA repectvely. The tranng proce of the neural network tructure n Fg. teratve and topped when the weght converge to ther true value. In real applcaton the tranng topped when the error of equaton (3) reache to a threhold named ε or maxmum number of teraton lmt the teratve proce. A. Tranng Lke all other tranng procee, n th phae a et of mage ample are elected to tran the network va the backpropagaton learnng rule. For compreon purpoe the target pattern n the output layer neuron of the network wll be ame a the nput pattern. The compreon repreented by the hdden layer whch equvalent to compre the nput nto k ( X ˆ ) k X Err = = k (3) B. Applcaton When tranng completed and the couplng weght are aduted, the tet mage fed nto the network and compreed mage obtaned n the output of hdden layer. 83

3 Thee output mut be quantzed to the dered number of bt. If the ame number of bt ued to repreent nput and hdden neuron, then the Compreon Rato (CR) wll be the rato of number of nput to hdden neuron. For example, to compre an mage block of 8 8, 64 nput and output neuron are requred. In th cae, f the number of hdden neuron are 6 (.e. block mage of ze 4 4), the compreon rato would be 64:6=4:. But for the ame network, f 3 bt floatng pont ued for codng the compreed mage, then the compreon raton wll be :, whch ndcate no compreon ha occurred. In general, the compreon rato of the bac network llutrated n the Fg. for an mage wth n block computed a Eq. (4). Internatonal Journal of Sgnal Proceng 5; Sprng 009 nb CR = B I I = (4) nkb H KB H Where B I and B are the number of bt needed to code H the output of nput and hdden layer, repectvely. In th equaton and K are the number of neuron n the nput and hdden layer, repectvely. In de-compreor, the compreed mage converted to a veron mlar to orgnal mage by applyng the hdden to output layer de-compreon weght on output of hdden layer. The output of output neuron mut be caled back to the orgnal graycale range,.e. [0~55] for 8 bt pxel. C. Adaptve approach A mentoned n the prevou ecton, the bac tructure of neural network for mage compreon provde an approxmaton of PCA tranform. Th tructure tre to decorrelate the nput ample of pxel; th proce a maor ue n data compreon. But becaue of dependablty of th tranform to traned data, t not ued n many real applcaton. Th the man reaon that PCA replaced wth t nearet approxmate, the data-ndependent Dcrete Cone Tranform (DCT) tranform n real applcaton. Due to th lmtaton of the bac neural network tructure for compreon, the reult obtaned from th network how that n t too weak to be ued. One method for mprovng the performance of th mple tructure the adaptve approach whch ue dfferent network to compre block of the mage [,5-]. Dong th, at frt, mage block are dvded nto everal clae accordng to ther complexty. Then mage block of each cla are ued to tran a network n the way the compreon rato of the network related to the complexty of th cla. All of the network have dentcal tructure, but they have dfferent number of neuron n hdden layer, whch wll reult n dfferent compreon rato. Conderng the network of Fg. a the bac tructure, we can preent the adaptve method a n Fg.. A t hown n th fgure, to tran the network the amount of nformaton avalable n each block etmated by mean of a value accordng to a complexty meaure crteron lke average of the gray-level n mage block or ome other method. Then 84 Fg. eural network-baed adaptve tructure for mage compreon accordng to th complexty value, one of the avalable network elected. Each network traned ung t correpondng tran data by Back-propagaton algorthm. To dentfy for de-compreor whch network ued n compreor tage to compre the mage block, a code agned to each traned network. Th code hould be tranmtted or be aved along the compreed mage. It clear that the number of network and conequently the number of bt needed to preent th code wll affect the compreon rato. The lower number of bt preferred from the overhead vew of pont but on the other hand the, lower number of network reduce the adaptvely ablty of the algorthm. In de-compreor th aved or tranmtted code along wth the compreed mage extracted and therefore, the correpondng network (.e. the ame network ued n compreon tage) can be elected for de-compreon. In adaptve approach, we aume to have M dfferent network wth k - k M neuron n hdden layer. In th cae for an mage wth n block each havng pxel, the compreon rato a equaton (5) that obtaned by modfyng equaton (4).

4 CR a = n = n BI = BH BH K + q ( n BI ; M n q K ) + n = In the above equaton, K the number of neuron n the hdden layer of elected network for th block mage and M. q the number of bt that are needed to code the network number. In fact q equal to the mallet potve nteger uch that q M. III. COMPLEXITY MEASUREMET METHODS In the followng three method are preented for calculatng the detal level of mage block to ncorporate n adaptve BP algorthm. Dependng on the value of detal level, mage block are clafed nto everal clae. One network agned to each cla and the compreon rato of that cla related to t complexty. In fact the complexty meaurement crtera hould reveal the amount of nformaton n an mage block. Alo, t hould be able to dcrmnate the mage block accordng to neural network-baed compreon. The complexty meaure crteron an mportant factor for th approach and t affect the compreon performance, gnfcantly. Here, we have ued three dfferent crtera, Entropy, Pattern-baed and Actvty. A. Complexty baed on Entropy It known that Entropy a meanngful crteron to meaure the amount of nformaton n a et of ymbol lke an mage. The entropy of an mage block wth dfferent graylevel calculated a (6). Where P(x ) the probablty of occurrence of gray-level x n th block. Entropy = P( x )log P( x ) (6) = An mage block that ha a hgher Entropy value contan more nformaton. It mean that, to prevent more lo of data, that block hould go through le compreon. Alo, a block wth lower Entropy value hould be compreed by a network whch provde hgher compreon rato. B. Complexty baed on Actvty Th meaurement method defned to cover the ubectve dea of actvty n an mage block. For an mage block wth pxel (.e. n ze ) the Actvty defned a equaton (7). Actvty = = m n, = even; = = = ( x, ( m, n) (0,0) x m, n In th meaurement, low actvty clae requre network wth hgh compreon rate and hgh actvty clae need to mantan more data whch mean that they hould ue network wth larger number of hdden neuron and lower compreon rate. Internatonal Journal of Sgnal Proceng 5; Sprng 009 ) (5) (7) 85 C. Pattern-baed complexty Although Actvty a good ubectve crteron n complexty approxmaton and Entropy a emantc meaure for calculatng the amount of nformaton n a block of data, but n our uage of thee method for learnng purpoe, we faced ome dffculte. It clear that the Entropy value of all mage block n Fg. 3-(5) to Fg. 3-(8) are equal. Th true for the Actvty value, too. Th becaue thee block have equal number of black and whte pxel, although each ha a dfferent hape than the other. So f Entropy ued a complexty meaure crteron to elect the approprate network all of thoe block wll be compreed by ame network. Each of thee block ha dfferent pattern and n order to obtan better compreon rato, t better to agn thee block to dfferent network. Therefore, we conclude that Entropy and Actvty can not dcrmnate thee dfferent pattern. Th caue a fale electon of approprate network n the algorthm and a poor etmaton n true complexty approxmaton. To overcome th problem we have ued another complexty meaure named pattern-baed method. In th method mage block are clafed baed on ther pattern. Th done by dvdng a block nto four equal ub-block. The dvon method baed on quad-tree repreentaton of an mage, o the cro-cut of block not condered. Then each mage block agned to one of the 6 pattern of Fg. 3. The ub-block are black or whte and t neceary to ue a threhold to agn black or whte level to a graycale ubblock. For each of thee pattern one network ued to compre the aocated mage block. etwork have varou compreon rate baed on ther related pattern. That, pattern number and n the Fg. 3 have maxmum compreon rate, 3 and 4 have the mnmum compreon rate. More detal about the compreon rate of thee pattern are dcued n ecton IV. IV. EXPERIMETAL RESULTS In th ecton we have evaluated the compreon ablty of the bac network tructure n Fg. and propoed adaptve approach of Fg. wth dfferent complexty meaure crtera. Alo we have compared the adaptve method wth JPEG tandard codng algorthm. In addton to Compreon Rato (CR) whch gven n equaton (4) and (5), the performance of thee method are compared accordng to Fg. 3 Pattern ued for clafcaton of mage block a a complexty meaure crteron

5 Peak Sgnal to oe Rato (PSR) crteron. PSR motly ued for t mplcty n calculaton a a crteron to expre the mage qualty generated by a loy compreon lke the neural network-baed method. Regardle to t mplcty, th method doe not pecfcally related to the reultng compreed mage qualty a oberved by a human. In th metrc, the orgnal mage X aumed a a clean gnal whch t de-compreed mage, Xˆ condered to depct the noy gnal. The orgnal and de-compreed mage are aumed to be of the ame ze. For an mage of ze R C (.e. Row Col ) PSR determned accordng to equaton (8) n decbel. 55 PSR = 0 log0 ( ) ( db) R C ( ˆ X X ) R C = = We have ued 8 bt/pxel graycale mage n our experment, o 55 ndcate the maxmum gray-level n the above equaton. The ze of mage block one of the parameter whch eem to need to be optmzed. We have ued 4 4, 8 8 and 6 6 a the ze of mage block whch repectvely reult 6, 64 and 56 neuron n nput and output layer. The evaluaton of block ze wth above value done n the bac tructure of Fg.. In all of thee network fx compreon rato 4: (.e. 6:4, 64:6 and 56:64, repectvely) are ued that correpond to 4, 6 and 64 neuron n the hdden layer (.e.,, 4 4 and 8 8 block). Our mulaton reult howed that the value of th parameter not o crucal, but there are ome conderaton about t. Larger block ze reult hgher number of parameter and requre more tranng pattern. Alo th lead to hgher error varance and relatvely better PSR for compreng the mage whch are out of the tranng et. Obvouly th revered for mall block ze. Speed another parameter whch eem to be affected by the block ze. The number of block n a partcular mage decreae a the ze of block ncreae, o t eem that the peed of algorthm mprove wth larger block ze. But the followng conderaton reect th uperfcal reaonng. Suppoe an mage wth pxel dvded nto K block, each block n ze. In the bac compreon tructure and wth CR 4:, there are K tme that a vector n ze multple wth the weght matrx of compreor n ze. Alo multplyng n the de-compreor (8) compreed block weght matrx hould be condered. So the number of multplcaton and ummaton are a equaton (9) and (0), repectvely. m R = K. +. =. R 3 K ( ). +. ( ). =.( ) = Internatonal Journal of Sgnal Proceng 5; Sprng 009 (9) (0) 86 Where K =. ow f a larger block ze, l l ued where l =., then the equaton (9) and (0) are changed a bellow. R =.(. ) =. R () m l m 3 3 R l =.(. ) =..( ). R () 4 It mean that no mprovement n peed obtaned by ung larger block ze. In general, the ze of mage block not very crtcal parameter and among the three experenced block ze we have ued 8 8 n all of the experment n th work. A. Evaluaton on bac network tructure To evaluate the bac network tructure we ued fx CR 4:. Input mage block are 8 8, a pxel ha 8 bt, and 8 bt/neuron aumed to code the output of the hdden layer. For tranng the network, we have ued the Lena mage of ze and no overlappng between mage block ued. Lena wth three another mage are ued a tet mage. Fg. 5 llutrate the reult of CODEC wth th tructure and Table I how the PSR obtaned by comparng the orgnal mage wth ther compreed veron. BP reult better performance for the traned mage compared to other mage n the tet et. Clearly, th method ha not provded acceptable qualty for tet mage that are not n the tranng et. Th fact due to data dependency problem n extracted tranform reulted by traned weght. Th bac tructure etmate PCA tranform ut for a traned mage that optmum only for th mage. There are ome conderaton n the mplementaton of the bac tructure that can affect the reult. The ntalzaton of network parameter, number of quantzaton bt n hdden layer and the amount of tranng data are ome mportant concept whch need more exploraton. The ntal weght for neural network tructure are the tartng pont of the earch n fndng optmum tranform. In thee experment we have ued random ntalzaton but there are other work lke [3] whch examne other value. They have ued a feed-forward 3-layered network a CODEC and expermented DCT value a ntal weght. Ther evaluaton ha howed that th ntalzaton doe not brng about any mprovement n decompreed mage qualty. The number of quantzaton bt n the hdden layer affect the compreon rato and the recontructed mage qualty. A mentoned, we have ued 8 bt per hdden neuron output. In [3] the quantzaton level wa vared from to 0 bt and n [4] th value wa changed between and 8. Almot ame reult wa acheved n both and the performance doe not gnfcantly ncreae n ung more than 6 bt, whle th mprove the compreon rato. Although there no determntc rule for the amount of tranng data n parameter tunng for neural network and the experence the better teacher, but a a rule of thumb for each unknown parameter, 4 to 0 tranng ample are requred. We condered th n our experment. Generally, ncreang the ze of the tranng et reult n ncreang n

6 Internatonal Journal of Sgnal Proceng 5; Sprng 009 TABLE I COMPRESSIO RESULTS USIG BASIC EBP STRUCTURE Tet mage PSR (db) Lena 34.9 Camera man 6.67 Crowd 3.4 Pepper.0 Camera man Pepper Lena Crowd Fg. 4 Tet et mage (Lena alo n tranng et) Camera man Pepper Lena Crowd Fg. 5 Recontructed tet et mage ung network of Fg. for CODEC learnng error, but decreang tet error. A the tranng ample are ncreaed, thee two error value (.e. learnng error and tet error) are converged to the ame value. B. Reult of adaptve method In order to mprove the performance of the bac network tructure we have ued the adaptve approach decrbed n ecton II part C. Th method need more tranng data due to hgher number of network parameter. Selecton of the tranng et done n uch a way that a wde range of the complexte n mage have been covered. Alo the number of tranng pattern for all network hould be uffcent to acheve the convergence wth mnmum error. We have elected 05 mage whch contan a wde range of complexte for all gray-level. Fg. 6 how ome ample of our tranng mage. Lke the bac tructure, n tranng the adaptve network, 8 8 mage block are ued,.e. 64 neuron n the nput layer. Accordng to each complexty meaure method, each block gven to t approprate network. The block wth low level of complexty are gven to network wth hgher compreon rato and thoe wth hgh level of complexty are gven to network wth lower compreon rato. In thee tructure the number of neuron n hdden layer determne the compreon rato and trctly related to the complexty value of block. We have choen th value for each network n each complexty crteron a dcu n the followng. Havng the traned network, gven an nput tet mage, the compreon done a the tranng routne. The mage are dvded nto block and the complexty value for each block computed. After that, the network related to that complexty value elected and the compreon done by that network. We have called th method a complexty-baed n our reult n the followng. Another choce n electng a network from among traned network to chooe a network whch optmum for compreng an mage block. In th approach the complexty meaure not condered and a network elected uch that t mnmze an error meaure crteron. We have ued th network electon method by conderng maxmzaton of gnal to noe rato crteron for each block. Here, an mage block gven to all network and the network whch reult maxmum SR for the block elected. We named th approach bet-sr a hown n our reult n the next ecton. Of coure, th a tme conumng proce; however t reult the mnmum error n recontructed mage. It clear that f the complexty meaure crteron ha been choen precely, t would have been expected that the reult of thee two approache were the ame or cloe together. Alo, n order to reduce the che-board effect n recontructed mage and mprove t vblty qualty, overlappng the adacent mage block allowed. We have realzed th dea by conderng a %50 overlap between row and column of neghborng block. In the overlapped area, for each pxel, the average value of overlapped pxel calculated. A the reult of the followng ecton how, overlappng mproved mage vblty qualty and ncreaed t PSR. For all three adaptve method, the Lena mage preented n the tranng et and the other three mage of Fg. 4 are not. The toppng condton for Back-Propagaton learnng n all 87

7 Fg. 6 Some ample mage of the tranng et ued n the adaptve approach. Internatonal Journal of Sgnal Proceng 5; Sprng 009 value of for all tranng mage and Fg. 7 how th for Lena and Camera man mage n the tet et. The dtrbuton of the number of pattern for each network n the tranng data, how the uffcently of data for tranng the network. In Entropy-baed adaptve method the error threhold condton wa atfed before reachng the maxmum number of teraton for convergence condton n BP learnng. The reult of th adaptve tructure are hown n table II. The evaluaton done on 4 tet mage hown n Fg. 4 n Complexty-baed and Bet-SR approache wth and wthout overlap for each mage. The Compreon Rato (CR a ) calculated ung Eq. (5). The ablty of th method n good recontructon of out-oftran mage (.e. mage that are not preent n tranng et) conderable. The PSR for all mage of tet et are cloe and due to the hgher complexty of the Crowd mage t CR le than other. The recontructed Lena mage for experment (a) to (d) of table II are llutrated n Fg. 8. A Fg. 8 (a) how, the che-board effect evdence. Utlzng the block overlappng reduce th defect a hown n Fg. 8 and ncreae the PSR about db wthout affectng the CR. The Bet-SR network electon for tet block reult three adaptve tructure (.e. Entropy, Actvty and Patternbaed) have been both the maxmum number of teraton 0000 and the error threhold ε =.0e 5 for equaton (3).. Expermental reult ung Entropy meaure In Entropy complexty meaure crteron, x network are ued whch reult 3 bt overhead for codng the number of network (q n Eq. (5)). The number of hdden neuron for thee network are 4, 9, 6, 5, 36 and 49 that reult 6, 7., 4,.5,.7 and.3 compreon rato, repectvely. Of coure, there are other poblte n electng the number of hdden layer neuron but n all of them hgher complexty need hgher number of neuron and vce vera. An mportant notce n choong thee number that large number of hdden neuron not necearly lead to mall error for tet et, although t reult mall error n tranng data. Regard to the avalable range for gray-level value, 0 to 55, the maxmum Entropy value wll be log 56 = 8. Th maxmum achevable when all of the gray-level have the ame probably. In the other word, an mage block receve t maxmum value of Entropy when t contan the ame number of all of the gray value n that block. For a 56 level mage the maxmum Entropy value of 8 achevable only when that mage block ha at leat 56 pxel but wherea we have ued 8 8 mage block, th maxmum value wll be log 64 = 6. We have ued Eq. (3) to agn the block to the network. Th reult value of network number n 6. = Entropy = 6 + ; Entropy ; Entropy 6 = 6 (3) Alo the elected number of hdden neuron baed on the fact that mage block wth hgher Entropy hould be coded wth lower compreon rato network. Fg. 7 (a) how the 88 umber of pattern umber of block etwork number (a) [05 (56 56) mage=0750 pattern] Lena Camera man etwork number Fg. 7 (a) The htogram of the Entropy value for all mage n the tranng et and for Lena and Camera man tet mage 8

8 TABLE II COMPRESSIO RESULTS BY ADAPTIVE BP STRUCTURE USIG ETROPY COMPLEXITY MEASURE CRITERIO etwork PSR Tet mage CR Selecton (db) a Lena (a) Camera man Complexty-baed one- Crowd Pepper Lena Camera man Complexty-baed Crowd (c) Bet-SR one- (d) Bet-SR Pepper Lena Camera man Crowd Pepper Lena Camera man Crowd Pepper TABLE III THE AVERAGE COMPLEXITY (ETROPY) FOR THE TEST SET IMAGES (56*56 IMAGES: 04 BLOCKS I SIZE 8*8) Image Crowd Pepper Lena Camera man Average Complexty (a) (c) Fg. 8 Recontructed Lena mage ung Entropy-baed adaptve compreon approach wth 4 dfferent compreon method (a) to (d) from Table II conderable mprovement n PSR value and vblty qualty a part (c) and (d) how n Table II and Fg. 8 (c) and Fg. 8 (d). From the other pont of vew, the drawback of th Internatonal Journal of Sgnal Proceng 5; Sprng 009 (d) 89 approach are ncreang CODEC tme and decreang CR. The CR declne how that the network wth lower CR are alo elected to code the block wth lower complexty. A remarkable note of reult (a) to (d) n Table II the dtncton n PSR mprovement between Lena and Crowd mage. Th becaue of dfference n the complexty level of thee mage. In our tet et the average complexty (Entropy) value are hown n Table III. Lena and Camera man mage are le complex than Pepper and Crowd. Crowd the mot complex one but ung the Bet-SR ha not provded gnfcant mprovement n the PSR of t recontructed mage. Th becaue the mprovement reulted by the Bet-SR method due to the property of th method n ung network wth lower CR for le complex block n an mage. The fact that, n Crowd mage, 85% of the block have the complexty relate to = 6 and only 5% of them relate to 4. Th mean that we could ue network wth lower CR only for 5% of block. So, le degradaton n the CR of th mage compare to other mage can be alo utfed. Expermental reult ung Actvty meaure In th method 4 network wth the ame nput block ze a Entropy method are ued. The network have 9, 6, 5 and 36 hdden neuron that reult 7., 4,.5 and.7 CR, repectvely. Theoretcally the maxmum value of the Actvty n Eq. (8) for a 56 level 8 8 mage block hgher than 3.0e+6 but th value for our tranng et about.9e+6 whch there are very mall number of block that have hgh Actvty near to th value. We have elected 4 dfferent range [0,465), [465, 4073) and [4073, 054) and [054, ), each for a network. Th done regard to all Actvty value n tranng et. Fg. 9 how the number of pattern n tranng et for thee 4 network. Table IV how the reult of th adaptve method. The reulted PSR n th method better than Entropy for le complex mage n (a) and tet. Thee reult how that th meaurement method etmate the complexty better than Entropy only for le-complex mage. The maller number of network n th method caue that the Bet-SR doe not provde PSR a good a Entropybaed method. On the other hand, thee number of network caued only bt overhead compared to 3 bt n Entropybaed method. Alo regard to the electon of number of neuron n the hdden layer, th method provde better CR. The reult of th method n cae (d) ndcate that Bet-SR, for complex mage, Crowd and Pepper, do not how hgh mprovement. Th becaue the complexty of thee mage and ame reaonng a prevou ecton correct about them.. Expermental reult ung Pattern-baed meaure The mulaton of th method done ung 6 network, one network for each pattern n Fg. 3. The CR related to thee pattern are 6: for pattern number and, 4: for pattern number 6~8 and 9~, 7.: for pattern number 3~6 and.5: for pattern 3 and 4. Selecton of the number of hdden layer neuron baed on the vual and ntutve

9 umber of pattern etwork number Fg. 9 The htogram of number of tranng block for 4 Actvty value range for 05 mage n tranng et. (.e. umber of pattern= 05 (56 56: mage ze) =0750) TABLE IV COMPRESSIO RESULTS BY ADAPTIVE BP STRUCTURE USIG ACTIVITY COMPLEXITY CRITERIO etwork PSR Tet mage CR Selecton (db) a Lena (a) Camera man Complexty-baed one- Crowd Pepper Complexty-baed (c) Bet-SR one- (d) Bet-SR Lena Camera man Crowd Pepper Lena Camera man Crowd Pepper Lena Camera man Crowd Pepper TABLE V COMPRESSIO RESULTS BY ADAPTIVE BP STRUCTURE USIG PATTER-BASED COMPLEXITY CRITERIO etwork PSR Tet mage CR Selecton (db) a Lena (a) Camera man Complexty-baed one- Crowd Pepper Lena Camera man Complexty-baed Crowd (c) Bet-SR one- (d) Bet-SR Pepper Lena Camera man Crowd Pepper Lena Camera man Crowd Pepper complexty of the related pattern. Alo, there ext other Internatonal Journal of Sgnal Proceng 5; Sprng method to elect thee number. We can aume the compreed pattern n the hdden neuron a a maller veron of the orgnal pattern and ue the fx 64:6 CR for all network. The CODEC reult of th method are hown n Table V. Thee reult are almot n the ame drecton of two former method. The overlappng ncreae the PSR about db and Bet-SR network electon method ha reulted hgher qualty recontructed mage even for complex mage. Th becaue of the hgher number of network ued n th method compared to prevou method. Alo due to the network tructure the CR of mage hgher than Entropy-bae tructure and lower than Actvty-baed. There are 4 overhead bt n th method to code the network number. In addton, the reducton of CR value wth Bet-SR reaonable becaue of the hgher number of network. C. Comparon of Entropy, Actvty and Pattern-baed method In the followng we have compared three adaptve method together and then compared thee method n ther bet cae, Bet-SR wth overlappng and wth JPEG tandard. The compreon of three propoed adaptve method ung ther reult not o reaonable becaue each one ue dfferent number of network and dfferent tructure n each network. In any compreon approache rate dtorton or the tradeoff between the CR and data dtorton an mportant ubect. In A-baed adaptve approach t poble to etmate the rate dtorton functon (RDF) theoretcally and t can be done by makng all poble network wth any CR. Havng RDF for each compreon method enable u to compare varou method more precely. Etmaton of RDF not performed for propoed method n th reearch and the reult are ued to compare method. A the reult of Table III, IV and V how, the Entropy preent good etmaton of complexty for complex mage. On the other hand Actvty perform better etmaton for le-complex and mpler mage. Th method ha reulted hgher CR due to t network tructure. The Pattern-baed complexty meaure method ha reult almot the ame PSR wth hgher CR than Entropy and lower CR than Actvty. For better comparon of thee method and conderng both CR and PSR together, we have compared them wth JPEG tandard. The reult are hown n Fg. 0. It llutrate the ablty of adaptve compreon method compared to the tandard JPEG algorthm. Th comparon done n the ame bt rate for each method. Thee reult how the achevement and even uperorty of A-baed compreon to th compreon tandard. In addton to the compreon reult, the three propoed adaptve method are dfferent from fundamental prncple pont of vew. Entropy a meaure of uncertanty of a random varable whch quantfe the amount of nformaton of a ource, lke an mage. The Actvty an ntutonal method for etmatng the complexty of an mage block ung the dfference between each pxel and t neghbor. Thee two method do not dcrmnate the place or drecton of the complexty and gve an average value of complexty. For

10 example the complexty value that meaured by Entropy or Actvty for pattern number 5 and 6 n Fg. 3 are ame, whle thee two pattern are completely dfferent n A learnng pont of vew. On the other hand, Pattern-baed method clafe the mage block nto ome predefned pattern. Actually, th method not a complexty meaure crteron and ha not the mentoned problem of other method, but th method ndcate another problem. It doe not conder graycale value exactly and fnally map each 4 4 ub-block nto one block or whte pattern. One oluton to th problem the combnaton of Pattern-baed method wth other method. (a) Internatonal Journal of Sgnal Proceng 5; Sprng 009 V. SUMMARY AD COCLUSIO We have revewed the ue of Mult-Layer Preceptoron eural etwork for mage compreon. Snce acceptable reult not reulted by compreon wth one network, an adaptve approach ued. It ue dfferent network for dfferent mage block regardng to ther complexty value. Three complexty meaurement method Entropy, Actvty and Pattern-baed are preented and evaluated. Our expermental reult how that better vual qualty obtaned by overlappng neghborng mage block. Alo electng mage wth Bet-SR crteron rather than the complexty crteron provde hgher mage qualty and better PSR. Hgher number of network provde better performance n Bet-SR approach but th wll reult n lower CR. However, overlappng and network electon need more nvetgaton and t can be accepted to obtan better recontructed mage qualty. Comparng reult wth tandard JPEG algorthm how better performance for our method both wth PSR meaure and vblty qualty. In th paper the number of network that provde dfferent compreon rato are not optmzed. It expected that ung larger number of network and electng optmum compreon rato for network, provde better reult. For th purpoe ome type of neural network uch a cacadecorrelaton can be ued n addton to the heurtc or try and error approache. In thee network we can elect the number of neuron n hdden layer n uch a way that an optmum compreon rato could be acheved. Among three propoed method the Entropy and Actvty do not ue the orentaton of pattern and the Pattern-baed doe not ue the gray-level properly. Conderng the gray-level value n the Patternbaed method, can provde better reult. Th can be realzed by combnng the Actvty or Entropy wth Pattern-baed. In addton, from a compreon method vewpont, the ratecontrol ablty or havng rate-dtorton functon an mportant factor. However, t eem that A-baed method are not flexble n controllng the compreon rato, but t poble to have a et of traned network wth dfferent compreon rato rather than one network n each cae. (c) Fg. 0 The comparon of the adaptve method wth the JPEG compreon tandard: (a) Entropy, Actvty and (c) Pattern-baed REFERECES [] R. C. Gonzale, R. E. Wood, Dgtal Image Proceng, Second Edton, Prentce-Hall, 00. [] Ve H., Jamzad M., Image Compreon Ung eural etwork, Image Proceng and Machne Von Conference (MVIP), Tehran, Iran, 005. [3].Sonehara, M.Kawato, S.Myake, K.akane, Image compreon ung a neural network model, Internatonal Jont Conference on eural etwork, Wahngton DC, 989. [4] G.L. Scuranza, G. Rampon, S. Mar, Artfcal neural network for mage compreon, Electronc letter 6, , 990. [5] S. Mar, G. Rampon, G. L. Scuranza, Improved neural tructure for mage compreon, Proceedng of Internatonal Conference on Acoutc Speech and Sgnal Proceng, Torento, 99. [6] S. Carrato, G. Rampon, Improved tructure baed on neural network for mage compreon, IEEE Workhop on eural etwork for Sgnal Proceng, ew Jerey, September 99. [7] S. Carrato, S. Mar, Compreon of ubband-flterd mage va neural network, IEEE Workhop on eural etwork for Sgnal Proceng. Augut 99. 9

11 [8] G. Qu, M. Varley, T. Terrel, Image compreon by edge pattern learnng ung multlayer perceptron, Electronc letter, Vol 9, o 7, Aprl 993. [9] R.Sentono, G. Lu, Image compreon ung a feedforward neural network, Internatonal Conference on eural etwork, 994. [0] J. Jang, Image compreon wth neural network -A urvey, Image Communcaton, ELSEVIER, Vol. 4, o. 9, 999. [] C. Cramer, eural network for mage and vdeo compreon: A revew, European Journal of Operatonal Reearch, Vol. 08, July 998. [] B. Verma, M. Blumenten, and S. Kulkarn, A eural etwork Baed Technque for Data Compreon, Proceedng of the IASTED Internatonal Conference on Modellng and Smulaton, MSO97, Sngapore, 997. [3] A.amphol, S.Chn, M. Arozullah, Image compreon wth a herarchcal neural network, IEEE Tran. Aeropace Electronc Sytem Vol. 3 o., January 996. [4] J. S. Ln, S.H. Lu, A compettve contnuou Hopfeld neural network for vector quantzaton n mage compreon, Engneerng Applcaton of Artfcal Intellgence, Vol., 999. [5] G. Pavld, A. Tompanopoulo, A. Atalak,. Papamarko, C. Chamza, A Vector Quantzaton Entropy Coder Image Compreon Sytem, IX Spanh Sympoum on Pattern Recognton and Image Proceng, 00. [6] C. Amerckx, J. D. Legaty, M. Verleyenz, Image Compreon Ung Self-Organzng Map, Sytem Analy Modelng Smulaton Vol. 43, o., ovember 003. [7] S. Cota, S. For, Image compreon ung prncpal component neural network, Image and von computng, Vol. 9, 00. [8] M. Egmont-Peteren, D. de Rdder, and H. Handel, Image proceng wth neural network - a revew, Pattern Recognton, vol. 35, pp , 00. [9] A. Rahman and Chowdhury Mofzur Rahman, "A ew Approach for Compreng Color Image ung eural etwork", Proceedng of Internatonal Conference on Computatonal Intellgence for Modelng, Control and Automaton - CIMCA 003, Venna, Autra, 003. [0] Thoma M. Cover and Joy A. Thoma. Element of Informaton Theory, John Wley and Son Inc., ew York,.Y., 99. [] Sona Grgc, Marta Mrak, Mlav Grgc, Comparon of JPEG Image Coder Proceedng of the 3rd Internatonal Sympoum on Vdeo Proceng and Multmeda Communcaton, VIPromCom, pp , Zadar, June 00. Internatonal Journal of Sgnal Proceng 5; Sprng 009 Had Ve receved h MS n computer engneerng (artfcal ntellgent) from Sharf Unverty of Technology, Tehran, Iran n 005. He currently nvolvng h Ph.D. n the ame department. H reearch nteret are Dgtal Sgnal Proceng, Image Proceng, and eural etwork. Manour Jamzad Receved h MS n Computer Scence from McGll Unverty n Montreal, Canada and h PhD n Electrcal Engneerng from Waeda Unverty, Tokyo, Japan n 989. He wa a pot doctorate reearcher n Department of Communcaton and Electronc Engneerng, Waeda Unverty, Tokyo, from 989 to 990. He wa a vtng reearcher n Tokyo metropoltan nttute of gerontology, durng He ha become an atant profeor n Dept. of Computer Eng., Sharf Unverty of Technology, Tehran, Iran, nce 995. H man reearch nteret are Image proceng, Machne Von and Robotc. 9

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