Face recognition:

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Face recognition New technologies, new
challenges
Michael M. Bronstein
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The coin that betrayed Louis XVI
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Modern challenges
Is this the same person?
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What is a face?


GEOMETRIC (3D)
PHOTOMETRIC (2D)
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What is more important 2D or 3D?


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What is more important 2D or 3D?


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Conclusion 1

• 3D data conceals valuable information about
  identity
• Less sensitive to external factors (light, pose,
  makeup)
• More difficult to forge

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The curse of expressions
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Is geometry sensitive to expressions?
A
A'
B'
B
EUCLIDEAN DISTANCES A ? B ? A' ? B'
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Is geometry sensitive to expressions?
A
A'
B'
B
GEODESIC DISTANCES d(A,B) ? d'(A',B')
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Conclusion 2
ERROR DISTRIBUTION

• Extrinsic (Euclidean) geometry is sensitive to
  expressions
• Intrinsic (Riemannian) geometry is insensitive to
  expressions
• Expression-invariant face recognition using
  intrinsic geometry

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Mapmakers nightmare
Find a planar map of the Earth which preserves
the geodesic distances in the best way
B
B'
A'
A
d(A,B) ? A' ? B'
PLANE (EUCLIDEAN)
SPHERE (RIEMANNIAN)
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Isometric embedding
A
B
A'
B'
EMBEDDING
EUCLIDEAN
RIEMANNIAN
Expression-invariant representation of face
canonical form
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A remark from Gauss
Theorema Egregium (Remarkable Theorem) A face
has non-zero curvature, therefore, it is not
isometric to the plane.
Result the embedding is only approximately
isometric, and therefore, introduces an error.
Carl Friedrich Gauss  (1777-1855)
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How to canonize a person?
CANONIZATION
SMOOTHING
CROPPING
3D SURFACE ACQUISITION
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Examples of canonical forms
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Canonical forms
ORIGINAL SURFACES
CANONICAL FORMS
Michael
Alex
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Telling identical twins apart
Michael
Alex
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(No Transcript)
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CAMERA
PROJECTOR
CARD READER
MONITOR
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SCANNED FACE
CANONICAL FORM
DISTANCES
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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