Face Recognition and Biometric Systems

Elastic Bunch Graph Matching

Face Recognition and Biometric Systems

Plan of the lecture

Eigenfaces – main drawbacksAlternative approachesEBGM method (Elastic Bunch Graph Matching) Gabor Wavelets face feature points detection feature vectors comparison

Face Recognition and Biometric Systems

Recognition process

Detection Normalisation

Ekstrakcjacech

Feature vectorscomparison

Featureextraction

Face Recognition and Biometric Systems

Eigenfaces

Face represented by a vector loss of 2D information

Holistic approach face is treated as a monolithic

object

No difference between intra- and extra-personal features

Face Recognition and Biometric Systems

Feature extraction methods

Based on PCA nature of features taken into

account 2D information utilised face topology taken into account

Based on feature points similarity wavelets methods shape comparison

Face Recognition and Biometric Systems

EBGM - introduction

Approximate location of feature pointsFrequency analysis of feature points a set of wavelets

convolution between wavelet and image

Feature vectors comparison based on exact feature points detection

Face Recognition and Biometric Systems

EBGM - introduction

Face Recognition and Biometric Systems

Wavelet transform

Fourier transform frequency domain

Gaussian distribution addedLocal frequency analysis wavelength () wavelet orientation () Gaussian radius ()

Set of various wavelets

Face Recognition and Biometric Systems

Wavelet transform

Point (x0, y0)

'

2sin'

2cos2

22

2

22

2

''

2

''x

eix

eWyxyx

sin)(cos)(' 00 yyxxx

cos)(sin)(' 00 yyxxy

Face Recognition and Biometric Systems

Wavelet transform

Point (x0, y0)

λλσσ '

2sin'

2cos2

22

2

22

2

''

2

''x

eix

eWyxyx

θyθx 00 sin)(cos)(' yxx

θyθx 00 cos)(sin)(' yxy

Face Recognition and Biometric Systems

Wavelet transform

Imaginary part can be eliminated

Phase shift () can be modified to get two values

)'

2cos(2

22

2

''

xeW

yx

Face Recognition and Biometric Systems

Wavelet transform

Varying wavelet orientation ()

Varying wavelength ()

Face Recognition and Biometric Systems

Wavelet transform

Varying phase ()

Varying Gaussian radius ()

Face Recognition and Biometric Systems

Wavelet transform

Convolution calculated in a point

C is a complex numberThe result presented in phazor form

i j

jiji yyxxIyxWyxC ),(),(),( 0000

Face Recognition and Biometric Systems

Wavelet transform

Set of N wavelets various properties optimisation – wavelets calculated once

Set of feature pointsConvolution between wavelets and the image in every feature pointFeature vector of a feature point (J - jet): values of convolutions

jijj eaJ

Face Recognition and Biometric Systems

Wavelet transform

Modification of feature point location module (aj) – value rather stable argument (j) – value can change

significantlyji

jj eaJ

Face Recognition and Biometric Systems

Feature vectors comparison

Correlation N – number of wavelets

N

jj

N

jj

N

jjjjj

aa

aa

JJS

1

2

1

2

1

'

)'cos('

)',(

Face Recognition and Biometric Systems

Feature vectors comparison

Covariance

N

jj

N

jj

N

jjj

a

aa

aaJJS

1

2

1

2

1

'

')',(

Face Recognition and Biometric Systems

Feature vectors comparison

Correlation with displacement correction

N

jj

N

jj

N

jjjjjj

D

aa

kdaa

dJJS

1

2

1

2

1

'

'cos'

),',(

]sin2

;cos2

[

jk

Face Recognition and Biometric Systems

Displacement correction

Influence on phase shift works for displacements smaller

than /2

Displacement estimation convolution calculated in every point results comparison displacement found by correlation

maximisation

Face Recognition and Biometric Systems

Displacement correction

Approximation with Taylor expansion

Analytical solution

N

jj

N

jj

N

jjjjjj

D

aa

kdaa

dJJS

1

2

1

2

1

2

'

'5.01'

),',(

2

2

11cos

Face Recognition and Biometric Systems

Displacement correction

This works for small displacements only maximal acceptable displacement

depends on the wavelength it’s better to start with low frequencies

Face Recognition and Biometric Systems

Features detection

Set of perfect data (M images) real positions of feature points in M

images average dependencies between

positions

A „bunch” created for every feature point bunch – set of M feature vectors

Face Recognition and Biometric Systems

Features detection

New image approximate feature points’ locations

For every feature point: compare with every feature vector in

a bunch (maximized correlation) choose the „expert” correct the position based on

displacement from the „expert”

Face Recognition and Biometric Systems

Features detection

Set of detected

feature points

Estimated location

of a new point

Exact location (find the

displacement)

Add the pointto the set

Face Recognition and Biometric Systems

EBGM algorithm1. Estimate location of features 2. For every point:

1. calculate convolutions with all wavelets (create a Jet)

2. find the displacement (it can be used for detection)

3. correct the Jet for the new location

3. Feature vectors comparison:1. sum of correlations, feature points location 2. SVM-based comparison (correlations

classified)

Face Recognition and Biometric Systems

EBGM algorithm

Image normalisation for EBGM frequency must not be affected

Standard operations geometric normalisation histogram modifications

Smoothed edges sharp edges influence the frequency

Face Recognition and Biometric Systems

EBGM algorithm

Face Recognition and Biometric Systems

Summary

Slower method than EigenfacesHigh effectivenessFeature-based approach possible fusion with the Eigenfaces

Helpful for feature detection

Face Recognition and Biometric Systems

Thank you for your attention!

Plan:

20/05 Filtering, lab @12am (2nd sect.)27/05 No lecture, lab @8am (2nd sect.)03/06 Summary, lab @10am + @ 1pm

(1st & 3rd sect.)