Statistical Approach for Offline Handwritten Signature Verification

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1 Journal of Computer Scence 4 (3): , 2008 ISSN Scence Publcatons Statstcal Approach for Offlne Handwrtten Sgnature Verfcaton 2 Debnath Bhattacharyya, 1 Samr Kumar Bandyopadhyay, 2 Poulam Das, 2 Debashs Ganguly and 2 Swarnendu Mukherjee 1 Department of Computer Scence and Engneerng, Unversty of Calcutta, Rajabazar Scence College, Inda 2 Department of Computer Scence and Engneerng, Hertage Insttute of Technology, Kolkata, Inda Abstract: Sgnatures were consdered an mportant tool for authentcatng the dentty of human bengs. So, sgnature verfcaton was one of the bggest uses for that. We proposed an algorthmc approach for the verfcaton of handwrtten sgnatures by applyng some statstcal methods. The research work was based on the collecton of set of sgnatures from whch an average sgnature was obtaned based on our algorthm and then takng decson of acceptance after analyzng the correlaton n between the sample sgnature and the average sgnature. Key words: Sgnatures, authentcatng, statstcal methods, acceptance, analyzng, correlaton, sample sgnature and average sgnature INTRODUCTION Sgnatures are composed of specal characters and flourshes and therefore most of the tme they can be unreadable. Also ntrapersonal varatons and the dfferences make t necessary to analyze them as complete mages and not as letters and words put together [1]. As sgnatures are the prmary mechansm both for authentcaton and authorzaton n legal transactons, the need for research n effcent automated solutons for sgnature recognton and verfcaton has ncreased n recent years. Varous methods have already been ntroduced n ths feld and applcaton of Statstcal models s one of them n ths regard. Usng statstcal knowledge, we can easly perform the relaton, devaton, etc between two or more data tems. Strctly speakng, to fnd out the relaton between some set of data tems we generally follow the concept of Correlaton Coeffcents. In general statstcal usage, correlaton or correlaton refers to the departure of two varables from ndependence, although correlaton does not mply causaton. Our approach s based on the above concept. To verfy an entered sgnature wth the help an average sgnature, whch s obtaned from the set of, prevously collected sgnatures, we have followed the concept of correlaton to fnd out the amount of dvergence n between them. Based on some predefned dvergence, we have taken the decson of acceptance of the entered sgnature. RELATED WORKS Handwrtten Sgnature Identfcaton both offlne and onlne s a classcal work area n the lne of Computer Scence and Technology snce last two decades. Numerous approaches have been proposed for Handwrtten Sgnature Identfcaton, Recognton and Authentcaton systems. Apart from the all, the approach whch makes our attracton s the applcaton of Artfcal Neural Network at the tme of dentfcaton. An Artfcal Neural Network s traned to dentfy patterns among dfferent suppled handwrtng samples. Handwrtten sgnature samples are consdered nput for the artfcal neural network model and typcally weghts also suppled for recognton. In March, 2007, Debnath Bhattacharyya, Samr Kumar Bandyopadhyay and Poulam Das [12] have proposed a new recognton technque; an Artfcal Neural Network s traned to dentfy patterns among dfferent suppled handwrtng samples. Handwrtten sgnature samples are consdered nput for that artfcal neural network model and typcally weghts also suppled for recognton [2]. Correspondng Author: Debnath Bhattacharyya, Computer Scence and Engneerng Department, Hertage Insttute of Technology, Kolkata , Inda 181

2 J. Computer Sc., 4 (3): , 2008 Another mportant method for offlne sgnature verfcaton s the applcaton of Hdden Markov s rule. Justno, Bortolozz and Sabourn proposed an off-lne sgnature verfcaton system usng Hdden Markov Model [3]. Hdden Markov Model (HMM) s one of the most wdely used models for sequence analyss n sgnature verfcaton. Handwrtten sgnature s a sequence of vectors of values related to each pont of sgnature n ts trajectory. Therefore, a well chosen set of feature vectors for HMM could lead to the desgn of an effcent sgnature verfcaton system. Applcaton of Support Vector machne (SVM) at the tme of sgnature verfcaton s also a new dmenson n ths feld. Emre Ozgunduz, Tuln enturk and M. Elf Karslıgl has proposed an algorthmc approach accordng to whch off-lne sgnature verfcaton and recognton can be done by Support Vector Machne [4]. Statstcal approach for offlne handwrtten sgnature verfcaton also drves our attenton towards t. In ths method, generally usng some statstcal tool a devaton n between testng sample and the predefned samples s calculated and based on that value decson s taken up. Debnath Bhattacharyya, Samr Kumar Bandyopadhyay and Deepskha Chaudhury, 2007, proposed a scheme where the Standard Devaton for each byte of the Tranng Image Fles (sample sgnatures) s computed and then each correspondng byte of Test Sgnature s compared to check whether t falls wthn the range of (Mean ± Standard Devaton). If 70% cases match, then the Test Sgnature s accepted [5]. X = E (X) = (X )/N For extractng the mean of data values a constant value, named as avgsgnthresoldvalue, s compared wth the actual mean to take the decson for selecton between the bnary values to be placed and ths constant value s to be calculated after conductng a survey on a test data set of known features and as per the strctness n the securty concern of the nsttute n concern. From the bnary data value calculated as above the Avg_Sgn s generated n turn followng the same algorthm. The algorthm for verfcaton of handwrtten sgnatures s requred an addtonal nput of Sample_Sgn, whch s to be tested for verfcaton of acceptance or rejecton. Here, another constant value s mantaned, named as decsonvalue, whch s also calculated and set by professonal statstcan and securty admnstrator decdng the securty concern and polces of the organzaton after conductng surveys and testng over some sample expermental data set wth already known results. The algorthm compares between two bnary data sets obtaned after analyss of Avg_Sgn and Sample_Sgn and calculates out the correlaton coeffcent, r xy between them usng the followng statstcal formula: r = (S X Y X Y ) X,Y 2 2 1/ / 2 ((S X ( X ) ) ((S Y ( Y ) ) In turn, r xy s compared wth the decsonvalue and accordngly return TRUE or FALSE as for acceptance or rejecton respectvely. MATERIALS AND METHODS The algorthm proposed n ths paper s bascally deals wth the scheme of handwrtten sgnature verfcaton n an offlne system, but t can also be realzed as the verfcaton method of extended onlne verfcaton of sgnatures for forgery control and securty purpose. The algorthmc approach mentoned n the followng sectons has the flexblty of choosng the number of sgnatures,.e., no_of_sgn for testng purpose to generate a sgnature as Avg_Sgn contanng the specalzed mean features set from the test sgnatures set. After collectng the sgnatures for testng, the algorthm converts them nto a set of 2D arrays of bnary data values-0 and 1. From these bnary arrays usng statstcal methods of calculatng expected mean an average data set s calculated usng the formula gven by: 182 Saohsv_avgpccalc (No of sgn, sgn1_pc,..): Ths s the man functon n our algorthm. Ths functon wll be used for the verfcaton of the handwrtten sgnature by comparng wth a standard sgnature, whch s obtaned by applyng statstcal analyss on a set of sgnatures. Ths functon wll take Number of total sgnatures and correspondng sgnatures as argument and fnally t wll output the decson for the acceptance of the gven sgnature: Declare one 2-D array namely statdatainputsgn [no_of_sgn] [ndexrowmajor] and a 1-D array as statdataavgsgn [ndexrowmajor], frst one stored bnary data value for the number of sample sgns gven nput and second one holds bnary data values depctng and descrbng desred AVG_SIGN Consder the sample sgn gven nput as SIGN _PIC and analyze ts pxels

3 If the pxel value corresponds to colour whte then correspondng data value wll be zero and f the colour s black that sgn or scratch s present then t wll be 1 n statdatainputsgn [] Step back to Step-2 f any other sample test sgns are avalable else goes to next step Now calculate the sum of bnary values for each rowmajorindex of all the sgns and then dvde each one by no_of_sgn to calculate expected mean Compare the mean for each ndex wth the constant avgsgnthresoldvalue calculated as conductng survey, f mean s greater and equals to the constant values, then correspondng value n AVG_SIGN wll be 1 else 0 whch s to be stored n 1-D array of statdataavgsgn[] n row major fashon From the statdataavgsgn[] form new pcture as AVG_SIGN n such a fashon that pxel wll be of whte colour f value correspondng to an ndex n array s zero and black f value s 1 Saohsv_decson (avg_sgn, sample_sgn): Ths module wll be used for takng the decson whether the nput sgnature matches wth the average sgnature, whch s obtaned n the man functon. Ths functon wll take average sgnature and sample sgnature as arguments and fnally t wll output the decson for the acceptance of the gven sgnature: Declare two 1-D arrays namely statdataavgsgn [ndexrowmajor] and statdatasamplesgn [ndexrowmajor], where frst one stores bnary data corresponds to AVG_SIGN and second one for SAMPLE_SIGN Consder the sample sgn gven nput as SAMPLE_SIGN and analyze ts pxels If the pxel value corresponds to colour whte then correspondng data value wll be zero and f the colour s black that sgn or scratch s present then t wll be 1 n statdatasamplesgn [] Consder the average sgn gven nput as AVG_SIGN and analyze ts pxels If the pxel value corresponds to colour whte then correspondng data value wll be zero and f the colour s black that sgn or scratch s present then t wll be 1 n statdataavgsgn [] Now calculate correlaton coeffcent, r xy wth bvarate data set x and y taken as statdataavgsgn [] and statdatasamplesgn [] respectvely Compare r xy wth a constant value decsonvalue, calculated by statstcans and analyst keepng J. Computer Sc., 4 (3): , securty concern of organzaton. If former exceeds later then return TRUE else return FALSE RESULTS AND DISCUSSIONS The Algorthm stated n above secton conssts of two dstnct dvsons. a. Average Sgnature calculaton, b. Decson: comparson between Average Sgnature and Sample Sgnature to fnd the correlaton between them. Complexty analyss of the stated algorthm: For converson from btmap pctures nto 1D array: Consderng the rowsze and columnsze as wdth and heght of the pxel matrx of the btmap pctures depctng the sgnatures, the total number of pxels,.e., sze of the pxel matrx s gven by (row sze column sze). So, for converson from pxels to bnary data as per suggested by algorthm, the tme complexty requred for each pcture s gven by O (row sze column sze) O(szeOfPxelMatrx) and thus total tme complexty of converson for no_of_sgn s gven by O (no_of_sgn row Sze column sze). For calculaton of AVG_SIGN: For calculaton of mean out of no_of_sgn number of pctures correspondng to the sample sgnatures total tme complexty ncurred s as follow: O (no_of_sgn row sze column sze) For SAOHSV_DECISION: In ths module correlaton coeffcent s beng calculated between two bvarate data sets of bnary values correspondng to AVG_SIGN and SAMPLE_SIGN respectvely. The tme taken n ths procedure s of order of O (row sze column sze). Here n mplementaton of the above stated procedures through programs no extras varable spaces are requred to be allocated n memory, so consderng the space complexty of the algorthm, ths s an nplace algorthm. Test Results: In mplementaton of the algorthm proposed n above secton database of 15 sgnatures for each of 100 dfferent users s consdered. Out of these 15 sgnatures, one Avg_Sgn for each of the 100 users s calculated usng the procedure descrbed n Secton III.A. Testng s done here wth two traned forgery sgnatures and two true acceptable sgnatures, whch are sent as Sample_Sgn to the argument of the procedure of Secton III.B. The Array of 15 sgnatures for an arbtrarly chosen user from database s represented n the Fg. 1.

4 J. Computer Sc., 4 (3): , 2008 Sgn1_pc Sgn2_pc Sgn15_pc Fg. 1: Set of Sample Sgnatures Table 2: Analyzed value and Rejected sample Sgnatures Avg_sgn Sample_Sgn Correlaton Coeffcent, r x,y Sample1_false Sample2_false (Rejecton: r xy < 0.50) CONCLUSION Fg. 2: Stat Data Avg Sgn (After pxel by pxel transformaton of nput sgnatures nto bnary data values and calculatng ther mean) Sample1_true Sample2_true Sample1_false Sample2_false Fg. 3: Sample Sgnatures Table 1 : Analyzed values for accepted sample sgnatures Avg_sgn Sample_Sgn Correlaton Coeffcent, r x,y Sample1_true Sample2_true (Acceptance: r xy > = 0.50) The 1D array of bnary data value correspondng to the Avg_Sgn of the above taken user s same as n Fg. 2. The Sample_Sgn s taken as varable argument for the monochrome btmap pctures, namely Sample1_true, Sample2_true, Sample1_false, Sample2_false and t s shown as n Fg. 3. The test results of decson functons for the above gven data set are shown n Table 1 and Amongst the dfferent bometrc authentcaton schemes for securty verfcaton ncludng voce detecton, retna scan, fngerprnt verfcaton, handwrtten sgnature verfcaton, durng montory transactons and other securty polces both on-lne and off-lne, s ncreasngly becomng popular. Our motvaton behnd ths paper s to mplement a smple statstcal approach for such handwrtten sgnature verfcaton avodng all such complextes of handlng a huge database of monochrome pctures correspondng to sgnatures of each ndvdual. Here to avod complex mage processng methods lke thnnng, scalng and other morphologcal schemes, the sgnatures taken n the form of monochrome btmap mages are frstly converted nto 1D data arrays of bnary values - 0 and 1. Then, Avg_Sgn s calculated followng Statstcal formula for Expected Mean, though t gves the same result f the formula for R.M.S.,.e., Root Mean Square s beng followed. The Recognton scheme s based on extensve Statstcal Analyss of Correlaton Coeffcent between bvarate data set. In mplementaton of proposed algorthm to constant factors carry major mpact on the valdty of the method and the strength of the verfcaton les n the effcency of selecton of these constant parameters, namely avg Sgn Thresold Value and decson value. We hope that our Study and Research wll defntely be focused to extend the above gven approach from offlne detecton scheme to onlne one through realzaton of neural networks and artfcal systems. REFERENCES 1. Velez, J.F., A. Sanchez and A.B. Moreno, Robust off-lne sgnature verfcaton usng compresson networks and postonal cuttngs. Proceedngs of 2003 IEEE Sgnal Processng Socety Workshop on Neural Networks, September, 2003, Toulouse, France, pp: Samr Kumar Bandyopadhyay, Debnath Bhattacharyya and Poulam Das, A Flexble ANN System for Handwrtten Sgnature Identfcaton, Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 2007 Volume II, IMECS '07, March 21-23, 2007, Hong Kong, Lecture Notes n Engneerng and Computer Scence, pp

5 J. Computer Sc., 4 (3): , Justno, E.J.R., F. Bortolozz and R. Sabourn, Off-lne sgnature verfcaton usng hmm for random, smple and sklled forgeres. 6th Internatonal Conference on Document Analyss and Recognton, September, 2001, Seattle, WA, USA, pp: Emre Ozgunduz, Tüln enturk and M. Elf Karslıgl, Off-lne sgnature verfcaton and recognton by support vector machne. Euspco- 2005, 4-8 September, 2005, Antalya, Turkey, pp co2005/defevent/papers/cr2010.pdf 5. Debnath Bhattacharyya, Samr Kumar Bandyopadhyay and Deepskha Chaudhury, Handwrtten sgnature authentcaton scheme usng ntegrated statstcal analyss of b-color mages, IEEE ICCSA 2007 Conference, Kuala Lumpur, Malaysa, August 26-29, pp:

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