Sparse Support Faces - Battista Biggio - Int'l Conf. Biometrics, ICB 2015, Phuket, Thailand, May 19-22, 2015

Pa#ern Recogni-on and Applica-ons Lab

University

of Cagliari, Italy

Department of Electrical and Electronic

Engineering

Sparse Support Faces

Ba#sta Biggio, Marco Melis, Giorgio Fumera, Fabio Roli

Dept. Of Electrical and Electronic Engineering University of Cagliari, Italy

Phuket, Thailand, May 19-‐22, 2015 ICB 2015

http://pralab.diee.unica.it

Template-based Face Verification

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gc ≥ϑ c

genuine

impostor

true

false

s(x, tci ){ }i=1

p

Matcher s(⋅, ⋅)

Fusion rule

gc (x)xFeature extrac-on

Verifica-on is based on how similar the submi#ed image is to the client’s templates

Client-‐specific one-‐class classifica:on

mean gc (x) =1p

s(x, tci )

i=1

p

∑

gc (x) = maxi=1,…,ps(x, tc

i )max

Claimed Iden-ty tc

1, …, tcp{ }

Claimed iden-ty’s templates


Cohort-based Face Verification

3

Verifica-on is based on how similar the submi#ed image is to the client’s templates and on how different it is from the cohorts’ templates

Client-‐specific two-‐class classifica:on (one-‐vs-‐all)

gc ≥ϑ c

genuine

impostor

true

false

s(x, tci ){ }i=1

n

Matcher s(⋅, ⋅)

Fusion rule

gc (x)xFeature extrac-on

tc1, …, tc

p{ }

Claimed iden-ty’s templates Cohorts

tcp+1, …, tc

n{ }Claimed Iden-ty


Cohort-based Fusion Rules

•  Cohort selection is heuristically driven –  e.g., selection of the closest cohorts to the client’s templates

•  Cohort-based fusion rules are also based on heuristics

–  Test-normalization [Auckenthaler et al., DSP 2000]

–  Aggarwal’s max rule [Aggarwal et al., CVPR-W 2006]

4

gc (x) =1

σ c (x)1p

s(x, tci )

i=1

p

∑ −µc (x)#

$%

&

'(

gc (x) =maxi=1,…,p

s(x, tci )

maxj=p+1,…,n

s(x, tcj )


Open Issues

•  Fusion rules and cohort selection are based on heuristics –  No guarantees of optimality in terms of verification error

•  Our goal: to design a procedure to optimally select the reference templates and the fusion rule –  Optimal in the sense that it minimizes verification error (FRR and FAR)

•  Underlying idea: to consider face verification as a two-class classification problem in similarity space

5


s(x, )

s(x, )

Face Verification in Similarity Space

•  The matching function maps faces onto a similarity space –  How to design an optimal decision function in this space?

6

?


Support Face Machines (SFMs)

•  We learn a two-class SVM for each client –  using the matching score as the kernel function –  genuine client y=+1, impostors y=-1

•  SVM minimizes the classification error (optimal in that sense) –  FRR and FAR in our case

•  The fusion rule is a linear combination of matching scores •  The templates are automatically selected for each client

–  support vectors à support faces

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gc (x) = αis(x, tci )

i∑ − α js(x, tcj )

j∑ + b


Support Face Machines (SFMs)

8

s(x, )

s(x, )

•  Maximum-margin classifiers

gc (x) = αis(x, tci )

i∑ − α js(x, tcj )

j∑ + b



•  Open issue: SFMs require too many support faces –  Number of support faces scales linearly with training set size

•  Our goal: to learn a much sparser combination of match scores

•  by jointly optimizing the weighting coefficients and support faces:

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hc (x) = βis(x, zck )+ b

k=1

m

∑ , m << n

minβ ,z

Ω β, z( ) = 1n

uk gc (xk )− hc (xk )( )2+λβTβ

i=1

n

∑


z-‐step


10

SFM with 12 support faces

−5 0 5−5

0

5

−5

0

5SSFM with 4 virtual faces

−5 0 5−5

0

5

−5

0

5

β-‐step

Solu:on algorithm is an itera-ve two-‐step procedure:

If s(x,z) is not differentiable or analytically given, gradient can be approximated


0.5 1 2 5 100

5

10

15

20 AT&T − RBF Kernel

FAR (%)

FR

R (

%)

mean (5)max (5)t−norm (10)aggarwal−max (10)SFM (37.5 ± 3.8)SFM−sel (10)SFM−red (2)SSFM (2)

Experiments

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Datasets: AT&T (40 clients, 10 images each) BioID (23 clients, 1,521 images) Matcher: PCA+RBF kernel (exact gradient) 5 repetitions, different clients in TR/TS splits TR: 5 images/client

0.5 1 2 5 100

10

20

30

40 BioID − RBF Kernel

FAR (%)

FR

R (

%)



Experiments

12 0.5 1 2 5 100

10

20

30

40 BioID − EBGM

FAR (%)

FR

R (

%)


0.5 1 2 5 100

5

10

15

20 AT&T − EBGM

FAR (%)

FR

R (

%)


Datasets: AT&T (40 clients, 10 images each) BioID (23 clients, 1,521 images) Matcher: EBGM (approx. gradient) 5 repetitions, different clients in TR/TS splits TR: 5 images/client


From Support Faces to Sparse Support Faces

•  A client’s gallery of 17 support faces (and weights) reduced to 5 virtual templates by our sparse support face machine –  Dataset: BioID –  Matching algorithm: EBGM

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4.040 2.854 −0.997 −3.525 −2.208


Conclusions and Future Research Directions

•  Sparse support face machines: –  reduce computational time and storing requirements during

verification without affecting verification accuracy –  by jointly learning an optimal combination of matching scores, and a

corresponding sparse set of virtual support faces

•  No explicit feature representation is required –  Matching algorithm exploited as kernel function –  Virtual templates created exploiting approximations of its gradient

•  Future work –  Fingerprint verification

–  Identification setting •  Joint reduction of virtual templates for each client-specific classifier

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? Any questions Thanks for your a#en-on!

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Code available at: http://pralab.diee.unica.it/en/SSFCodeProject

Education

Sparse Support Faces - Battista Biggio - Int'l Conf. Biometrics, ICB 2015, Phuket, Thailand, May 19-22, 2015