Aristotle University of Thessaloniki, Department of Informatics A. Tefas, C. Kotropoulos, I. Pitas A RISTOTLE U NIVERSITY OF T HESSALONIKI D EPARTMENT

Aristotle University of Thessaloniki, Department of Informatics

A. Tefas, C. Kotropoulos, I. Pitas

AARISTOTLERISTOTLE U UNIVERSITYNIVERSITY OFOF T THESSALONIKIHESSALONIKIDDEPARTMENTEPARTMENT OFOF I INFORMATICSNFORMATICS

FFRONTIERSRONTIERS OFOF

MMATHEMATICALATHEMATICAL M MORPHOLOGYORPHOLOGY

FFRONTIERSRONTIERS OFOF

MMATHEMATICALATHEMATICAL M MORPHOLOGYORPHOLOGY

April 17-20, 2000, Strasbourg, France

FFACE ACE AAUTHENTICATIONUTHENTICATION BASED BASED ONON M MATHEMATICALATHEMATICAL

MMORPHOLOGYORPHOLOGY

FFACE ACE AAUTHENTICATIONUTHENTICATION BASED BASED ONON M MATHEMATICALATHEMATICAL

MMORPHOLOGYORPHOLOGY


OOUTLINEUTLINEOOUTLINEUTLINE

Introduction

Morphological techniques in elastic graph matching

Morphological elastic graph matchingMorphological signal decomposition

Experimental Results

Conclusions


IINTRODUCTIONNTRODUCTIONIINTRODUCTIONNTRODUCTION

Face recognition has exhibited a tremendous Face recognition has exhibited a tremendous

growth for more than two decades.growth for more than two decades.

Face verification:“Given a reference facial Face verification:“Given a reference facial

image or images and a test one, decide whether image or images and a test one, decide whether

the test face corresponds to the reference one”.the test face corresponds to the reference one”.

Multi-modal person verification.Multi-modal person verification.


IINTRODUCTIONNTRODUCTIONIINTRODUCTIONNTRODUCTION

Elastic graph matchingElastic graph matching (EGM) exploits both the gray-level (EGM) exploits both the gray-level information and shape information.information and shape information.The response of a set of 2D Gabor filters tuned toThe response of a set of 2D Gabor filters tuned todifferent orientations and scales is measured at the griddifferent orientations and scales is measured at the gridnodes in EGM.nodes in EGM.Morphological elastic graph matchingMorphological elastic graph matching (MEGM) and (MEGM) and morphological signal decomposition elastic graph morphological signal decomposition elastic graph matchingmatching (MSD-EGM) use the multi-scale morphological (MSD-EGM) use the multi-scale morphological dilation-erosion and the morphological signal decomposition dilation-erosion and the morphological signal decomposition instead of Gabor filters.instead of Gabor filters.


Elastic Graph MatchingElastic Graph MatchingLocal descriptors extracted at the nodes of a sparse grid:Local descriptors extracted at the nodes of a sparse grid:

The objective is to minimize the cost function:The objective is to minimize the cost function:

Signal Similarity measure:Signal Similarity measure:

MMORPHOLOGICALORPHOLOGICAL T TECHNIQUESECHNIQUES ININ E ELASTICLASTIC G GRAPHRAPH M MATCHINGATCHINGMMORPHOLOGICALORPHOLOGICAL T TECHNIQUESECHNIQUES ININ E ELASTICLASTIC G GRAPHRAPH M MATCHINGATCHING



DefinitionsDefinitions


Multi-scale dilation-erosion of an image by a structuring function:

Feature vector located at a grid node:



Suitable structuring functionsSuitable structuring functions

Scaled hemisphere:Scaled hemisphere:

Flat:Flat:

Circular paraboloid:Circular paraboloid:





Output of multi-scale dilation-erosion for nine scales. The first nine pictures are dilated images and the remaining nine are eroded images.



MORPHOLOGICAL SIGNAL MORPHOLOGICAL SIGNAL DECOMPOSITIONDECOMPOSITION

MORPHOLOGICAL SIGNAL MORPHOLOGICAL SIGNAL DECOMPOSITIONDECOMPOSITION


objective:objective:

ii-th component:-th component:

spine:spine:

maximal function:maximal function:

first spine:first spine:

andand



MSD algorithmMSD algorithmStep 1Step 1: initialization.: initialization.

Step 2Step 2: : ii-th level of -th level of decomposition.decomposition.

Step 3Step 3: calculate : calculate ii-th -th component.component.

Step 4Step 4: calculate : calculate reconstructed image.reconstructed image.



Feature vector for Feature vector for MSD-EGM:MSD-EGM:

Reconstructed images Reconstructed images at nineteen levels of at nineteen levels of decompositiondecomposition


GGRID RID MMATCHING ATCHING PPROCEDUREROCEDURE

GGRID RID MMATCHING ATCHING PPROCEDUREROCEDURE

(a) (b) (c)

Grid matching procedure: (a) Model grid for person BP. (b) Best

grid for test person BP after elastic graph matching with the model

grid. (c) Best grid for test person BS after elastic graph matching

with the model grid for person BP.


DDISCRIMINANTISCRIMINANT A ANALYSISNALYSIS TTECHNIQUESECHNIQUES

DDISCRIMINANTISCRIMINANT A ANALYSISNALYSIS TTECHNIQUESECHNIQUES

Principal component analysis for feature Principal component analysis for feature dimension reduction.dimension reduction.Linear discriminant analysis for feature Linear discriminant analysis for feature selection.selection.Discriminatory power coefficients based on Discriminatory power coefficients based on Fisher linear discriminant function for node Fisher linear discriminant function for node weighting.weighting.Support vector machines for node weighting.Support vector machines for node weighting.


M2VTS databaseM2VTS databaseThe database contains 37 persons’ video data, which include speech consisting of uttering digits and image sequences or rotated heads. Four recordings (i.e., shots) of the 37 persons have been collected.Frontal facial images with uniform background were Frontal facial images with uniform background were used for the experiments.used for the experiments.

Experimental protocolExperimental protocol““Leave one out” principle.Leave one out” principle.5328 impostor and 5328 client claims.5328 impostor and 5328 client claims.

EEXPERIMENTAL XPERIMENTAL RRESULTS ESULTS EEXPERIMENTAL XPERIMENTAL RRESULTS ESULTS


EEXPERIMENTAL XPERIMENTAL RRESULTS ESULTS EEXPERIMENTAL XPERIMENTAL RRESULTS ESULTS Experimental protocolExperimental protocol



Performance evaluationPerformance evaluationFalse acceptance (FA) occurs when an False acceptance (FA) occurs when an impostor claim is accepted.impostor claim is accepted.False rejection (FR) occurs when a client False rejection (FR) occurs when a client claim is rejected.claim is rejected.Equal error rate (EER) is the operating state Equal error rate (EER) is the operating state where FA rate=FR rate.where FA rate=FR rate.Receiver operating characteristics (ROC) is Receiver operating characteristics (ROC) is the plot of FA rate versus FR rate.the plot of FA rate versus FR rate.



Comparison of equal error rates for several Comparison of equal error rates for several authentication techniques in the M2VTS database.authentication techniques in the M2VTS database.

Authentication Technique EER(%)MEGM with support vector machines 2.4

MEGM with discriminating grids 5.6MEGM 9.2

MSD-EGM with discriminatory powercoefficients

5.7

MSD-EGM 11.8Gray level frontal face Matching 8.5

Discriminant GDLA 6.0-9.2GDLA 10.8-14.4




PERFORMANCE OF MEGM IN PERFORMANCE OF MEGM IN XM2VTSdbXM2VTSdb


XM2VTS databaseXM2VTS database295 persons (8 images per person)295 persons (8 images per person)uniform backgrounduniform background

Four training images for each clientFour training images for each clientEvaluation: 40000 impostor and 400 client claimsEvaluation: 40000 impostor and 400 client claimsTesting: 112000 impostor and 400 client claimsTesting: 112000 impostor and 400 client claims

Training: 39800 impostor and 200 client claimsTraining: 39800 impostor and 200 client claimsEvaluation: 40000 impostor and 600 client claimsEvaluation: 40000 impostor and 600 client claimsTesting: 112000 impostor and 400 client claimsTesting: 112000 impostor and 400 client claims

Experimental protocol Configuration IIExperimental protocol Configuration II

Experimental protocol Configuration IExperimental protocol Configuration I




Receiver Operating Characteristics MEGMReceiver Operating Characteristics MEGM

Configuration IConfiguration I Configuration IIConfiguration II




Rates at several FAR on XM2VTSdb in the two Rates at several FAR on XM2VTSdb in the two configurations of the experimental protocol. configurations of the experimental protocol.

All rates are in %.All rates are in %.


CCONCLUSIONSONCLUSIONSCCONCLUSIONSONCLUSIONSNovel methods for image analysis into the elastic graph matching have been proposed.They are based on multi-scale erosion dilation and morphological signal decomposition of the facial image. Discriminant analysis was applied in order to enhance the performance of the proposed methods.The experimental results indicated the success of the proposed methods in frontal face authentication.

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Aristotle University of Thessaloniki, Department of Informatics A. Tefas, C. Kotropoulos, I. Pitas A RISTOTLE U NIVERSITY OF T HESSALONIKI D EPARTMENT