Transcript Elastic Bunch Graph Matching Face Recognition and Biometric Systems Plan of the lecture Eigenfaces – main drawbacks Alternative approaches EBGM method (Elastic Bunch Graph Matching)    Gabor.

Elastic Bunch Graph Matching
Face Recognition and Biometric Systems
Plan of the lecture
Eigenfaces – main drawbacks
Alternative approaches
EBGM method (Elastic Bunch Graph
Matching)
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

Gabor Wavelets
face feature points detection
feature vectors comparison
Face Recognition and Biometric Systems
Recognition process
Detection
Normalisation
Feature vectors
comparison
Ekstrakcja
Feature
extraction
cech
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

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nature of features taken into account
2D information utilised
face topology taken into account
Based on feature points similarity

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wavelets methods
shape comparison
Face Recognition and Biometric Systems
EBGM - introduction
Approximate location of feature points
Frequency 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 added
Local frequency analysis
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wavelength ()
wavelet orientation ()
Gaussian radius ()
Set of various wavelets
Face Recognition and Biometric Systems
Wavelet transform
Point (x0, y0)
2
W e

x'  y'
2
2
2
2
 cos 2
x'

 i e

x'  y'
2
2
2
 sin 2
x'

x'  ( x  x0 ) cos  ( y  y0 ) sin 
y'  ( x  x0 ) sin   ( y  y0 ) cos
Face Recognition and Biometric Systems
Wavelet transform
Point (x0, y0)
2
W e

x'  y'
2σ
2
2
2
 cos 2
x'
λ
 i e

x'  y'
2σ
2
2
 sin 2
x'
λ
x'  ( x  x0 ) cos θ  ( y  y 0 ) sin θ
y'  ( x  x0 ) sin θ  ( y  y 0 ) cos θ
Face Recognition and Biometric Systems
Wavelet transform
Imaginary part can be eliminated
2
W e

x'  y'
2
2
2
 cos( 2
x'

)
Phase shift () can be modified to get
two values
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 ( x0 , y0 )  W ( xi , y j )  I ( x0  xi , y0  y j )
i
j
C is a complex number
The result presented in phazor form
Face Recognition and Biometric Systems
Wavelet transform
Set of N wavelets
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various properties
optimisation – wavelets calculated once
Set of feature points
Convolution between wavelets and the image in
every feature point
Feature vector of a feature point (J - jet): values of
convolutions
J j  a je
i j
Face Recognition and Biometric Systems
Wavelet transform
Modification of feature point location
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module (aj) – value rather stable
argument (j) – value can change
significantly
J j  a je
i j
Face Recognition and Biometric Systems
Feature vectors comparison
Correlation

N – number of wavelets
N
a a
j
S ( J , J ' ) 
j
' cos( j   j ' )
j 1
N
N
a a
2
j
j 1
j
'
2
j 1
Face Recognition and Biometric Systems
Feature vectors comparison
Covariance
N
 a ja j '
Sa ( J , J ' ) 
j 1
N
2
N
aj aj'
j 1
2
j 1
Face Recognition and Biometric Systems
Feature vectors comparison
Correlation with displacement
correction N
 a j a j ' cos  j   j ' d  k j
 
SD (J , J ', d ) 

j 1
N
N
a a
2
j
j 1
j
'
2
j 1
2 cos  2 sin 
kj [
;
]


Face Recognition and Biometric Systems
Displacement correction
Influence on phase shift

works for displacements smaller than /2
Displacement estimation
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convolution calculated in every point
results comparison
displacement found by correlation
maximisation
Face Recognition and Biometric Systems
Displacement correction
Approximation with Taylor expansion
1
cos   1  
2
2

N
SD (J , J ', d ) 

2


a
a
'
1

0
.
5



'

d

k
 j j 
j
j
j

j 1
N
aj
Analytical solution
j 1
N
2
aj'
2
j 1
Face Recognition and Biometric Systems
Displacement correction
This works for small displacements only
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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)
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real positions of feature points in M
images
average dependencies between positions
A „bunch” created for every feature
point
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bunch – set of M feature vectors
Face Recognition and Biometric Systems
Features detection
New image
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approximate feature points’ locations
For every feature point:
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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
Add the point
to the set
Exact location
(find the
displacement)
Face Recognition and Biometric Systems
EBGM algorithm
1. Estimate location of features
2. For every point:
1.
2.
3.
calculate convolutions with all wavelets
(create a Jet)
find the displacement
(it can be used for detection)
correct the Jet for the new location
3. Feature vectors comparison:
1.
2.
sum of correlations, feature points location
SVM-based comparison (correlations classified)
Face Recognition and Biometric Systems
EBGM algorithm
Image normalisation for EBGM

frequency must not be affected
Standard operations
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geometric normalisation
histogram modifications
Smoothed edges
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sharp edges influence the frequency
Face Recognition and Biometric Systems
EBGM algorithm
Face Recognition and Biometric Systems
Summary
Slower method than Eigenfaces
High effectiveness
Feature-based approach

possible fusion with the Eigenfaces
Helpful for feature detection
Face Recognition and Biometric Systems
Thank you for your attention!
Plan:
20/05
27/05
03/06
Filtering, lab @12am (2nd sect.)
No lecture, lab @8am (2nd sect.)
Summary, lab @10am + @ 1pm
(1st & 3rd sect.)
Face Recognition and Biometric Systems