A Fast Block Motion Estimation Algorithm Using Gray Code Kernels

Transcription

1 A Fat Bloc Moton Etaton Algorth Ung Gray Code Kernel Yar Mohe, Hagt Hel-Or Det. of Couter Scence, Unverty of Hafa 3195 Hafa, Irael Abtract Moton etaton lay an ortant role n odern vdeo coder. In uch coder, oton etated ung a bloc atchng algorth that etate the aount of oton on a blocby-bloc ba. A full earch technque for fndng the bet atchng bloc delver good accuracy but uually not ractcal due to t hgh coutatonal colexty. In th aer, a novel fat blocbaed oton etaton algorth rooed. Th algorth ue an effcent roecton fraewor whch bound the dtance between a telate bloc and canddate bloc. Fat roecton erfored wth a faly of hghly effcent flter ernel the Gray Code Kernel ung only oeraton er xel for each flter ernel. The roecton fraewor cobned wth a reecton chee whch allow rad reecton of canddate bloc that are dtant fro the telate bloc. Exerent how that the rooed algorth gnfcantly outerfor oular fat oton etaton algorth, uch a three-te earch and daond earch. In addton, the tradeoff between coutatonal colexty and qualty of reult could be ealy controlled n the rooed algorth, thu t enable adatvty to age content. Keyword fat oton etaton, bloc atchng, vdeo coreon, vdeo codng, Gray Code Kernel (GCK). I. INTRODUCTION Vdeo coreon ha becoe an eental art of odern ulteda yte nce t enable gnfcant bt rate reducton of the vdeo gnal for tranon or torage. A vdeo coder coact a dgtal vdeo equence by decreang vdeo redundance. Mot effectve the reoval of teoral redundance whch are gnfcant due to the fact that the dfference between conecutve frae of vdeo all. In recent year, everal vdeo coreon tandard have been rooed for varou alcaton uch a MPEG-1//4 [1] [], H.61/3/4 [3] [4]. Although dfferng n any detal, thee tandard antan the ae general hybrd DPCM/tranfor codng tructure. In th tructure, teoral redundancy exloted ung bloc-baed oton etaton and coenaton. Bloc-baed oton etaton and coenaton coenate for oveent of rectangular nonoverlang regon called acrobloc. Two dfferent tye of acrobloc are defned Intra and Inter. Moton etaton and coenaton erfored on Inter acrobloc only. For each telate Inter bloc n the current frae, the encoder erfor the followng rocedure: Ste 1: Search an area (earch wndow) n the reference frae to fnd the 'bet' atchng bloc fro aongt all canddate bloc n the earch area. A oular atchng crteron the MSE (Mean Squared Error) between a canddate bloc and a telate bloc, whch eaure the energy of the dfference between the two bloc. Ste : The choen canddate bloc ubtracted fro the telate bloc to for a redual bloc. Ste 3: The redual bloc encoded and trantted wth a oton vector rereentng the dlaceent between the telate bloc and choen bloc. The decoder later ue the redual bloc and the oton vector to recontruct the orgnal telate bloc [5]. A brute force technque for erforng Ste 1 called full earch. It erfored by coarng all canddate bloc n the earch wndow wth the telate bloc. Full earch oton etaton conue 6%-8% of a tycal vdeo encoder' coutaton te. It delver good accuracy n oton etaton but ncur hgh coutaton colexty and not utable for ot real-te alcaton. Obtanng near-otal bloc atchng reult eental for achevng hgh codng effcency. Thu a fat and accurate bloc atchng algorth a crtcal art of every ractcal vdeo coder wth gnfcant act on codng effcency. Many ubotal fat oton etaton algorth have been rooed n the lterature. Soe of thee algorth reduce earch colexty by ltng the ze of the earch wndow and the nuber of canddate bloc under the auton that the atchng error onotoncally ncreae wth the dtance fro the earch oton defned by the otal oton vector. Th auton not alway vald and the roce ay converge to a local nu on the error urface rather than to the global nu a n the full earch algorth [11]. Exale for uch algorth are the three-te earch [6], -D logarthc earch [7], cro earch [8], daond earch [9], etc. Another aroach to eed u the calculaton of atchng error for each canddate bloc. In [1], th aroach leented by ubalng the xel n the telate and canddate bloc. Th technque, a well, doe not guarantee fndng the otal atch wth nu atchng error. The technque ay be cobned wth a ethod to lt the nuber of earch oton. A dfferent aroach for fat oton etaton to ue oe atchng crtera to rule out earch oton whle enurng the global nu atchng error tll attaned. One uch algorth ue the bloc u yrad [11]. In th ethod, a u yrad tructure contructed for each bloc. Succeve elnaton then erfored herarchcally fro the to level to the botto level of the yrad. Many earch oton are deterned a ubotal and can be excluded fro beng further conderaton n the oton vector earch. Thu, earch colexty reduced. An roveent of th algorth baed on a wnner-udate trategy reented n [1].

2 Orthogonal tranfor have alo been hown to be ueful for atchng. However, only very few algorth ung the fat Walh-Hadaard Tranfor (WHT) for bloc oton etaton, have been rooed n the lterature. Two exale of uch algorth are reented n [13] and [14]. The bloc oton etaton roble a varant of the attern atchng roble that nvolve fndng a artcular attern n an age. In [15] [16] a novel attern atchng technque ung Walh-Hadaard (WH) roecton ernel reented. The uggeted aroach ue an effcent roecton chee whch bound the dtance between a attern and an age wndow ung very few oeraton on average. The roecton fraewor cobned wth a reecton chee whch allow rad reecton of age wndow that are dtant fro the attern. In [17] [18] a faly of effcent flter ernel the Gray Code Kernel (GCK) ntroduced. Flterng an age wth a equence of Gray Code Kernel hghly effcent. Advantageouly, th faly nclude the WH ernel aongt other. In th aer, a novel fat bloc oton etaton technque for vdeo coreon reented baed on the fat attern atchng technque develoed n [15] [16] [17] [18], hence denoted FME-GCK. The aer organzed a follow: Fat attern atchng algorth ung WH roecton ernel and GCK are frt decrbed n ecton II and III, reectvely. The rooed fat boc oton etaton algorth reented n ecton IV. Colexty analy and reult are gven n ecton V. Fnally, concluon are drawn n ecton VI. II. FAST PATTERN MATCHING USING WALSH-HADAMARD PROJECTION KERNELS Fndng a gven attern n an age can be erfored navely by cannng the entre age and evaluatng the larty between the attern and a local D wndow about each xel. Aue a D attern, ( x, y), to be atched wthn an age I ( x, y) of ze n n. For each xel locaton ( x, y ) n the age, the Eucldean dtance ay be calculated: E x, y 1 {, } = d ( I, ) = I( x, y ) (, ) (1) where I xy, denote a local wndow of I at coordnate ( x, y ). In the context of oton etaton, th rocedure equvalent to full earch bloc atchng of a telate bloc (, x y) to a et of canddate bloc n a earch wndow of ze n n wth the MSE crteron. Referrng to the attern and wndow w a vector n R, d = w the dfference vector between and w. The Eucldean dtance can then be rewrtten n vectoral for: T d ( w, ) = d = dd () E Now aue that and w are not gven but only the value of ther roecton onto a vector u (Fg. 1). Let T T T b = u d = u u w (3) be the roected dtance value. Snce the Eucldean dtance a nor, t follow fro the Cauchy-Schwartz nequalty that a lower bound on the actual Eucldean dtance can be nferred fro the roecton value: de ( w, ) b / u (4) If a collecton of roecton vector are gven u 1... u along wth the correondng roected dtance T value b = u d, the lower bound on the dtance can then be tghtened: T T 1 d E ( w, ) b ( UU) b (5) where U = [ u1... u ] and ( 1... ) T T b = b b o that Ud= b. Note that, f the roecton vector are orthonoral, the lower bound reduce to bb. T A the nuber of roecton vector ncreae, the lower bound on the dtance de ( w, ) becoe tghter. In the extree cae when the ran of U equal, the lower bound reache the Eucldean dtance. An teratve chee for calculatng the lower bound alo oble; gven an addtonal roecton vector u 1 and roecton value b 1, the revouly couted lower bound can be udated wthout recalculatng the nvere of the entre 1 yte ( T U U ) (ee [15][16] for detal). Many calculaton can be ared f the vector are choen accordng to the followng two neceary requreent: The roecton vector hould be hghly robable of beng arallel to the vector d = w. Proecton of age wndow onto the roecton vector hould be fat to coute. One et of roecton vector hown n [15][16] to atfy the above two requreent are the WH ba vector. Thee vector cature a large orton of the attern-wndow dtance wth very few roecton on average. The eleent of the WH (non-noralzed) ba vector are orthogonal and contan only bnary value (±1). Thu, coutaton of the tranfor requre only nteger addton and ubtracton. The WHT of an age wndow of ze (wth a ower of ) obtaned by roectng the wndow onto WH ba vector. In our cae, t requred to roect each wndow of the n n age onto the vector. Th reult a hghly overcolete age Fg. 1. Proecton of w onto roecton vector on dtance d = w w b 1 d b u u 1 u roduce lower bound

3 rereentaton. The roecton vector aocated wth the D WHT of order = 8 are hown n Fg.. Each ba vector of ze 8 8, where whte rereent the value 1 and blac rereent the value -1. In Fg., the ba vector are dlayed n order of ncreang equency (the nuber of gn change along row and colun of the ba vector). A 'nae' orderng of thee vector hown by the overlad arrow. Th orderng nduced by the algorth dcued n ecton IV and, although not exactly accordng to equency, cature the ncreae n atal frequency. A dcued above, a econd crtcal requreent of the roecton vector the eed and effcency of coutaton. An effcent ethod for calculatng the roecton of all age wndow onto a equence of WH vector dcued n ecton III. III. THE GRAY CODE KERNELS In [17][18] a faly of flter ernel the Gray-Code Kernel (GCK) ntroduced. Flterng an age wth a equence of GCK hghly effcent and requre only oeraton er xel for each flter ernel, ndeendent of the ze or denon of the ernel. Th faly of ernel nclude the WH ernel aong other, thu t enable very effcent roecton onto the WH ba vector. Conder frt the 1D cae where gnal and ernel are one-denonal vector. Denote by V a et of 1D flter ernel exanded recurvely fro an ntal eed vector a follow: () V = ( ) ( 1) ( 1) ( 1) ( 1) V = { v αv } t.. v V, (6) α 1, 1 { } where α v ndcate the ultlcaton of ernel v by the value α and [] denote concatenaton. The et of ernel and the recurve defnton can be vualzed a a bnary tree of deth. An exale hown n Fg. 3 for = 3. The node of the bnary tree at level () rereent the ernel of V. The leave of the tree rereent (3) the 8 ernel of V. The branche are ared wth the value of α ued to create the ernel (where /- ndcate 1/-1). Denote = t the length of. It ealy hown that ( ) V an orthogonal et of ernel of length t. Furtherore, gven an orthogonal et of eed vector 1,... n, t can be ( ) ( ) hown that the unon et V... V 1 orthogonal wth n n vector of length t. If n= t the et for a ba. Fg. 3 alo deontrate the fact that the value, α1... α along the tree branche, unquely defne a ernel n V. The equence α = α1,... α α { 1, 1} that unquely defne a ernel v V called the α-ndex of v. Two ( ) ernel v, v V are defned to be α-related f and only f the hang dtance of ther α-ndex one. Wthout lo of generalty, let the α-ndce of two α-related ernel be ( α1... αr 1, 1,... α) and ( α1... αr 1, 1,... α). We denote the correondng ernel a v and v reectvely. Snce ( r1) α1... α r 1 unquely defne a ernel n V, two α-related 1 ernel alway hare the ae refx vector of length r t. The arrow of Fg. 3 ndcate exale of α-related ernel n the bnary tree of deth = 3. Of ecal nteret are equence of ernel that are conecutvely α-related. An ordered et of ernel... ( ) v vn V that are conecutvely α-related for a equence of GCK. The equence called a Gray Code Sequence (GCS). The ernel at the leave of the tree n Fg. 4 n a left to rght can, are conecutvely α-related, and for a GCS. Note, however that th equence not unque and that there are any oble way of reorderng the ernel to for a GCS. The an dea reented n [17][18] rele on the fact that two α-related ernel hare a ecal relatonh. Gven two α-related ernel v, v V ther u v and ther dfference v are defned a follow: [ ] - [ -] - - [ ] - [ - -] [ - -] [ - - ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Fg.. The roecton vector of the WHT of order n = 8 ordered wth ncreang atal frequency. Whte rereent the value 1 and blac rereent the value -1. A 'nae' orderng of thee ba vector hown by the overlad arrow. α-related α-related Fg. 3. The et of ernel and the recurve defnton can be vualzed a a bnary tree. In th exale the tree of deth = 3 and create 3 = 8 ernel of length 8. Arrow ndcate ar of ernel that are α-related.

4 v = v v (7) v = v v In [17][18] t roven that the followng relaton hold: [ Δ v] = [ v Δ] (8) where Δ the length of the coon refx and Δ denote a vector wth Δ zero. For lcty of exlanaton, we now exand v V to an nfnte equence uch that v () = for < and for > t. Ung th conventon, the relaton (8) can be rewrtten n a new notaton: v( Δ ) = v (9) and th gve re to the followng Corollary: v () = v ( Δ ) v() v( Δ) (1) v() =v ( Δ ) v () v ( Δ) Let b and b be the gnal reultng fro convolvng a gnal x wth flter ernel v and v reectvely: b () = x v ( ) b () = x v ( ) (11) Then, by lnearty of the convoluton oeraton and corollary (1) we have the followng: b () = b ( Δ ) b() b( Δ) (1) b () =b ( Δ ) b () b ( Δ) Th for the ba of an effcent chee for convolvng a gnal wth a et of GCK. Gven the reult of convolvng the gnal wth the flter ernel v ( v ), convolvng wth the flter ernel v ( v ) requre only oeraton er xel ndeendent of the ernel ze. Conderng Defnton (6), and ettng the refx trng to = [1], we obtan that V the WH ba et of order. A bnary tree can be degned uch that t leave are the WH ernel ordered n dyadcally ncreang equency and they for a GCS (.e. are conecutvely α-related). An exale for = hown n Fg. 4 where every two conecutve ernel are α-related. Thu, by orderng the WH ernel to for a GCS and gven the reult of flterng an age wth the frt WH ernel, flterng wth the other ernel can be erfored ung only oeraton er xel er ernel [1-1] - [ ] [ ] [1] - α-related regardle Fg. 4. Ung of ntal gnal vector and = [1] ernel and deth ze. = Th a bnary reult tree could create the be WH ba et of order 4. Conecutve ernel are α-related, a hown by the arrow. - [ ] [1 1] [ ] ealy generalzed to two denon due to the earablty of the WHT [17] [18]. IV. FAST BLOCK MOTION ESTIMATION The rooed fat bloc atchng algorth, FME-GCK, wll now be decrbed. Aue the vdeo equence cooed of age I, I 1, I,... of ze n1 n, acrobloc are of ze, and earch wndow of ze n n. Alo aue a et of WH ba vector { v } 1 that for a GCS gven. = ( ) Denote by b the roecton value of acrobloc of age I onto WH ba vector v. Denote by xy, or w xy, a acrobloc of age I at coordnate ( x, y ), and denote by w( ) the earch wndow around acrobloc. For each age I I onto { } 1 v to obtan { } 1 1) Proect b =. = ) For each Inter acrobloc ( 1).1) For each acrobloc wx, y w( ).1.1) Calculate lower bound on dtance between ( 1) and w ung { b } 1 and ( 1) { } 1 b. = x, y =.) Calculate the MSE between ( ) and the q ( 1) acrobloc w x, y wth the allet dtance lower bound fro. ( 1).3) Fro the q acrobloc, elect w x, y wth the allet Eucldean dtance fro ( ) a the bet atched acrobloc. The FME-GCK algorth wll now be dcued n detal. In order to erfor effcent GCK calculaton, the et of WH ba vector ut be conecutvely α-related, thu forng a GCS. Fndng an otal GCS hown to be NP- Colete [17] [18]. The equence of ernel that wa ued wth the FME-GCK hown a overlad arrow n Fg.. Th 'nae' order for a GCS and cature the ncreae n atal frequency. Ste 1 of the algorth erfored ung GCK wth only oeraton er xel for each WH ernel. An exceton for th effcent calculaton the frt ernel (DC coonent) that can be calculated ung 4 oeraton er xel a decrbed n [19]. Notce that the GCK aroach can not be ued effcently for roectng acrobloc on the age boundary (ecfcally at the to and left age boundare). Th ltaton, although nor, ght ncreae algorth colexty ubtantally. In an exerent for a CIF

5 (35x88) vdeo equence, boundary acrobloc roecton were erfored by drect flterng wth WH ba vector and nonboundary acrobloc roecton were erfored ung the FME-GCK. Boundary roecton were found to requre about 55% of the calculaton te ent on all roecton. A oluton to th roble to zero-ad the uer and left boundare of the age by Δ 1 row and Δ 1 colun reectvely. Th, naturally, alo ncreae the ze of the roecton age { b } 1. The uer Δ row and left = Δ colun of thee roecton age { b } 1 = are flled wth zero. Th correct nce roectng a zero acrobloc onto any ernel reult n zero. For all other age xel tartng fro the Δ 1 row and colun, roecton are erfored ung the effcent GCK ethod. The rooed technque for fat boundary calculaton dected n Fg. 5. Ste.1.1 baed on the roecton fraewor decrbed n ecton II. Although the WH ba vector are not orthornoral, they are orthogonal. Therefore, the ter T 1 ( UU) n equaton (5) can be gnored. V. COMPLEXITY ANALYSIS AND RESULTS FME-GCK ue two araeter that affect the tradeoff between colexty (te and eory) and accuracy of reultng oton vector. Thee araeter are, the nuber of roecton to erfor for each age, and q, the nuber of canddate acrobloc for whch the true MSE value calculated (Ste. n algorth). Larger roduce ore accurate reult at the cot of hgher te and eory colexty. Meory colexty affected nce roecton of age I and roecton of age I 1 ut be tored n eory, thu, eory colexty aroxately ( 1) nn 1. Note that f = the algorth reult are guaranteed to be dentcal to that of the full earch. Larger q alo roduce ore accurate reult at the cot of hgher te colexty; t doe not however, affect eory. Boundary Δ -1 Boundary Iage Fg. A 5. Zero-addng a reference each for age ettng wth Δ and 1 row q and we Δ conder 1 colun the enable rad boundary calculaton. The Δ uer row and Δ left colun erforance of the daond earch algorth. Th algorth of each correondng roecton age are flled wth zero. GCK baed hown n [9] to roduce reult of lar accuracy to that coutaton tart wth the Δ 1 row and Δ 1 colun. Δ -1 of the three-te earch algorth, whle reducng bloc atchng oeraton to an average of 15.5 er bloc wth = 16, n= 15. Aung 1 te unt for each oeraton of addton, ubtracton, ultlcaton and nu of two nuber, we obtan that erforng a ngle MSE coutaton between two bloc requre 3 1 te unt. Thu, erforng a daond earch requre 15.5(3 1) te unt lu 14.5 te unt (for calculatng the nu over all MSE value) er telate acrobloc. In the gven confguraton th u to 11,93 te unt er telate acrobloc. Perforng the FME-GCK algorth nvolve roecton of each age. Te colexty of th te te unt er xel for every roecton wth the exceton of the frt roecton that requre 4 te unt er xel to calculate a total of ( 1) te unt er telate acrobloc. Calculatng the lower bound for canddate acrobloc requre another 3n te unt er telate acrobloc. Fndng the q canddate acrobloc wth the lowet lower bound, f erfored navely, requre le than qn te unt. Calculatng the MSE for thee canddate acrobloc and electng the one wth the nal MSE requre q(3 1) ( q 1) te unt. Thu, a total of ( 1) 3n qn 3 q 1 ε te unt are requred er telate acrobloc. The ε added due to two addtonal overhead: 1) The aforeentoned addtonal boundary calculaton and ) The fact that both Inter and Intra acrobloc ut be roected, n contradcton to zero calculaton for Intra acrobloc ncurred by the daond earch algorth. A reaonable value for ε one that add about 1% to the total algorth te colexty. Th etaton tae nto account the fact that fndng the bet q canddate could be erfored ung a ore effcent nontrval rocedure. In order to coare erforance of our uggeted aroach we chooe araeter q and uch that run te of the FME-GCK equal that of the daond earch. Fro the run te couted above we fnd that uch electon are = 5, q = 3 and = 4, q = 4. Note that t ha been verfed by real-te code roflng that both electon are coarable n te colexty to the daond earch. Table 1 coare the reult of full earch, daond earch, and the FME-GCK algorth. The electon of araeter for the FME-GCK uch that t te colexty equal the te colexty of daond earch. Reult are gven n average MSE value between telate bloc and 'bet' found canddate bloc. It can clearly be een that FME-GCK gnfcantly outerfor daond earch n both confguraton for all equence n Table 1 excet Ayo. For th equence the dfference between the reult very all. We conclude that for the ae aount of calculaton, FME-

6 GCK gnfcantly outerfor the daond earch on average. Table 1. Perforance of FME-GCK algorth coared to full earch and daond earch. The electon of araeter for the FME-GCK uch that t te colexty equal the te colexty of daond earch ( = 5, q = 3 and = 4, q = 4 ). Macrobloc are of ze 8 8, earch wndow of ze 15 15, and GOP ze 15. Reult are gven n average MSE between telate bloc and 'bet' canddate bloc. Sequence Re. FS Daond GCK53 GCK44 Ayo CIF Slent CIF Coatguard QCIF 6,47 1,751 8,57 1,89 Carhone QCIF 8,37 13,954 1,4 11,675 Moble CIF 69, ,359 9,981 95,5 An ortant roerty of the FME-GCK algorth that the tradeoff between colexty and accuracy of the reult controlled by the araeter and q. The nuber of roecton to erfor for each age,, could adat to the vdeo equence charactertc wth one frae of delay. The nuber of canddate acrobloc to erfor MSE wth for every telate bloc, q, enable even ore flexblty nce t could be dfferent for every acrobloc. Fg. 6 dect the effect of dfferent value of araeter on FME-GCK erforance wth a contant q = 3. A exected, ncreang the nuber of roecton roduce reult whch are cloer to the otal. Th fgure how, that FME-GCK outerfor the daond earch tartng fro = 4. VI. CONCLUSION In th aer a novel fat bloc oton etaton algorth called FME-GCK ha been reented. FME-GCK ue an effcent roecton fraewor whch bound the dtance between a telate bloc and canddate bloc ung hghly effcent flter ernel. Canddate bloc that are dtant fro the telate bloc are qucly reected. Th algorth gnfcantly outerfor daond earch and three-te earch. In addton, th algorth guaranteed to converge to the otal (full earch) reult and enable Mean MSE er Macrobloc 6 x 15 4 FS Daond FME-GCK (nuber or WH roecton) Fg. 6. FME-GCK algorth erforance for the equence oble CIF. Dfferent value of are hown whle q = 3 contant. Perforance eaured n ean MSE between telate acrobloc and the 'bet' found acrobloc. Full earch and daond earch reult are hown a reference. adatvty of the bloc atchng roce baed on age content and colexty ltaton. ACKNOWLEDGMENT The author would le to than Prof. Davd Malah and Mr. Nrod Peleg fro the Sgnal and Iage Proceng Lab (SIPL), Det. of EE., Technon - IIT, for ther uort and valuable advce. REFERENCES [1] ISO/IEC CD ITU-T H.6 (MPEG- Vdeo), "Inforaton technology - Generc codng of ovng cture and aocated audo nforaton: Vdeo, " [] ISO/IEC (MPEG-4 Vdeo), "Inforaton technology Codng of audo vual obect," [3] ITU-T Rec. H.63, "Vdeo codng for low bt rate councaton," [4] ITU-T Rec. H.64 and ISO/IEC AVC, "Advanced vdeo codng for generc audovual ervce," 3. [5] I. E. G. Rchardon E. G. I., H.64 and MPEG-4 Vdeo Coreon - Vdeo Codng for Next-generaton Multeda. England: Wley, 3. [6] T. Koga, et al., "Moton-Coenated Interfrae Codng for Vdeo Conferencng," Proc. NTC'81,. G , Dec [7] J. R. Jan and A. K. Jan, "Dlaceent Meaureent and It Alcaton n Interfrae Iage Codng," IEEE Tran. Coun., COM-9, vol. 1, , Dec [8] M. Ghanbar, The Cro-Search Algorth for Moton Etaton, IEEE Tran. Coun., vol. 38,. 95 3, July 199. [9] J. Y. Tha, "A Novel Unretrcted Center-Baed Daond Search Algorth for Bloc Moton Etaton," IEEE Tran. Crcut and Syte for Vdeo Technology, vol. 8(4), , Aug [1] B. Lu and A. Zaccarn, "New Fat Algorth for the Etaton of Bloc Moton Vector," IEEE Tran. Crcut and Syte for Vdeo Technology, vol. 3(), , Ar [11] L. C. Hng and C. L. Hwe, "A Fat Moton Etaton Algorth Baed on the Bloc Su Pyrad," IEEE Tran. Iage Proce., vol. 6 (11), , Nov [1] C. Y. Sheng, H. Y. Png and F. C. Shann, "A Fat Bloc Matchng Algorth Baed on the Wnner-Udate Strategy," IEEE Tran. Iage Proce., vol. 1(8),. 11-, Aug. 1. [13] C. S. Young and C. S. I, "Herarchcal Moton Etaton n Hadaard Tranfor Doan," Electronc Letter, vol. 35(5), , Dec [14] M. Brüng and B. Mene, "A Fat Exhautve Search Algorth Ung Orthogonal Tranfor," Proc. 7 th Int. Worho on Syte, Sgnal and Iage Proce. IWSSIP,.111-4, June. [15] Y. Hel-Or and H. Hel-Or, "Real-Te Pattern Matchng Ung Proecton Kernel," 9 th IEEE Int. Conf. Couter Von, , Oct. 3. [16] Y. Hel-Or and H. Hel-Or, "Real-Te Pattern Matchng Ung Proecton Kernel," IEEE Tran. Pattern Analy and Machne Intellgence, vol. 7, , Se. 5. [17] G. Ben-Artz, H. Hel-Or and Y. Hel-Or, "Flterng wth Gray Code Kernel," Proc. of the 17 th Int. Conf. Pattern Recognton, vol. 1, , Aug. 4. [18] G. Ben-Artz, H. Hel-Or and Y. Hel-Or, "The Gray Code Flter Kernel," ubtted to IEEE Tran. Pattern Analy and Machne Intellgence. [19] P. T. Sard, et al., "Boxlet: A Fat Convoluton Algorth for Neural Networ and Sgnal Proceng," Advance n Neural Inforaton Proceng Syte, vol. 11, , MIT Pre, 1998.