1. 1 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Three Dimensional Face Recognition “And in stature he is small, chest broad, one arm shorter than the other, blue eyes, red hair, a wart on his cheek, another on his forehead.” Then is it not you, my friend? A.S. Pushkin, Boris Godunov Alexander Bronstein, Michael Bronstein © 2008 All rights reserved. Web: tosca.cs.technion.ac.il

2. 2 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Biometrics in the age of Patriarchs “The voice is the voice of Jacob, but the hands are the hands of Esau”

3. 3 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition First face recognition Galton’s mechanical face recognition machine I contrieved an apparatus […] which I call a mechanical selector. Its object is to find which set out of a standard collection of many sets of measures, resembles any one of given set within specified degree of unlikeness. “ ” Nature, 1888 Sir Francis Galton (1822-1911)

4. 4 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Face recognition today = ? Is this the same person?

5. 5 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Some terminology Gallery Instances of faces of a person with known identity Probe A face unseen before with unknown identity Impostor False rejection Probe deemed dissimilar to gallery of same identity False acceptance Probe of different identity deemed similar to gallery

6. 6 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition The coin that betrayed Louis XVI Gallery Probe

7. 7 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition How face recognition works Gallery Probe FACE DISTANCE > threshold? REJECTACCEPT NoYes

8. 8 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Recognition accuracy False acceptance rate (FRR) False rejection rate (FAR) High threshold (loose) Low threshold (conservative) Equal Error Eate (EER) FAR = FRR

9. 9 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Face distance Discriminative Large between faces of different persons Invariant Small between faces of same person in different conditions

10. 10 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition + GEOMETRIC (3D) PHOTOMETRIC (2D) What is a face? =

11. 11 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition What is more important: 2D or 3D? + =

12. 12 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition What is more important: 2D or 3D? + =

13. 13 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition

14. 14 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Conclusion 1 3D data encodes valuable information about person’s identity Less sensitive to external factors (light, pose, makeup) More difficult to forge

15. 15 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition The curse of expressions

16. 16 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Is geometry sensitive to expressions? x x’ y y’ Euclidean distances

17. 17 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Is geometry sensitive to expressions? x x’ y y’ Geodesic distances

18. 18 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Conclusion 2 Distance distortion distribution Extrinsic geometry sensitive to expressions Intrinsic geometry insensitive to expressions

19. 19 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Isometric model of expressions Facial expressions are approximate isometries of the facial surface Identity = intrinsic geometry Expression = extrinsic geometry A. M. Bronstein et al., IJCV, 2005

20. 20 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition

21. 21 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition How to canonize a person? 3D scan Smooting Canonization Cropping

22. 22 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Canonical forms of faces

23. 23 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition SCANNED FACE CANONICAL FORM DISTANCES

24. 24 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Telling identical twins apart Extrinsic similarity Intrinsic similarity MichaelAlex

25. 25 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Telling identical twins apart MichaelAlex

26. 26 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition

27. 27 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition

28. 28 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Comparing photometric properties Facial surface with texture 3D canonical form 2D canonical form Two-dimensional canonical form can be used as a common parametrization of the facial textures

29. 29 Numerical geometry of non-rigid shapes Three-Dimensional Face Recognition Spherical embedding R = 80 mmR = 100 mmR = 150 mm