1. Aristotle University of Thessaloniki, Department of Informatics A. Tefas, C. Kotropoulos, I. Pitas A RISTOTLE U NIVERSITY OF T HESSALONIKI D EPARTMENT OF I NFORMATICS F RONTIERS OF M ATHEMATICAL M ORPHOLOGY F RONTIERS OF M ATHEMATICAL M ORPHOLOGY April 17-20, 2000, Strasbourg, France F ACE A UTHENTICATION BASED ON M ATHEMATICAL M ORPHOLOGY

2. Aristotle University of Thessaloniki, Department of Informatics O UTLINE 4 4 Introduction 4 4 Morphological techniques in elastic graph matching 4 4 Morphological elastic graph matching 4 4 Morphological signal decomposition 4 4 Experimental Results 4 4 Conclusions

3. Aristotle University of Thessaloniki, Department of Informatics I NTRODUCTION 4 Face recognition has exhibited a tremendous growth for more than two decades. 4 Face verification:“Given a reference facial image or images and a test one, decide whether the test face corresponds to the reference one”. 4 Multi-modal person verification.

4. Aristotle University of Thessaloniki, Department of Informatics I NTRODUCTION 4 Elastic graph matching (EGM) exploits both the gray- level information and shape information. 4 The response of a set of 2D Gabor filters tuned to different orientations and scales is measured at the grid nodes in EGM. 4 Morphological elastic graph matching (MEGM) and morphological signal decomposition elastic graph matching (MSD-EGM) use the multi-scale morphological dilation-erosion and the morphological signal decomposition instead of Gabor filters.

5. Aristotle University of Thessaloniki, Department of Informatics Elastic Graph Matching 4 Local descriptors extracted at the nodes of a sparse grid: 4 The objective is to minimize the cost function: 4 Signal Similarity measure: M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING

6. Aristotle University of Thessaloniki, Department of Informatics M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING Definitions

7. Aristotle University of Thessaloniki, Department of Informatics Multi-scale dilation-erosion of an image by a structuring function: Feature vector located at a grid node: M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING

8. Aristotle University of Thessaloniki, Department of Informatics Suitable structuring functions 4 Scaled hemisphere: 4 Flat: 4 Circular paraboloid: M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING

9. Aristotle University of Thessaloniki, Department of Informatics M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING

10. Aristotle University of Thessaloniki, Department of Informatics Output of multi-scale dilation-erosion for nine scales. The first nine pictures are dilated images and the remaining nine are eroded images. M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING

11. Aristotle University of Thessaloniki, Department of Informatics MORPHOLOGICAL SIGNAL DECOMPOSITION M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING 4 objective: 4 i-th component: 4 spine: 4 maximal function: 4 first spine: and

12. Aristotle University of Thessaloniki, Department of Informatics M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING MSD algorithm 4 Step 1: initialization. 4 Step 2: i-th level of decomposition. 4 Step 3: calculate i-th component. 4 Step 4: calculate reconstructed image.

13. Aristotle University of Thessaloniki, Department of Informatics M ORPHOLOGICAL T ECHNIQUES IN E LASTIC G RAPH M ATCHING 4 Feature vector for MSD-EGM: 4 Reconstructed images at nineteen levels of decomposition

14. Aristotle University of Thessaloniki, Department of Informatics G RID M ATCHING P ROCEDURE (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.

15. Aristotle University of Thessaloniki, Department of Informatics D ISCRIMINANT A NALYSIS T ECHNIQUES 4 Principal component analysis for feature dimension reduction. 4 Linear discriminant analysis for feature selection. 4 Discriminatory power coefficients based on Fisher linear discriminant function for node weighting. 4 Support vector machines for node weighting.

16. Aristotle University of Thessaloniki, Department of Informatics M2VTS database   The 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 used for the experiments. Experimental protocol  “Leave one out” principle.  5328 impostor and 5328 client claims. E XPERIMENTAL R ESULTS

17. Aristotle University of Thessaloniki, Department of Informatics E XPERIMENTAL R ESULTS Experimental protocol

18. Aristotle University of Thessaloniki, Department of Informatics E XPERIMENTAL R ESULTS Performance evaluation 4 False acceptance (FA) occurs when an impostor claim is accepted. 4 False rejection (FR) occurs when a client claim is rejected. 4 Equal error rate (EER) is the operating state where FA rate=FR rate. 4 Receiver operating characteristics (ROC) is the plot of FA rate versus FR rate.

19. Aristotle University of Thessaloniki, Department of Informatics E XPERIMENTAL R ESULTS Comparison of equal error rates for several authentication techniques in the M2VTS database.

20. Aristotle University of Thessaloniki, Department of Informatics E XPERIMENTAL R ESULTS

21. Aristotle University of Thessaloniki, Department of Informatics PERFORMANCE OF MEGM IN XM2VTSdb XM2VTS database  295 persons (8 images per person)  uniform background  Four training images for each client  Evaluation: 40000 impostor and 400 client claims  Testing: 112000 impostor and 400 client claims  Training: 39800 impostor and 200 client claims  Evaluation: 40000 impostor and 600 client claims  Testing: 112000 impostor and 400 client claims Experimental protocol Configuration II Experimental protocol Configuration I

22. Aristotle University of Thessaloniki, Department of Informatics PERFORMANCE OF MEGM IN XM2VTSdb Receiver Operating Characteristics MEGM Configuration I Configuration II

23. Aristotle University of Thessaloniki, Department of Informatics PERFORMANCE OF MEGM IN XM2VTSdb Rates at several FAR on XM2VTSdb in the two configurations of the experimental protocol. All rates are in %.

24. Aristotle University of Thessaloniki, Department of Informatics C ONCLUSIONS å åNovel methods for image analysis into the elastic graph matching have been proposed. å åThey are based on multi-scale erosion dilation and morphological signal decomposition of the facial image. å åDiscriminant analysis was applied in order to enhance the performance of the proposed methods. å åThe experimental results indicated the success of the proposed methods in frontal face authentication.