Improving Face Recognition Rate by Combining Eigenface Approach and Case-based Reasoning

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1 Improvig Face Recogitio Rate by Combiig Eigeface Approach ad Case-based Reasoig Haris Supic, ember, IAENG Abstract There are may approaches to the face recogitio. This paper presets a approach that combies advatage of geeralizatio ability of Pricipal Compoet Aalysis (PCA) ad specializatio ability of Case- based reasoig (CBR). CBR is expected to improve the geeralizatio ability of PCA i the recogitio process. By usig PCA the ew image is projected ito its eigeface compoets. The projected vector represets a descriptio compoet of a ew face case. The CBR module compares the similarity of the ew face case ad previously stored face cases i the face casebase ad retrieves the most similar case. The solutio compoet of the retrieved case represets the results of the recogitio process. Idex Terms case based reasoig, face recogitio, eigevalues, eigevectors, pricipal compoet aalysis. I. INTRODUCTION As oe of the most successful applicatios of image aalysis ad uderstadig, face recogitio has recetly received sigificat attetio. The problem of face recogitio ca be formulated as follows [1] : For a give image of scee, idetify or verify oe or more persos i the scee usig a stored database of faces. The iput to the face recogitio system is a ukow face, ad the system determies idetity from a database of kow idividuals. I verificatio problems, the face recogitio system eeds to cofirm or reject the claimed idetity of the iput face. I geeral, the huma face recogitio system utilizes a broad spectrum of stimuli obtaied from may of the seses: visual, auditory, olfactory, etc. I recogitio process cotextual kowledge is also used [2]. However, the huma brai has its limitatios i the total umber of persos that it ca remember. A mai advetage of a computer face recogitio system is its capacity to hadle large image databases. Some psychological studies have poited out that the iteral facial features, such as eyes, ose, ad mouth, are very importat for huma beigs to recogize familiar faces. A complete face recogitio system should iclud two stages. The first stage is detectig the locatio ad size of a face. This task is difficult because of the ukow positio ad orietatio of faces i image. The secod stage ivolves recogizig the faces obtaied i the first stage. It is very auscript received arch 21, This work was supported i part by the Cato Sarajevo, iistry of educatio ad sciece uder Grat , ad Grat /07. Haris Supic is with the Departmet of Computer Sciece, Faculty of Electrical Egieerig, Uiversity of Sarajevo, Bosia ad Herzegovia, Zmaja od Bose bb, phoe: +(387) ; fax: +(387) ; haris.supic@ etf.usa.ba. importat to emphasize that there are may problems that has to be solved for complete success of face recogitio systems. The followig two problems are the most importat: the ilumiatio problem ad the pose problem [3]. The illumiatio problem ca be described as the problem where same face appears differetly due to the chage i lightig. The chages produced by illumiatio could be larger tha the differeces betwee idividuals. The pose problem ca be described as a problem where the same face appears differetly due to chages i viewig coditio. Face recogitio approaches ca be broadly grouped ito geometric ad template matchig techiques. I the first case, geometric characteristics of faces to be matched, such as distaces betwee differet facial features, are compared. I the secod case, face images represeted as a two-dimesioal array of pixel itesity values are compared to a sigle or several templates represetig the whole face. ore successful template matchig approaches are: Pricipal Compoet Aalysis (PCA) ad Liear Discrimiat Aalysis (LDA). Template matchig approaches to face recogitio use the cocept of image space. A two-dimesioal image I(x,y) may be viewed as a poit i a very high dimesioal space, called image space, where each coordiate of the space correspods to a sample of the image. For example, a image with 32 rows ad 32 colums describes a poit i a 1024-dimesioal image space. I geeral, a image of N rows ad N colums describes a poit i N 2 -dimesioal image space. All the faces look like each other. They all have two eyes, a mouth, a ose, etc. Therefore, all the face vectors are located i a very arrow cluster i the image space [4]. II. THE EIGENFACE APPROACH Differet eigespace-based approaches have bee proposed for the face recogitio. They differ mostly i the kid of projectio method bee used ad i the similarity matchig criterio employed. Pricipal Compoet Aalysis (PCA) is a geeral method to idetify the liear directios i which a set of vectors are best represeted ad after that to make a dimesioal reductio of them. Turk ad Petlad used the PCA for dimesioality reductio to fid the vectors which best accout for the distributio of face images withi the etire image space [5], [6]. Let S deote the traiig set of face images [6]: S = {Γ 1, Γ 2, Γ 3,, Γ }. (1) The mea image of the set if defied by: Ψ = 1 (2) Γ = 1

2 NEW PROBLE RETRIEVE RETAIN PRIOR CASES REUSE SOLUTION CASEBASE REVISE Fig. 1. The CBR cycle. Adapted from [9] The set of deviatio-from-mea vectors, {Φ 1, Φ 2, Φ 3,..., Φ } cotais the idividual differece of each traiig image from the mea vector Ψ. Idividual differeces are defied as: Φ i = Γi Ψ, i=1,2, (3) To obtai the eigeface descriptio of the traiig set, the traiig images are subjected to PCA, which seeks a set of orthoormal vectors u ad their associated eigevalues λ k which best describes the distributio of the data. The vectors u k ad scalars λ k are the eigevectors ad eigevalues, respectively, of the covariace matrix. The covariace matrix is give by [6]: 1 T Φ T AA (4) =1 C = Φ = where the matrix A is A=[Φ 1 Φ 2.Φ ] The matrix C is a N 2 by N 2 matrix ad would geerate N 2 eigevectors ad eigevalues. With image sizes like 256 by 256, or eve lower tha that, such a calculatio would be = projected descriptio of ew face to be recogized (ew case) = projected descriptio of previously recogized faces (stored solved cases) = stored solutios (idetities) Problem space (face space) u 2 Ω 5 Ω 1 Ω 3 Ω 4 Ω 6 Ω 2 Ω m Solutio space (idetity space) u 1... Id 1 Id 2 Id 3 Id CB f ={(Ω 1, Id 1 ), (Ω 3,Id 1 ), (Ω 2,Id 2 ), (Ω 4,Id 2 ), (Ω 5,Id 3 ), (Ω 6,Id 3 ),...,(Ω m,id )} Fig. 2. Simplified represetatio of problem descriptio (face space) ad solutio (idetity) space

3 impractical to implemet. A computatioally feasible method was suggested to fid out the eigevectors [5]. If the umber of images i the traiig set is less tha the umber of pixels i a image (i.e < N 2), there will be oly -1, rather tha N 2, meaigful eigevectors. The remaiig eigevectors will have associated eigevalues of zero. Thus, we ca solve a by matrix istead of solvig a N 2 by N 2 matrix [5], [6]. A. Stadard Recogitio Procedure The sigificat eigevectors of the matrix L=A T A are chose as those with the largest associated eigevalues. The eigefaces spa a -dimesioal subspace of the origial N 2 image space. A ew face image Γ is trasformed ito its eigeface compoets (projected ito face space ) by a simple operatio, w k = u k T (Г - ψ), k=1,2,.. (5) The weights obtaied as above form a vector [6]: Ω T = [w 1, w 2, w 3,. w ] (6) that describes the cotributio of each eigeface i represetig the iput face image. The stadard method for determiig which face class provides the best descriptio of a iput face image is to fid the face class k that miimizes the Euclidia distace ε k 2 = Ω Ω k 2 (7) where Ω k is a vector describig the k th face class. The ew face is cosidered to belog to a class if ε k is bellow a established threshold θ ε. The the face image is cosidered to be a kow face. If the differece is above the give threshold, but bellow a secod threshold, the image ca be determied as a ukow face. If the iput image is above these two thresholds, the image is determied ot to be a face. III. THE EIGENFACE-CBR APPROACH I this sectio we will describe the eigeface-cbr approach to face recogitio. The mai purpose of eigeface-cbr approach is to take advatage of geeralizatio ability of PCA ad specializatio ability of CBR. CBR is expected to improve the geeralizatio ability i the recogitio process. CBR ability of a give approach should be maifested i the experimets as the ability to improve a recogitio rate whe icreasig the umber of retaied previously face recogitio cases. I order to evaluate this approach, we compared the approach with the stadard eigeface approach. A. Case-based reasoig Case-based reasoig (CBR) is able to utilize the specific kowledge of previously experieced, cocrete problem situatios (cases). A ew problem is solved by fidig a similar past case, ad reusig it i the ew problem situatio [7]. There are two mai ways to reuse past cases: reuse the past case solutio ad reuse the past method that costructed the solutio [8]. I CBR termiology, a case usually deotes a problem situatio. A previously experieced situatio, which has bee captured ad leared i a way that it ca be reused i the solvig of future problems, is referred to as a previous case, stored case, or retaied case. Correspodigly, a ew case or usolved case is the descriptio of a ew problem to be solved. Fig. 1 shows the model of the problem solvig cycle i CBR. Solvig a problem by CBR ivolves obtaiig a problem descriptio, measurig the similarity of the curret problem to previous problems stored i a case base with their kow solutios, retrievig oe or more similar cases, ad attemptig to reuse the solutio of oe of the retrieved cases, possibly after adaptig it to accout for differeces i problem descriptios [9]. The solutio proposed by the system is the evaluated (e.g.., by beig applied to the iitial problem or assessed by a domai expert). Followig revisio of the proposed solutio if required i light of its evaluatio, the problem descriptio ad its solutio ca the be retaied as a ew case, ad the system has leared to solve a ew problem [9]. CBR is fouded o the premise that similar problems have similar solutios. Thus, oe of the primary goals of a CBR system is to fid the most similar, or most relevat, cases for ew iput problems. The effectiveess of CBR depeds o the quality ad quatity of cases i a casebase. I some domais, eve a small umber of cases provide good solutios, but i other domais, a icreased umber of uique cases improve problem-solvig capabilities of CBR systems because there are more experieces to draw o. Case-based reasoig systems ca also be viewed as cotiuous kowledge acquisitio ad learig systems. B. Case Represetatio for Eigeface-CBR Approach I this sectio, we describe case represetatio used for the eigeface-cbr approach. Case represetatio is geerally regarded as oe of the most importat problems ad is crucial to success of case-based reasoig system. The case represetatio problem is primarily the problem of decidig what to store i a case, ad fidig a appropriate structure for describig case cotets. I geeral, a case cosists of a problem descriptio compoet ad a solutio compoet. I this work, face cases C f are represeted as two-tuples (see Fig. 2): C f =(Ω T, Id) where: Ω T is a face case descriptio compoet that represets projected image vector Γ, Id is a face case solutio compoet that represets idetity. C. CBR Recogitio Procedure Let CB f deotes the face casebase: where CB f = {C 1, C 2,...,C CB }, C i =(Ω i T,Id j ), i=1,2,... CB, j=1,2,... ID ad where ID is the set of all previously recogized persos. Fig. 3 shows the block diagram of the eigeface-cbr recogitio system. It is used PCA ad the ew image Γ is

4 Γ Ω T PCA CBR module NEW FACE C ew =(Ω T,?) same 90 images, obtaied i good illumiatio coditios. All preseted results were obtaied with oe processig for each amout of eigevectors (5, 15, ad 30). Table I presets the results obtaied with the stadard eigefaces recogitio procedure. Table II presets the results obtaied with the eigeface-cbr recogitio procedure, workig with the same 90 well illumiated images ad with the three differet casebase sizes: 60, 120, ad 180. We ca see that the experimetal results obtaied usig the eigeface-cbr approach icreases its recogitio rate. The recogitio rates icreases with icreasig umber of previously experieced face recogitio cases. Id r Result of the idetificatio Fig. 3. Block diagram of the eigeface-cbr approach Eigevectors Table I. Stadard eigeface results Errors Success Quatity Rate Quatity Rate trasformed ito its eigeface compoets. The resultig weights form the weight vector Ω T = [w 1, w 2, w 3,. w ]. Task of the CBR module is create the ew face recogitio case, fid a prior case similar to the ew oe, use that case to suggest a solutio to the curret face recogitio problem, ad update the system by learig from this experiece. The projected vector Ω T represets the descriptio compoet of the ew face case C =(Ω T,?). The symbol? deotes that the solutio compoet (idetity) is ukow. The CBR module compares the similarity of the descriptio compoet Ω T of the ew face case ad previously stored descriptio compoets Ω i, i=1,2,... CB, of face cases i the casebase CB f. The Euclidea distace betwee two descriptio compoets d(ω T,Ω i ), i=1,2,... CB, provides a measure of similarity betwee the ew case C ad previously stored cases C i,i=1,2,... CB. By usig the criterio of similarity based o Euclidia distace, CBR module determies ad retrieves the most similar case C r =(Ω r T, Id r ) i the case base. The solutio compoet Id r of the retrieved case C r represets the results of the recogitio process. The iput face is cosidered to belog to a idetity if distace d(ω T, Ω r T ) is bellow a established threshold θ r. If the distace d(ω T, Ω r T ) is above the give threshold, but bellow a secod threshold θ f, the image ca be cosidered as a ukow face. If the distace d(ω T, Ω r T ) is above these two thresholds, the ew face case is determied ot to be a face. A very importat characteristic of the eigeface-cbr approach is icremetal learig, sice a ew experiece is retaied each time a ew face has bee recogized, makig it immediately available for future face recogitio problems. IV. RECOGNITION EXPERIENTS This sectio is focused o the compariso of stadard eigespace based face recogitio usig the PCA projectio method ad the eigeface-cbr approach previously preseted i this paper. I order to compare the stadard eigeface recogitio procedure ad the eigeface-cbr recogitio procedure, we applied both procedures to the ,1% 71 78,9% ,7% 84 93,3% ,3% 87 96,7% Num. of stored cases Eige vect. Table II. Eigeface-CBR results Errors Success Quat. Rate Quat. Rate ,8% 74 82,2% ,7% 84 93,3% ,2% 88 97,8% % 77 85,6% ,4% 86 95,6% ,2% 88 97,8% 5 8 8,9% 82 91,1% ,3% 87 96,7% ,1% 89 98,9%

5 V. CONCLUSIONS AND FUTURE WORK I this paper we have preseted a approach that combies eigeface approach ad case-based reasoig. The case based approach to face recogitio was motivated by the desire to combie the advatage of geeralizatio ability of Pricipal Compoet Aalysis (PCA) ad the advatage of specializatio ability of case-based reasoig (CBR). The prelimiary experimetal results show that usig the eigeface-cbr approach icreases the recogitio rate. The recogitio rate icreases with icreasig umber of previously experieced face recogitio cases. As future work we are focusig o the extesio of the research, cosiderig other kid of eigespace-based approaches. Also, we are iterested i developmet of algorithms for more efficiet case retrieval from the casebase. ACKNOWLEDGENT The author is grateful for the support by the iistry of educatio ad sciece, Cato Sarajevo, B&H. REFERENCES [1] W. Zhao, R. Chellappa, A. Rosefeld, ad P.J. Phillips, Face recogitio: a literature survey, AC Computig Surveys, 2003, pp [2] A.. Burto, V. Bruce, ad P.J.B. Hacock, From pixels to people: a model of familiar face recogitio, Cogitive Sciece, Vol. 23, No. 1, 1999, pp [3] R. Gross, J. Shi, J. Coh, Quo vadis face recogitio? - The curret state of the art i face recogitio, Techical Report, Robotics Istitute, Caregie ello Uiversity, Pittsburgh, PA, [4] A. Schwaiger, S. Ryf, ad F. Hofer, Cofigural iformatio is processed differetly i perceptio ad recogitio of faces, Visio Research, Vol. 43, 2003, pp [5]. Turk, ad A. Petlad A, Eigefaces for recogitio, Joural of Cogitive Neurosciece, Volume 3, Number 1, arch [6]. Turk, ad A. Petlad, Face recogitio usig eigefaces, i Proc. IEEE Iteratioal Coferece o Computer Visio ad Patter Recogitio, aui, Hawaii, [7] A. Aamodt, ad E. Plaza, Case-based reasoig: Foudatioal issues, methodological variatios ad system approaches, I AICO (1994), vol 7(1), pp [8] J.L. Koloder, Case based reasoig, orga Kaufma Publishers, Ic., Sa ateo, CA, [9] L. ataras, et al. Retrieval, reuse, revisio, ad retetio i CBR. Kowledge Egieerig Review, 20(3), 2005, pp