1Michael Bronstein 3D face recognition

Face recognition:New technologies, new challenges

Michael M. Bronstein

2Michael Bronstein 3D face recognition

The coin that betrayed Louis XVI

3Michael Bronstein 3D face recognition

Modern challenges

=?

Is this the same person?

4Michael Bronstein 3D face recognition

+

GEOMETRIC(3D)

PHOTOMETRIC(2D)

What is a face?

=

5Michael Bronstein 3D face recognition

What is more important: 2D or 3D?

+ =

6Michael Bronstein 3D face recognition

What is more important: 2D or 3D?

+ =

7Michael 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

8Michael Bronstein 3D face recognition

The curse of expressions

9Michael Bronstein 3D face recognition

Is geometry sensitive to expressions?

A

B

A′

B′

EUCLIDEAN DISTANCES: |A B| |A′ B′|

10Michael Bronstein 3D face recognition

Is geometry sensitive to expressions?

A

B

A′

B′

GEODESIC DISTANCES: d(A,B) d′(A′,B′)

11Michael Bronstein 3D face recognition

Conclusion 2

Extrinsic (Euclidean) geometry is sensitive to expressionsIntrinsic (Riemannian) geometry is insensitive to expressionsExpression-invariant face recognition using intrinsic

geometry

-60 -40 -20 0 20 40 600

0.2

0.4

0.6

0.8

1

ERROR DISTRIBUTION

12Michael 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

13Michael Bronstein 3D face recognition

Isometric embedding

RIEMANNIAN EUCLIDEAN

A B A′ B′

EMBEDDING

Expression-invariant representation of face = canonical form

14Michael 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.

15Michael Bronstein 3D face recognition

How to canonize a person?

3D SURFACE ACQUISITION

SMOOTHING CANONIZATIONCROPPING

16Michael Bronstein 3D face recognition

Examples of canonical forms

17Michael Bronstein 3D face recognition

ORIGINAL SURFACES CANONICAL FORMS

Canonical forms

MichaelAlex

18Michael Bronstein 3D face recognition

Telling identical twins apart

MichaelAlex

19Michael Bronstein 3D face recognition

20Michael Bronstein 3D face recognition

CAMERA

PROJECTOR

MONITOR

CARD READER

21Michael Bronstein 3D face recognition

SCANNED FACE

CANONICAL FORM

DISTANCES

22Michael Bronstein 3D face recognition

Towards more accurate recognition

Embed one surface into another insteadof using a common embedding space

Avoid representation error

Beautiful theory: related to the Gromov-Hausdorff metric