Three Dimensional Face Recognition

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17 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

55 εμφανίσεις

1

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition



Three Dimensional

Face Recognition

“And in stature he is small, chest
broad, one arm shorter than the
other, blue eyes, red hair, a wart
on his cheek, another on his
forehead.” Then is it not you, my
friend?

A.S. Pushkin
, Boris Godunov

Alexander Bronstein, Michael Bronstein

© 2008 All rights reserved. Web:
tosca.cs.technion.ac.il

2

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Biometrics in the age of Patriarchs

“The voice is the voice

of Jacob, but the hands

are the hands of Esau”

3

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

First face recognition

Galton’s mechanical face recognition machine

I contrieved an apparatus […] which I call a
mechanical selector. Its object is to find
which set out of a standard collection of
many sets of measures, resembles any one
of given set within specified degree of
unlikeness.





Nature, 1888

Sir Francis Galton

(
1822
-
1911
)

4

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Face recognition today

=

?

Is this the same person?

5

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Some terminology

Gallery

Instances of faces of a

person with known identity

Probe

A face unseen before

with unknown identity

Impostor

False rejection

Probe deemed dissimilar
to gallery of same identity

False acceptance

Probe of different identity
deemed similar to gallery

6

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

The coin that betrayed Louis XVI

Gallery

Probe

7

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

How face recognition works

Gallery

Probe

FACE

DISTANCE

> threshold?

REJECT

ACCEPT

No

Yes

8

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Recognition accuracy

False acceptance rate (FRR)

False rejection rate (FAR)

High threshold

(loose)

Low threshold

(conservative)

Equal Error Eate (EER)

FAR = FRR

9

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Face distance

Discriminative

Large between faces

of different persons

Invariant

Small between faces

of same person

in different conditions

10

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

+

GEOMETRIC

(3D)

PHOTOMETRIC

(2D)

What is a face?

=

11

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

What is more important: 2D or 3D?

+

=

12

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

What is more important: 2D or 3D?

+

=

13

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

14

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Conclusion 1


3
D data encodes valuable information about person’s identity


Less sensitive to external factors (light, pose, makeup)


More difficult to forge

15

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

The curse of expressions

16

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Is geometry sensitive to expressions?

x

x’

y

y’

Euclidean distances

17

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Is geometry sensitive to expressions?

x

x’

y

y’

Geodesic distances

18

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Conclusion 2

Distance distortion distribution


Extrinsic

geometry sensitive to expressions


Intrinsic

geometry insensitive to expressions

19

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Isometric model of expressions


Facial expressions are approximate isometries of the facial surface


Identity

= intrinsic geometry


Expression

= extrinsic geometry


A. M. Bronstein
et al.
, IJCV, 2005

20

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

21

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

How to canonize a person?

3D scan

Smooting

Canonization

Cropping

22

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Canonical forms of faces

23

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

SCANNED

FACE

CANONICAL


FORM

DISTANCES

24

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Telling identical twins apart

Extrinsic similarity

Intrinsic similarity

Michael

Alex

25

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Telling identical twins apart

Michael

Alex

26

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

27

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

28

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Comparing photometric properties

Facial surface

with texture

3
D canonical

form

2D canonical

form

Two
-
dimensional canonical form can be used as a common parametrization
of the facial textures

29

Numerical geometry of non
-
rigid shapes
Three
-
Dimensional Face Recognition

Spherical embedding

R =
80
mm

R =
100
mm

R =
150
mm