Rotation, Scaling and Translation Analysis of Biometric Signature Templates

Rotation, Scaling and Transl ation Anal ysis of Biom etric Si gnature Templates Ama n C hadh a, D ivya J yot i, M. Ma ni Roj a Thadomal Shah ani Engin eering Colle ge , Mumbai , India aman.x64@ gmail .co m Ab strac t Biometric authentication systems that make use of sign ature verification methods of ten rende r opt imum performance only under limited and restr icted conditions. Such methods utilize s everal training samples s o as to achieve high accuracy. Moreove r, sever al const r aints are imposed on the end - user so that the sy stem may work optimally, and as expected. For example, the user is made to sign w ithin a sm all box, in order to limit their s ignature to a predefined set of dimensions, thus eliminating scaling. Moreover, the angular rotation with respect to the referenced signature that w ill be inadver tently introduced as human error, hampers perf orm ance of biometric signatur e ver ification sys tems. To eliminate this, traditionally, a user is as ked to sign exactly on t op of a reference line. In this paper, we propose a robu st system that optimi ze s the signature obtained f rom the user for a large range of var iation in Rotation - Sc aling- Translation (RST) and resolves these error parameters in the user signature acco rding to the ref ere nce signature s tored in the database. Ke ywo rds : rotation; scaling; translation; RST; image registr ation ; signature verification. 1. I nt rod uc ti on The aim o f a bio metric ver ification s y ste m is to det ermi ne if a perso n is who he/she purpo rts to be, ba sed o n o ne or mo re int r ins ic, p hy sic a l o r beha vi o r a l att rib ut es. Thi s t rai t or bio m etric att rib ut e can be t he signat ure, vo i ce, iris, fac e, f ingerpr in t, h and geo metr y et c. A s i mp le bi o me t r ic s yst e m h a s a s e n so r mo dul e , a f eatur e extracti on m odule, a m at chi ng m odule and a deci sion making m odu l e. T h e sen sor m odul e acqui res t h e bi ometric data o f an individual. In this case, t h e di gita l pen tablet functions as the sen sor. I n the f eatur e extract i on m odule, t he acqui red bio m et ri c dat a i s processed to extract a f eat ure se t that represents the data. Fo r ex a mp le , the po sit i o n a nd or ie nt atio n o f cert ain specifi c points in a sign at ure image are extracted in the f eat ure extract i on m odule o f a s i g n at ure authen t i c ation sys t em . In the matching modul e, t he ex tr ac t ed feature set is com pa red again st that of t he templ at e b y generating a matchin g sco re. In this m o dule, the number of matchin g po in t s between the acqui red an d r ef e rence sign at ures are determined, and a matchin g score is obtain ed. D e c is io n - ma k in g inv o lves e it her ver ific a t i o n or iden t ifi cat i o n. In the decisi o n - ma k ing module, the user's claim ed i de nti t y is ei t her accepted or rejected based on t he m at chin g sco re, i . e., verif icat i o n. Al t ernately , the sy st em m a y i de ntify a user b ased on t h e matchin g sco res, i .e., iden t ifi cat i o n [1],[11]. S ig n at ur e r ec ogni t io n is o ne o f t h e o lde st bi o me t r ic aut he nt i c at io n met ho ds , w ith w ide - spread l ega l acceptance. Han dw ri tt en si gnat ures a re co m monly used to appr o ba t e the c o n t en t s of a do cum ent or to authenti cat e a financi al t ransacti o n [1]. A trivi a l met h od of sign at ure verifi cat i o n i s visual inspecti o n. A ma nual compari so n of the two sign at ures is do ne and the giv e n sign at ure is accept ed if i t is sufficien t ly s i m ilar to the reference si g n at ure, for exam p l e, on a credit - c ard. I n m o st scenari os, where a si gnat ure i s used as t he m eans o f a ut h ent i cat i o n , n o verifi cat ion takes place at a l l due to t h e ent i re process being ex ces siv e ly t im e intensive and dem a nding. An automated si g natur e v er i ficat i on pro cess wil l he lp impr o ve t he c urr ent sit uat io n and t hus, e liminat e fra ud. Well - k n o w n bi o me t r ic methods incl ude i r is, retin a, face an d fi ngerpr in t based i dent i ficati o n an d ver if icat io n. Eve n t ho ugh hu m a n feat ur es s uch a s i r is, r etina a nd finge r pr int s do not change o ve r t im e and ha ve lo w i nt r a - cl ass v ar i at i o n, i . e., the vari at i o ns in the respectiv e bi o metric attr i bute ar e l o w, speci a l and relativ e ly e xpensive hardware i s needed for data acqui s i t ion in such systems. An important advantage of sign at ures as the hum an t rai t f o r bi o metric aut he nt i c at io n o ver ot her att ribut es is t he ir l o ng st and ing t r a di t io n in m a ny co mmo nl y enco un t er ed ve rific a t i o n t asks . I n ot her w or ds , si g n at ure verifi cat ion i s a lready accepted by t he gen er al public. I n a ddi t io n , it is a ls o relativ e ly less expensive than the ot h er biometr i c me t h ods [1 ],[2 ]. The diff icu l t i es asso ci at ed wi t h signature verif icat i o n sys t ems due to t he ex tensive intra - cl ass v ar iati o ns, make sign at ure verificati o n a diffi cu l t patt e r n r ec o gni t i o n pr oble m. E xa m p le s o f t he var i o us a l t e rat io ns obs er ved in t he s ignat ur e o f a n ind ividua l ha ve bee n illus t rat ed in F ig. 1 . Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1419 ISSN:2229-6093 Fig ure 1: Int ra - class variations, i.e. var iations in t he si gnat ure o f a n indi vidua l Depen d i ng on t he da t a acqui sit i on m et h od, automati c s i g nature verifi cat ion can be d i vided into two ma in t y pe s: o ff - line a nd o n - line s ig nat ur e ver ific at io n. The most accurate sy st em s a lm o st alway s take advan t age of dy na mic f eat ures li ke accelerat i o n, vel o city an d t he di fference between up and do wn stro kes [3]. Thi s c lass o f so l ut ions is ca lled o n - line sign at ure verificati o n. However in t he m ost com m o n real - worl d sce nari os, b ecause such syst em s r equire the o bser vat io n and re cor ding o ff t he s ig ning pr o ce ss, t his info r mat i o n is no t r eadi ly a va ilabl e. T his is t he ma in reason, why st a t i c s i g n at ure anal ysis is still i n f ocus o f many researchers. On - lin e si gnat ure verifi cat i o n uses speci a l hardware, such as a di g i t izing tablet or a pressure sensitive pen , to record the pen m o vements duri ng wri t ing. I n addi t i o n to shape, the dyn a m ics of writin g are also captured i n on - line s i g na t ure s, w hich is not pr es ent in t he 2 - D representation o f t he si g natur e and h ence i t i s difficult to f o rge. Off - line met hods do not require speci al acqu i sit i o n hardware, j ust a pen and a paper, and are t heref or e l ess i nva siv e and m o re user f r iendly . In the past decade a bunch o f so l u t io ns h as been intro duced, to overcome the li mi t at i o n s of o ff - line sign at ure verificati o n an d t o c o m pensat e f o r the l o ss of accuracy [2],[3]. I n o ff - li ne sig n at ure verif icat i o n , the sign at ure is available on a do cum ent whi c h is scanned to o bt a in it s d ig it a l im age. In al l app li cations where han dwr itten signatures currently serve as means of authenti cat i o n, auto m at i c signature verificati o n can be used such as cashi ng a check, si gning a cred i t card transacti o n or authenti cat i ng a l ega l do cum ent . Basically , any s y st em t hat uses a password can i nst ea d use an on - li ne sig n at ure f o r access. Th e advan t ages are such system s are obvi o us – a si gnatur e is mo r e d if ficu lt to s teal or gue ss than a pa ssword and i s a ls o easier to rememb er f o r the user. How e ver , t he hig h l e ve l o f int ra - class v ar i at i o ns i n si gnatur es , as sh own in Fig. 1, hi nder the pe r f orman ce of signature verificati on syst em s and t h us mi n imize t h e accuracy of such syst em s. Hence, to reduce errors and t he ine ff icie nc y pr o ble ms a sso ciat e d w i t h t he se s ys t ems, t he intr a - cl ass v ar iations in the signatures need to be min imiz ed. T his inv o lves e limina t ing o r r educ ing t he rotat i on, scalin g and t ransl at i o n factors between the reference an d t he test si gnat ure im ages. F i g. 2 shows t h e di agr am of a t y p i ca l s ign at ure verific a ti on sy s tem wi th rotat i on, scalin g and translati o n (RST) cancellati o n. The reference im age w i t hi n t h e database an d t h e user im age act as in put s to the sy st em . F eat ure extracti o n i s done f r om the ref er en ce signatur e wh ich describ e s certain characteris t i cs of the signature and stored as a t empl at e. For verif ication, the sam e featur es ar e extracted f ro m t h e test signature and co m pared t o the tem plate. Fig ure 2: A typical signatur e verificati on system with RST cancell at i on It sho u l d be noted that a dis t in ct advan t age of the propose d system , il lustrated in Fi g. 2, i s that it does not require m u l t ipl e s i g n at ure reference sam p l es for tr a ining in order t o achi eve high levels o f accuracy. Previous work by r esearchers h as witnessed the u se o f affine transf o rmati o n f or cal cu l at in g t he an gu l ar rotation between two i mages, the scal in g and tr an slati on [4] - [ 7]. In this paper, we propo se t he use of t he concept of correl at i o n to iden t ify t he rota t i o n an d a simple croppin g method to el iminat e s c aling and t rans lat ion, t her eby creatin g an optim u m templ at e after subj ect in g t he user im age to R S T c orrection . 2. I dea of the pro pos e d s olut i on The f o re m o st concern is fet ching t he angle o f r ot at ion be t we en t he user and the refere n ce imag es . I n order t o achieve this, t he concept of correlat ion is dep l o y ed. The ter m “corre l at ion” is a stat isti c a l measure, which re fers to a pro cess f o r est ablishi n g whether o r not relat i o nships exist b et wee n two var ia ble s [ 8] . The ma xi mu m va lue o f cr o ss - co rr el at i o n betwee n t h e o riginal, i.e. , the reference image and t he user image i s found by mea ns o f repet i t ive i t erations invo lv ing t he c alc u lat ion o f t he cr o ss - co rrelat i o n bet w ee n t he t wo image s in que s t io n. The proposed algori t hm essen t ially finds the cross - c o r r e la t io n be t wee n o r i g ina l ima ge a nd t he use r image . I f X ( m, n) is r efere n ce image and Y( m , n) is the us er Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1420 ISSN:2229-6093 image the n t he cross - co rrelat i o n r bet w ee n X a nd Y is given by t h e f o ll ow ing e quat ion: ( ) ( ) 00 mn mn mn r X XY Y = −− ∑∑ (1) M inimu m va lue o f r ind ic at es d iss i mi lar it y o f images a n d f or the sa me image ( autocor rel at ion) it wil l have a peak va l u e so as to indicate ‘ m a ximu m c o r r e la t io n ’. X 0 and Y 0 repr esen t mean of Image X an d Y respect iv e ly. W e us e n orm ali zed cros s - cor rel ati on to s im plif y an aly si s and com pari s ons of coe ff i cien t val ues corr esponding to the respective angular values. M in - max normali z at i on is the procedure used to ob t ain nor m a lized cross - correl at i on [9]. Min - ma x nor m a lizat i o n pr eserves t he relat i o nships a m o ng t he or i g inal dat a values. The normalizat i o n operat io n t ransf o rms the dat a in t o a new range, generally [ 0, 1]. Given a dat a set x i , suc h th at i = 1, 2, . . , n , th e nor m a lized value x ’ is giv en by the fo l lowing equation: min( ) ' max( ) min( ) i ii xx x xx − = − (2) The second ai m is to deal w i t h the t ransl at io n asso ci ated w i t h the imag es. This i s ac hieved by a simple cro pping technique. Ini t ially, we ca lculate t he number o f ro ws a nd col umns b o rder i ng the s i g nature p ixe ls w i t hin t he ima ge . The ima ge de vo id o f t hese ro ws and co l u m ns is ext racted. T h e resu l t i s an im ag e c o nsis t ing o f o nl y t he s ig nat ur e p ixe ls. Add i t io na l bac kgr ound surroundin g t he im age i s t h us el im inated. Third fact or i s t he scal i ng between t h e t wo images. For ca l cu lat i o n o f t he scal i ng fact or, the cro pped images o btain ed during tr an slat i o n are ut i l i zed. The size o f t he referenc e image div ided by t he size of the user i mage g ives the scaling rat i o . The proposed s o l ut i o n is ill u strated by Fig. 3. Fig ure 3: Sch ematic block dia gram of the propo sed sy stem 3. Implementation steps 3. 1 . I mage a cqui si tion a nd p re - pro cessin g Our ima ge acqu is it io n is inhe re nt ly si mp le and do es no t emplo y a ny spe c ia l i llu mina t io n. T he sys t e m imp le me nt ed he re u se s a d ig ita l pe n t a blet , na mel y, WACOM Ba mb o o [ 10], as t he data - cap t uring device. T he pe n ha s a to uc h se ns it ive sw it ch in it s t ip suc h t hat only pen - do wn s am pl es ( i. e. , w he n t he pe n t o uc hes t he paper) are recorde d . T he database cons i st s of a set of signat ure sam p les of 90 pe opl e . For each perso n , t here are 9 t est i mag es a nd 1 tr aini ng o r re f erence i mage in t h e dat abase . Upo n s igna t ur e acqu is it ion, t he ne xt st ep is co l o ur nor m a lization and binar izat i o n. Co l o ur nor m a lizat i o n is the co nversio n o f the im a ge f ro m the RGB for m to t h e co rr esp o ndin g Grayscale i m age . Binarizat i o n i s t he co nv er si o n of t his gra ys ca le imag e to a n image co ns is t ing o f t wo lu mina nc e e le me nt s, namely, black a n d w hi t e. O n co m p let i o n o f the im ag e acquisi t ion and pre - pr ocess i ng stage, the resu l t ant image thu s obta in ed, beco m es read y f o r t he correct ive phases : rotati o n, scaling an d t rans l at ion cancellat ion. Fig ure 4: Wac om Bamboo Digit al Pen T ablet 3.2 . R otati on c o rrection While co ll ect ing signat ure samples, it was o bs er ved t h at users gave consecut iv e samp l es having angu l ar variat i o ns approximat ely fro m – 60° to +60°. Hence, bef or e feat ure extract i o n , the user image sho uld be aligned w i t h the re ference image. Fo r simplici ty in com puti ng rota ti on an gl e, w e ch oose to al ign the refere n ce image w i t h t h e tr i a l image fetched f r om the user, i.e., t he user image. The prepr ocessed re ference imag e is cro pped in orde r t o ex tra ct onl y th e si gna ture pi xel s wi thout any additional background and used for a l l f urther computations . In order to m ake the progra m t im e efficient and less resour ce i nt ensive, t wo stages of rot a ti o n co rr ec t i o n are applied. The f i r st stage i s desig n ed t o offer a re l at ively lower r eso l ut i o n o f 5° so as to o ff er an appr oxi m at e v a lue of the angle o f rot ati o n. In co ntrast, t he seco n d stage is designed for a comparat ively higher r esol ut i o n. Wi t hin a range of +3° to – 3° of the appro xim at e value, a reso lut i o n o f 1° is select ed f o r a m o re pr eci se va l u e of the rotat i on a ngle. Af ter pre - pro cessin g, the user image is t hen rotat ed by 5° within t h e ra n ge o f – 60° to +60° in s uc cessive it e r a t io n s. C r o s s - co rrelat i o n va lue s bet w een t he refere n ce im a ge a n d t he user image are reco rded on complet i o n o f ea ch i t eration o f t he rot ati o n pro cess. T he ma xi mum c ro ss - corre l at ion v alue re fers to t h e corr ect angle o f ro tat i o n w i t hin a 5 ° ra n ge, furt h er , after t h e appr oxim at e angle va lue is o bta ine d, +3 ° o r – 3° o f Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1421 ISSN:2229-6093 t hi s ang l e ca n be inspected f o r maximum corr elation value whic h co rrespo nds to angle o f rot at i o n acc urat e to up to 1°. The u ser image i s rot a t ed by the negat iv e o f t h e ang l e t hus o b t ained, and t h e n subject ed to f eat ure ext ra ct io n. Thus , rot at ion c anc e llat ion is a chi e ved. The steps inv o lved in the rot ation co rrection pro cess can be summar i zed as f o ll ow s: 1) Obtain user image and the re f ere nce image. 2) Carry out pre - processing by conver ting bot h images to grayscale and per f orming normalization. 3) Trim the reference signature to remove any excess backgr ound; this w ill act as the template. 4) Starting w i th the angle as –60°, in increments of 5°, record nor malized correlation values bet w een pre - proce ssed r ef erence image and user image. 5) I f angle is less than or equal to 60°, go to step 4. 6) M aximum c orrelation value corresponds to angle w it hin a 5° range . Let th i s angular value be x°. 7) Starting w i th the angle as (x – 3)°, in inc rements of 1°, record norm alized correlation values bet w een the preproce ss ed ref erence image and the user image . 8) I f angle is less than or equal to (x + 3)°, go to step 7. 9) Correct the user image by the obtained angle and proceed for f urther cor rection, if required. Fig. 5 shows a referenc e image and the co rr espo nd ing ima ge rot a ted by 20. 9° . Fig ure 5: Ref erence image an d t h e corr epondin g rota ted ima ge 3.3 . Scaling c orrection An e nd u ser o ft en m o d ifie s hi s/ her s ig nat ur e accor din g t o the size of s i g ning box. For sm a ller spaces, t he signatur e m ay be co m pr essed, f o r no space limi t ation, the sign may be e nl arged. Thus, be f o re extract i o n o f feature po in t s, i t is essent ial that an y scaling, if pr esent i n t he test sample, b e r em o ved. Upon t rimm ing bo t h ima ge s, t he r at io o f he ight g ive s Y scaling and rat i o o f w i dt h gives X sca li ng. However, to res i ze t he user image a n d make it t h e same s ize as the reg i st ered image, e i t h er of the scaling rat i o s can be used. Fo r a rot ati o n range o f – 60° t o +60°, h e ight was observed t o v ar y s ignifica n t ly as co m pared t o t he length. Hence, Y scalin g was ch osen as th e s cali ng rat i o . To acco un t for sca l ing, the above m e nti o ned cropping technique is app lie d t o both the us er as well a s refere n ce image. Sca ling r atio is ca lculated by t he f o ll o wing equation: Sca l ing r atio = Size of the reference image Size of the test i mage (3) T he user image is res i zed a s per t he o b t ained scaling r a t io and t hen sent t o the feat ure extr action se g m ent. Fi g. 6 s ho ws a ref eren ce im age and th e cor res pon din g im age down scaled by a sc a ling ratio o f 1.4045. Fig ure 6 : Ref erence image an d th e co rre s pondin g down - scaled im age 3.4 . Transla tion c orrection On the apparatus used for t akin g si g nature i nput, the user is free to si g n w i t hout usin g a ny fixed start in g po int . T his m ay int ro duc e t r ans lat io n in X a nd/ o r Y direct i o n, having a maximu m va l u e equ al to the wi dt h or height o f t he signatur e canvas respect ively . T h e boundar y co nditions f o r translat i o n er ror are comput ed assuming t hat the user st a rt s to si g n f r o m t h e edge . This problem is overco m e by cropp i ng the pre - pro cessed reference i mag e so as to ext r act o nly t he si g natur e pi xels without any addit i o nal backgro und. This cro pping pro cess truncat es the e x t ra backgr ound reg i o n by t rimming the i ma ge canvas. Thu s, translat i o n is removed co mplete ly . For r epresentat i o nal pur po ses, b ott om l ef t cor ne r of te st image is a ssu med t o be or igin. The number of co lumns f ro m l e f t an d nu mber of r ow s fro m t he bo t to m, whic h c o nt ain no bla ck p ixel s corr esponding to the act ual signat ure, i.e., which co ns ist so lel y o f ima ge - backgro und, are co unted. These va lue s g ive X t r a ns lat i o n a nd Y t r ans la t i o n respect ively . Fig. 7 sh o ws a re f ere nce image a nd the Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1422 ISSN:2229-6093 cor res pon din g im age t ran s l at ed by 35px a l o ng X - Axi s and 9p x a lo ng Y - Axi s . Fig ure 7: Ref erence image an d th e co rre s pondin g translat ed i mag e 3.5 . C ombine d Rotat ion – S cali ng – Trans lati on It i s easy t o m anipu late t he samples t o get pure rot ati o n, translat i o n and scaling, ho wever, for act ual signat ures, all the abo v e ment i o n ed facto rs are alt ered s imu l t a ne o us ly. H e nc e, rot at io n, t r ans lat io n and sc a ling corr ections are applied in the same o rder. Rot a t i o n corr ecti on precede s translat i o n corr ec t ion as the assumed o ri g in at botto m lef t cor ner al so get s rot ated and tr an s lati on effects ca nn o t b e e liminated unless t h e o rigin is retur ned to botto m l eft as accu rat ely as poss ible. Ther efore, rotat i o n co rrect i o n needs to be perfor m ed fi r st as the scaling rat i o calcu l at ed by t h e pure sca ling metho d is not consistent w i t h scal i ng rat i o of the rot a t ed im age , as shown in Fig. 8. Co nse que nt ly, t he e f fec t ive ne ss o f sc al ing corr ection depends, t o a large ext en t , on the percentage er ro r o bt a ined dur ing r ot at io n co r re ct i o n. Fig ure 8: Chang e in t he w idt h and heig ht of the im age be fore an d after rota tion c orrec tion Af t er co rrect i ng t he an g le of r ot ati o n, the user image pre- pro cessed cop y is cro pped to elimi na te t ranslat i o n and the image so o btained is a case o f pure sc aling whi c h ha s be en d is cu ss ed a bo ve. Thus, rotation –s ca ling –t ranslat i o n can cell ati on is achieved. 4. R es ult s 4.1 . R otati on Re su lts o bt a ined fo r pur e rot at i o n ha ve bee n ta bu l at ed as foll o ws: Table 1: Resu lts o btain ed for p ure r ota tion Signatur e Sampl es Ac tu al An gle Detected An gle % E rro r S a mp le 1 -60 -60 0 S a mp le 2 -48 -48 0 S a mp le 3 -20 -20 0 S a mp le 4 -6 -6 0 S a mp le 5 0 0 0 S a mp le 6 4 4 0 S a mp le 7 13 13 0 S a mp le 8 27 27 0 S a mp le 9 37 37 0 S a mp le 10 59 60 1.69 Figure 9: Plot of % e r ror values in case of pure rotation f or variou s samples 4.2 . Scaling Results o b t ained for pur e scaling ha ve been t ab u l at ed as foll o ws: Table 2: Resu lts o btain ed for p ure scalin g Signatur e Sampl es Ac tu al Scaling Ratio Detected Scaling Ratio % E rro r S a mp le 1 7.69 10.55 37.2 S a mp le 2 5 5.70 14 S a mp le 3 4 4.22 5.5 S a mp le 4 2.17 2.27 4.6 % Error Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1423 ISSN:2229-6093 Signatur e Sampl es Ac tu al Scaling Ratio Detected Scaling Ratio % E rro r S a mp le 5 1.28 1.34 4.7 S a mp le 6 1 1.05 5 S a mp le 7 0.63 0.66 4.8 S a mp le 8 0.54 0.57 5.6 S a mp le 9 0.48 0.49 2.1 S a mp le 10 0.31 0.33 6.5 Figure 10: P lot of % error valu es in case of pure scal ing for v arious samples 4.3 . Transla tion Re su lts o bt aine d for pur e tr ans lat ion ha ve bee n t ab u l at ed as follow s: Table 3: Resu lts o btain ed for p ure tran slation Signatur e Sampl es Ac tu al Translation Recove r ed Translation % E rro r S a mp le 1 0,5 0,5 0 S a mp le 2 5,5 5,5 0 S a mp le 3 10,0 10,0 0 S a mp le 4 15,10 15,10 0 S a mp le 5 0,25 0,25 0 S a mp le 6 25,25 25,25 0 S a mp le 7 25,50 25,50 0 S a mp le 8 50,50 50,50 0 S a mp le 9 50,100 50,100 0 S a mp le 10 150,150 150,150 0 Figu re 1 1 : Plo t o f % error valu es in case of pure tran slatio n 4.4 . Rotat ion - Scaling - Tr ansl ation Resul t s obta in ed upo n co mbi ning rot ati o n , s ca lin g and tr an s l at i o n ha ve been tabulat ed as f o ll o ws: Table 4: Res ults ob tai ned o n co mbini ng rotation, scalin g and transla t ion Signatur e Sampl es Ac tu al Pa ram et e rs Detected Pa ram et e rs Rotation Scaling Rotation Scaling S a mp le 1 50 1.67 52 1.90 S a mp le 2 12 1.33 10 1.39 S a mp le 3 31 1.11 34 1.25 S a mp le 4 -40 0.91 -42 0.94 S a mp le 5 -30 0.8 -32 0.82 Figure 12: U ser image befor e RST corr ection ( top ); r eferen ce image (bo ttom - le ft) and th e user image after RS T Corr ec tio n (bottom - right ) % Error % Error Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1424 ISSN:2229-6093 5. C oncl us ion T he s yst e m ha s be e n des ig ned t o cor r ect var iat ions in a ng le o f r o t at ion, in t he r ange o f – 60° to +60° . Ho wev er , it can be e xtended t o co v er t he ent i re 360° pl ana r rot a ti on , to de si gn a f ool pr oof sy stem ca pabl e of creat in g a n optimum te m p late after RST cancellation, eve n in a s i t ua t ion w he re t he input pa d ma y ha ve bee n invert ed. On similar l i ne s, the reso lut i on o f ro t a t i o n can be improved f r om 1° to 0.5° or 0.25° or even more, wi th the tra de - o ff b eing increased pr ogram e x e c ution t imes. Pure sca li ng and pure t ransl at ion can be det ected ac cur a te ly a s lo ng as s ig nat ur e p ixe ls do no t go be y o nd t h e de fini ng boundar ies o f the t em p l at e. For t h e si g natur es used, a m a ximum translation o f 200 pix els was det ected a l o n g X a n d Y axe s. M axi mu m sc a ling rat i o was f o und to be 0.55. H o weve r , maximum var ia nc e o f bo t h tr ans la t io n and s ca ling ma y sho w slight var iati o ns fro m o n e s ignature to another. For co mbined RST, i t was e xperimenta lly observed t h at the cor rel at ion appro ach tends t o be less r eli abl e with signi ficant in cr ease or decrease in the sc aling rat i o . Signatur e images used for test i ng ga ve opt i mu m result for scaling rati o , i . e., within 0.67 to 1.33, however, t he scaling ra n ge giving a n g le and t ranslation accurat ely may i ncr ease or de cre ase de p end ing o n t he signat ure sam p le under t est. Thus, an opt imum t emplate was ge nerated by t h e pro posed system a f t er subject ing the user image t o RST corr ection wi t h respect t o t he ref er ence im age. 6. Ref eren ces [1] A . K . Jai n, F . D. Gri ess and S. D. Conn e ll , “O n - line s i g natur e v er ificat i o n”, Elsevie r , Patt ern Recogni t ion 35, 2002, pp. 2963 -2972. [2] M. Mani Ro ja and S. Sawarkar, “A Hybr id Approach using Major i t y Vot in g f o r Signat ure Recognit i o n”, I nter nat ional Conference on E lectronics Computer Technology (I CECT) 2011 , pp. 1 - 3. [3] B. Kovar i , I . Albert an d H. Chara f , “A Genera l R epr es en tati on f or M odel ing an d Ben chm arki ng Of f - line Sig nature Ver ifi er s”, BME P ublicat ions, 12th WSEAS Int ernational Conf erence on Computers , 2008, p. 1 [4] M. Ho li a and V. T hakar, “I m age re g i stration f o r reco vering affine tr an s f o r m at i o n using Nelder Mead S imp le x met ho d f o r o pt imiza t i o n” , International Journal of Image Pr oces s i ng ( I JIP) , Vol ume 3, Issue 5, 2009. pp. 218 -221. [5] G. W o l b er g an d S. Zoka i , “R ob ust I ma ge R egi str ati on U si ng Log - Pol ar T ransf o r m ”, P roce e dings of the I EEE I nternational Con f er ence on Image Proce ssing , Sep. 2000 pp. 1 - 2. [6] Z. Y . Cohen , “I m age r egistr ation and objec t recognition using affi ne inv ar i a n t s an d co nv e x hulls ”, IEEE Transactions on Image Pr oc essing , July 1999, p p. 1 - 3. [7] N. Chu mc ho b and K. C he n, “ A Robus t Affi n e I m age Reg i st rat i o n M et hod”, International Journ al Of Numerical Analysis A nd Modeling , Vol u m e 6, Num ber 2, pp. 311 -334. [8] R. J. Rumme l, U nder st and ing Co r re l a t io n , H o n o lu l u: D epa r t me nt o f P o l it ic a l S c i e nc e , U ni v e r s it y of Hawaii , 1976. [9] J. H an , M. K a m ber, Data mining: concepts an d techniques , Morgan K au fm ann, 2006, pp. 70 - 72. [10] W ACO M B ambo o D i g it al P e n Ta blet , www.wacom.co.in / bamb o o, June 2011. [11] H enk C . A . van Til b o rg, E ncyclopedia of cryptography and secu r i ty , Sprin ger, 2005, pp. 34 - 36. Aman Chadha et al, Int. J. Comp. Tech. Appl., Vol 2 (5), 1419-1425 IJCTA | SEPT-OCT 2011 Available online@www.ijcta.com 1425 ISSN:2229-6093