1. 1 Michael Bronstein 3D face recognition Face recognition: New technologies, new challenges Michael M. Bronstein

2. 2 Michael Bronstein 3D face recognition The coin that betrayed Louis XVI

3. 3 Michael Bronstein 3D face recognition Modern challenges = ? Is this the same person?

4. 4 Michael Bronstein 3D face recognition + GEOMETRIC (3D) PHOTOMETRIC (2D) What is a face? =

5. 5 Michael Bronstein 3D face recognition What is more important: 2D or 3D? + =

6. 6 Michael Bronstein 3D face recognition What is more important: 2D or 3D? + =

7. 7 Michael Bronstein 3D face recognition Conclusion 1 3D data conceals valuable information about identity Less sensitive to external factors (light, pose, makeup) More difficult to forge

8. 8 Michael Bronstein 3D face recognition The curse of expressions

9. 9 Michael Bronstein 3D face recognition Is geometry sensitive to expressions? A B A′ B′ EUCLIDEAN DISTANCES: |A  B|  |A′  B′|

10. 10 Michael Bronstein 3D face recognition Is geometry sensitive to expressions? A B A′ B′ GEODESIC DISTANCES: d(A,B)  d′(A′,B′)

11. 11 Michael Bronstein 3D face recognition Conclusion 2 Extrinsic (Euclidean) geometry is sensitive to expressions Intrinsic (Riemannian) geometry is insensitive to expressions Expression-invariant face recognition using intrinsic geometry -60-40-200204060 0 0.2 0.4 0.6 0.8 1 ERROR DISTRIBUTION

12. 12 Michael Bronstein 3D face recognition Mapmaker’s nightmare SPHERE (RIEMANNIAN) PLANE (EUCLIDEAN) A B A′ B′ d(A,B)  |A′  B′| Find a planar map of the Earth which preserves the geodesic distances in the best way

13. 13 Michael Bronstein 3D face recognition Isometric embedding RIEMANNIAN EUCLIDEAN AB A′B′ EMBEDDING Expression-invariant representation of face = canonical form

14. 14 Michael Bronstein 3D face recognition A remark from Gauss Result: the embedding is only approximately isometric, and therefore, introduces an error. Carl Friedrich Gauss (1777-1855) Theorema Egregium (Remarkable Theorem): A face has non-zero curvature, therefore, it is not isometric to the plane.

15. 15 Michael Bronstein 3D face recognition How to canonize a person? 3D SURFACE ACQUISITION SMOOTHING CANONIZATION CROPPING

16. 16 Michael Bronstein 3D face recognition Examples of canonical forms

17. 17 Michael Bronstein 3D face recognition ORIGINAL SURFACES CANONICAL FORMS Canonical forms MichaelAlex

18. 18 Michael Bronstein 3D face recognition Telling identical twins apart MichaelAlex

19. 19 Michael Bronstein 3D face recognition

20. 20 Michael Bronstein 3D face recognition CAMERA PROJECTOR MONITOR CARD READER

21. 21 Michael Bronstein 3D face recognition SCANNED FACE CANONICAL FORM DISTANCES

22. 22 Michael Bronstein 3D face recognition Towards more accurate recognition Embed one surface into another instead of using a common embedding space Avoid representation error Beautiful theory: related to the Gromov-Hausdorff metric