Numerical geometry of nonrigid shapes Expressioninvariant face recognition

Numerical geometry of non-rigid shapes Expression-invariant face recognition 1 Expression-invariant face recognition Lecture 8 © Alexander & Michael Bronstein tosca. cs. technion. ac. il/book Numerical geometry of non-rigid shapes Stanford University, Winter 2009

Numerical geometry of non-rigid shapes Expression-invariant face recognition Biometrics in the age of Patriarchs “The voice is the voice of Jacob, but the hands are the hands of Esau” 2

Numerical geometry of non-rigid shapes Expression-invariant face recognition Biometrics in fairy tales 3

Numerical geometry of non-rigid shapes Expression-invariant face recognition Biometrics in opera 4

Numerical geometry of non-rigid shapes Expression-invariant face recognition First face recognition “ 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 Galton’s mechanical face recognition machine Sir Francis Galton (1822 -1911) 5

Numerical geometry of non-rigid shapes Expression-invariant face recognition Face recognition today ? = Is this the same person? 6

Numerical geometry of non-rigid shapes Expression-invariant face recognition 7 Some terminology False rejection Probe deemed dissimilar to gallery of same identity Gallery Instances of faces of a person with known identity Probe A face unseen before with unknown identity False acceptance Probe of different identity deemed similar to gallery Impostor

Numerical geometry of non-rigid shapes Expression-invariant face recognition Probe The coin that betrayed Louis XVI Gallery 8

Numerical geometry of non-rigid shapes Expression-invariant face recognition How face recognition works FACE DISTANCE Probe Gallery ACCEPT No > threshold? Yes REJECT 9

Numerical geometry of non-rigid shapes Expression-invariant face recognition False rejection rate (FAR) Recognition accuracy Low threshold (conservative) Equal Error Eate (EER) FAR = FRR High threshold (loose) False acceptance rate (FRR) 10

Numerical geometry of non-rigid shapes Expression-invariant face recognition Face distance Discriminative Invariant Large between faces of different persons Small between faces of same person in different conditions 11

Numerical geometry of non-rigid shapes Expression-invariant face recognition What is a face? + = PHOTOMETRIC (2 D) GEOMETRIC (3 D) 12

Numerical geometry of non-rigid shapes Expression-invariant face recognition What is more important: 2 D or 3 D? + = 13

Numerical geometry of non-rigid shapes Expression-invariant face recognition What is more important: 2 D or 3 D? + = 14

Numerical geometry of non-rigid shapes Expression-invariant face recognition Live statue Acco Turkish bath museum, Israel 15

Numerical geometry of non-rigid shapes Expression-invariant face recognition Conclusion 1 n 3 D data encodes valuable information about person’s identity n Less sensitive to external factors (light, pose, makeup) n More difficult to forge 16

Numerical geometry of non-rigid shapes Expression-invariant face recognition The curse of expressions 17

Numerical geometry of non-rigid shapes Expression-invariant face recognition Is geometry sensitive to expressions? x y x’ Euclidean distances y’ 18

Numerical geometry of non-rigid shapes Expression-invariant face recognition Is geometry sensitive to expressions? x y x’ Geodesic distances y’ 19

Numerical geometry of non-rigid shapes Expression-invariant face recognition Conclusion 2 Distance distortion distribution n Extrinsic geometry sensitive to expressions n Intrinsic geometry insensitive to expressions 20

Numerical geometry of non-rigid shapes Expression-invariant face recognition Isometric model of expressions n Facial expressions are approximate isometries of the facial surface n Identity = intrinsic geometry n Expression = extrinsic geometry A. M. Bronstein et al. , IJCV, 2005 21

Numerical geometry of non-rigid shapes Expression-invariant face recognition 22

Numerical geometry of non-rigid shapes Expression-invariant face recognition 23 How to canonize a person? 3 D scan Cropping Smooting Canonization

Numerical geometry of non-rigid shapes Expression-invariant face recognition Canonical forms of faces 24

Numerical geometry of non-rigid shapes Expression-invariant face recognition SCANNED FACE CANONICAL DISTANCES FORM 25

Numerical geometry of non-rigid shapes Expression-invariant face recognition Telling identical twins apart Extrinsic similarity Intrinsic similarity Alex Michael 26

Numerical geometry of non-rigid shapes Expression-invariant face recognition Telling identical twins apart Alex Michael 27

Numerical geometry of non-rigid shapes Expression-invariant face recognition 28

Numerical geometry of non-rigid shapes Expression-invariant face recognition 30 Comparing photometric properties Facial surface with texture 3 D canonical form 2 D canonical form Two-dimensional canonical form can be used as a common parametrization of the facial textures

Numerical geometry of non-rigid shapes Expression-invariant face recognition Spherical embedding R = 80 mm R = 100 mm R = 150 mm 31

Numerical geometry of non-rigid shapes Expression-invariant face recognition Partial similarity 32