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

1Michael Bronstein 3D face recognition

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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+

GEOMETRIC(3D)

PHOTOMETRIC(2D)

What is a face?

=

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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

B

A′

B′

EUCLIDEAN DISTANCES: |A B| |A′ B′|

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Is geometry sensitive to expressions?

A

B

A′

B′

GEODESIC DISTANCES: d(A,B) d′(A′,B′)

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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

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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

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Isometric embedding

RIEMANNIAN EUCLIDEAN

A B A′ B′

EMBEDDING

Expression-invariant representation of face = canonical form

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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.

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How to canonize a person?

3D SURFACE ACQUISITION

SMOOTHING CANONIZATIONCROPPING

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Examples of canonical forms

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ORIGINAL SURFACES CANONICAL FORMS

Canonical forms

MichaelAlex

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Telling identical twins apart

MichaelAlex

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CAMERA

PROJECTOR

MONITOR

CARD READER

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SCANNED FACE

CANONICAL FORM

DISTANCES

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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