& Florentin SMARANDACHE 2

Transcription

1 A DSmT Based System for Wrter-Independent Handwrtten Sgnature Verfcaton Nassm ABBAS 1 nabbas@usthb.dz, Youcef CHIBANI 1, Blal HADJADJI 1, ychban@usthb.dz bhadjadj@usthb.dz & Florentn SMARANDACHE 2 smarand@unm.edu Zayen AZZOUZ OMAR 1 azzouz-omar.zayen.1@ens.etsmtl.ca 1 Communcatng and Intellgent System Engneerng Laboratory Faculty of Electronc and Computer Scence Unversty of Scences and Technology Houar Boumedene Algers, Algera 2 Department of Mathematcs Unversty of New Mexco Gallup, NM 87301, U.S.A.

2 Outlne Introducton One Class Support Vector Machnes Classfer Belef Functon Theores Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton Concluson and future works 2

3 1. Introducton (1) Statement of the problem Input pattern Data Acquston Preprocessng Feature Generaton Classfcaton Decson Soluton Parallel combnaton scheme Fgure 1. Structure of the recognton system 1 n Input pattern Preprocessng Feature Generaton 1 Feature Generaton p Classfer-1 Classfer-p Output-1 Output-p Parallel Combnaton Module Fnal decson Fgure 2. Parallel combnaton of classfers 3

4 1. Introducton (2) Combnaton levels Class level combnaton Rank level combnaton Measure level combnaton Dstance Posteror probablty Confdence value Match score Belef functon Credblty Possblty Fuzzy measure Belef functons take nto consderatons two notons: Uncertanty: s an unrealstc measure nduced by the outputs of classfer, whch leads to nterpret the response of the classfer as the result of a random phenomenon Imprecson: s measure representng the uncertanty lnked to ncomplete knowledge 4

5 1. Introducton (3) Three theores dealng wth uncertanty and mprecse nformaton have been ntroduced Probablty theory (PT): uncertanty Evdence theory (Dempster-Shafer Theory): uncertanty + mprecson Plausble and paradoxcal reasonng theory (Dezert-Smarandache Theory): uncertanty + mprecson Output (Classfer-c 1 ) Estmaton of Masses 1 Output (Classfer-c 2 ) Estmaton of Masses Combnaton Rule Decson Measure Decson Rule 2 n Output (Classfer-c p ) Estmaton of Masses Estmaton Combnaton Decson Fgure 3. Belef Functon Theores-Based Parallel Combnaton of Classfers 5

6 2. One Class Support Vector Machnes Classfer One Class Support Vector Machnes (OC-SVM) Support vector Tranng data Outlers f ( x) 0 Support vector K( x, x ) Hyper sphere Decson functon: Orgnal space f ( x) K( x, ) Sv j1 j x j Projecton w f ( x) 0 Feature space f ( x) Sv : Number of Support Vectors j : Lagrangan multplers : Dstance of the hyperplane from the orgn 0 Pattern x s accepted when f ( x) 0 Otherwse t s rejected 6

7 3. Belef Functon Theores: Probablty Theory (1) Mathematcal Formalsm Dscernment space: s defned as a fnte set of exhaustve and mutually exclusve hypotheses G, 1 2.., n Basc probablty assgnment (bpa): m P : 0,1 m m m 0 1, m 0 Bayesan rule: P x n P x. P P x. P 1 7

8 3. Belef Functon Theores: Probablty Theory (2) Basc Sum combnaton rule m c A m sum A 1 p m j p 1 0 f A, otherwse. j A p m. : Smple class belongng to dscernment space : Number of nformaton sources : bpa ssued from the -th source Advantage: Smple Lmtaton: No managng conflct between two sources 8

9 3. Belef Functon Theores: Dempster-Shafer Theory (1) Evdence Theory Dempster-Shafer theory (DST) allows to model both gnorance and mprecson, and to consder compound hypotheses such as the unon of classes. It s generally recognzed as a convenent and flexble alternatve to the bayesan theory. Mathematcal Formalsm Dscernment space: Power-set:.., 1, 2 n G 2, 1, 2,, n, 1 2, 1 3,, 1 2 n 1, Basc belef assgnment (bba): m : 2 0,1 m 0 A m ma 1, ma 0 A A 2 9

10 Bayesan Model Transfer Model 3. Belef Functon Theores: Dempster-Shafer Theory (2) Estmaton of belef mass functons It's not drectly explct n term of modellng of the problem under consderaton. It's specfc to each applcaton area accordng the nature of the data. Handwrtng recognton. 1 P x 1 m x A 1 2 P x 2 m x A 2 n P x n m x 10

11 3. Belef Functon Theores: Dempster-Shafer Theory (3) Dssonant model of Approu Axom (1): Consstency wth the Bayesan approach Axom (2): Separablty of the evaluaton of the hypotheses Axom (3): Consstency wth the probablstc assocaton of sources m m j j mj. Rj. P 1 R. P j x x, 1 Rj. P, 1 x, P x R j R j 0, maxsup 1, n P x : Condtonal probablty of an object x gven the class. : Normalzaton factor : Coarsenng factor. 11

12 3. Belef Functon Theores: Dempster-Shafer Theory (4) Dempster s orthogonal sum rule m m c A m B, A 2 A K c B1, B2,, B p 2 k 1 B B B A 1 m m DS 2 A p p A m 1 K k k, A 2 c m B B1, B2,, B p 2 k 1 B B B 1 2 p p k k A m A K c : Focal element of the power-set 2. : Combned mass of Dempster s conjunctve rule. : Conflct measure between the dfferent masses sources m k S k. ssued from nformaton, respectvely. Advantage: Takng nto account the mprecse and uncertan nformaton Lmtaton: No managng hgh conflct between two sources of nformaton 12

13 3. Belef Functon Theores: Dempster-Shafer Theory (5) Decson rules Combned mass functon : uncertanty [Belef functon, Plausblty functon] : mprecson Selectng the more realstc hypothess. Rules used for decson-makng: Maxmum of belef functon. Maxmum of plausblty functon. Maxmum of Pgnstc Probablty. Mnmzaton of mass functon wth an acceptance threshold. 13

14 3. Belef Functon Theores: Dempster-Shafer Theory (6) Lmtatons of DST Foundaton of the DST Does not take nto account the paradoxcal nformaton Sgnfcant conflct measure DST based combnaton s not possble Soluton: Dezert-Smarandache Theory (DSmT) 14

15 3. Belef Functon Theores: Dezert-Smarandache Theory (1) Plausble and Paradoxcal Reasonng Theory It has been orgnally developed snce 2003 by Jean Dezert and Florentn Smarandache. It has the advantage of beng able to represent explctly the uncertanty from mprecse knowledge. It was elaborated for dealng wth paradoxcal sources of nformaton (.e. classes, descrptors, classfers, sensors, etc). It s based on a partcular framework where the fnte dscrete frame of dscernment s exhaustve but not necessarly exclusve. 15

16 3. Belef Functon Theores: Dezert-Smarandache Theory (2) Mathematcal Formalsm Dscernment space:.., 1, 2 n 1. Ø, 1,, n D. Hyperpower-set: G D 2. If A, B D, then A B D and A B D. 3. No other elements belong to D, except those obtaned by usng rules 1 or 2. Generalzed belef assgnment (gbba): m : D 0,1 m 0 A m ma 1, ma 0 A A D Estmaton technques of masses n DST framework Vald n DSmT framework 16

17 3. Belef Functon Theores: Dezert-Smarandache Theory (3) Combnaton rules Classcal DSm combnaton rule (DSmC) DSm Hybrd combnaton rule (DSmH) Proportonal Conflct Redstrbuton rules (PCR1,, PCR5, PCR6) Decson rules Mnmum of mass functon wth an acceptance threshold Note: m test Accepted Decson Rejected t opt. f mn m otherwse test, m t 1 test 2 opt : Denotes the optmal value of the acceptance decson threshold : Defnes the combned mass of the smple class 17

18 Parallel Combnaton of Classfers for Handwrtten Sgnature Verfcaton Handwrtten Sgnature Verfcaton (HSV) Applcaton Wrter-Independent HSV 18

19 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton (1) Motvaton Physologcal Bologcal Behavoral Fngerprnt Face DNA Wrtng Keyboardng Irs Hand geometry Smell Gat Sgnature 19

20 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton (2) Motvaton Sgn a document to dentfy hmself s a natural gesture. Handwrtten sgnature s the bometrc modalty the most accepted by many peoples. It s used n many countres as legal or admnstratve element. Desgn of a sgnature verfcaton system s cheaper and more smple comparatvely to other bometrc systems (for nstance rs or face). 20

21 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton (3) Motvaton Dynamc features (Velocty, Pressure,.) Acquston of the handwrtten sgnature Electronc tablet Statc features (Image) Scanner Dffcultes of the offlne handwrtten sgnature verfcaton: Hgh varablty ntra-wrter Easy to mtate Qualty of the sgnature (Paper, Pen, Scanner) 21

22 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Off-lne HSV problem Why use a wrter-ndependent HSV approach? Wrter-dependent approach Wrter-ndependent approach Off-lne HSV wrter-dependent approach: Advantage: Provdng a hgh performance verfcaton Lmtaton: Need of learnng the model each tme when a new wrter should be ncluded n the system Soluton: (1) Off-lne HSV wrter-ndependent approach, (2) Usng only genune sgnatures, (3) through combnaton scheme of two ndvdual verfcaton systems 22

23 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Verfcaton scheme usng an OC-SVM classfer Learnng phase Verfcaton phase Learnng data Testng data Vectors of (ds) smlarty measures Vectors of (ds) smlarty measures Learnng algorthm OC-SVM classfer Generaton of the model Selecton of the optmal threshold Decson 23

24 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Source 1 Source 2 ( OC SVM1) ( OC SVM 2) Combnaton (Conflct management) Combned sources Classfcaton based on DSmT Space of dscernment: Mass functon: Combnaton space: PT: DST: DSmT: G Combned masses: m ( A j ) [0,1] m c ( 2 A) m1 ( X ) m ( Y) Card ( G) j1 1, 2 m c ( A j ) 1 G 2 ø, G D 1, 2, 1 1 descrptor 1, 2 descrptor 2 Such that: 2 ø, 1, 2, 1 2, 1 A, X, Y 1, 2 (Source 1 or 2) 2 G G G 24

25 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Decson makng n both DST and DSmT frameworks Select outputs of both classfers (valdaton phase) t m mass mn mc 1, c 2 1 Combnason of masses (valdaton phase) Combnason of masses (learnng and valdaton) t mass m, m mn mn learn 1 mn learn 2 2 Compute the optmal decson threshold Decson makng t mass opt t t mass 1 mass 2 2 Accepted f Decson Rejected mn m test otherwse, m t 1 test 2 mass opt 25

26 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Case study: Combnng two Off-Lne HSV Systems (1) Parttonng of the CEDAR database: 25 Wrters 55 Wrters 30 Wrters 1 Wrter 1 Wrter 24 genune sgnatures 24 genune sgnatures 24 mpostor sgnatures 5 Sgnatures for learnng 5 Reference sgnatures 14 Sgnatures for valdaton 5 Reference sgnatures 43 Sgnatures for testng 26

27 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Case study: Combnng two Off-Lne HSV Systems (2) Feature generaton: Smple features are generated from each off-lne sgnature mage, whch are: Dscrete cosne transform (DCT) based features Curvelet transform (CT) based features Advantage of both transforms : DCT: Two mportant propertes: Decorrelaton and energy compacton CT: Analyzng local lne or curve sngulartes Sources of nformaton: Two sources are consdered Source 1: DCT based descrptor Source 2: CT based descrptor Performance crtera: Three popular errors are consdered False Rejecton Rate (FRR) False Acceptance Rate (FAR) Average Error Rate (AER) 27

28 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Comparatve analyss: Case study: Combnng two Off-Lne HSV Systems (3) Algorthm Optmal Threshold Verfcaton Error Rates (%) FRR FAR AER OC-SVM classfer 1 (DCT) OC-SVM classfer 2 (CT) Max combnaton rule Sum combnaton rule Mn combnaton rule Table 3. Expermental results of proposed ndvdual systems and classcal combnaton algorthms 28

29 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Case study: Combnng two Off-Lne HSV Systems (4) Conflct managng n DSmT framework: K c Conflct measure Sgnature ndex Fgure 1. Conflct between both OC-SVM classfers usng DCT and CT-based descrptors for testng sgnatures 29

30 4. Proposed Combnaton Scheme for Handwrtten Sgnature Verfcaton: Wrter-Independent Handwrtten Sgnature Verfcaton Comparatve analyss: Case study: Combnng two Off-Lne HSV Systems (5) Algorthm Optmal Threshold Verfcaton Error Rates (%) FRR FAR AER OC-SVM classfer 1 (DCT) OC-SVM classfer 2 (CT) Max combnaton rule Sum combnaton rule Mn combnaton rule DS combnaton rule PCR6 combnaton rule Table 4. Expermental results of proposed algorthms 30

31 6. Concluson and futur work Concluson Proposed combnaton scheme wth PCR6 rule yelds the best verfcaton accuracy compared to the statstcal match score combnaton algorthms and DS theory-based combnaton algorthm even when the ndvdual wrter-ndependent off-lne HSV systems provde conflctng outputs. Futur works Adapt the use of the evdence supportng measure of smlarty (ESMS) crtera to select complementary sources of nformaton usng the same proposed combnaton scheme n order to attempt to mprove the FRR. Replace the OC-SVM classfer by the Hstogram Symbolc Representaton (SHR) based one class classfer. 31

32 Many thanks for your attenton Questons Florentn SMARANDACHE 2 Department of Mathematcs Unversty of New Mexco Gallup, NM 87301, U.S.A. 32