Post on 19-Dec-2015
1Michael Bronstein 3D face recognition
Face recognition:New technologies, new challenges
Michael M. Bronstein
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
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
17Michael Bronstein 3D face recognition
ORIGINAL SURFACES CANONICAL FORMS
Canonical forms
MichaelAlex