face recognition and biometric systems elastic bunch graph matching
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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.)