Post on 14-Dec-2015
Face Recognition and Biometric Systems
Eigenfaces (2)
Face Recognition and Biometric Systems
Plan of the lecture
PCA – repeatedBack projectionFeature vectors comparisonMethods based on the Eigenfaces
Face Recognition and Biometric Systems
Eigenfaces
Feature extraction methodRedundant information reduction (dimensionality reduction)Two stages: training projection (feature extraction)
Possibility of back projection
Face Recognition and Biometric Systems
Eigenfaces: training
Normalisedimages
C00
Cn0
C0n
Cnn
...
...
... ......
Covariancematrix
Eigenfaces
Face Recognition and Biometric Systems
Eigenfaces: laboratory
Input data: normalised images, number and size
Implementation: covariance matrix eigenvalues and eigenvectors (OpenCV) output buffer – eigenvectors / eigenfaces
Testing: dimensionality reduction
Face Recognition and Biometric Systems
...
Scalar products betweennormalised image and
eigenvectors
...
K1
K2
K3
Feature vector
Eigenfaces: feature extraction
Face Recognition and Biometric Systems
matrix can be cut to reduce dimensions
Feature vector element is a scalar product:
Feature vector – cut projected vector x’xv T
iiw
’ ’’
xψw T'
Eigenfaces: feature extraction
Face Recognition and Biometric Systems
Back projection: example
2-dimensional space: eigenvectors:
average vector [0, 0]
Vectors projection: [3; 1], [-2; -2], [10, 9]
Back projection
]2
2;
2
2[ ]
2
2;
2
2[
Face Recognition and Biometric Systems
Back projection
Feature vector -> face image
Projection error – difference between original and recovered image
μvx
'
1
N
iiiP w
Pxx
μwψx 'P
Face Recognition and Biometric Systems
Back projection: 2D
Face Recognition and Biometric Systems
Back projection: 2D
Face Recognition and Biometric Systems
Back projection: 2D
Face Recognition and Biometric Systems
Back projection: 2D
Face Recognition and Biometric Systems
Back projection: face image
Feature vector – face description information reduction
Back projection: face image recovered from feature vector reduced information are lost
Projection error: depends on similarity to the training
set 2D example face images
Face Recognition and Biometric Systems
Back projection: detection
Back projection of images: face -> slightly modified face image flower -> image similar to a face
Back projection error is higher for non-face imagesCan be used as a verifier threshold of accepted projection
error
Face Recognition and Biometric Systems
Feature vectors comparison
Similarity based on distance metric
Euclidean distance (norm L2) Mahalanobis distance angle between vectors
Classifier-based similarity SVM, ANN
2121 ,1
1),(
wwww
distS
Face Recognition and Biometric Systems
Feature vectors comparison
Euclidean distance (L2 norm) distance between two points
in Euclidean space
'
1
22121 )(),(
N
iii wwdist ww
Face Recognition and Biometric Systems
Feature vectors comparison
Mahalanobis distance variance normalised in all directions
(a.k.a. whitening)
- eigenvalue
'
1
221
21
)(),(
N
i i
ii wwdist
ww
Face Recognition and Biometric Systems
Feature vectors comparison
Weak whitening:
Eigenvalue filter:
'
1
221
21
)(),(
N
ii
ii wwdist
ww
'
12
'
22121 )(
)(),(N
i Ni
iii wwdist
ww
Face Recognition and Biometric Systems
Feature vectors comparison
Based on cosine of the angle
feature vector length not taken into consideration
||||),(
21
2121 ww
wwww
dist
Face Recognition and Biometric Systems
Feature vectors comparison
Classifiers single vector can be classified two or more classes long training stage
One person – one class training necessary when gallery is
changed
Similarity between any two vectors universal training two vectors -> one vector
K11
K12
K1n
...
K21
K22
K2n
...
SVM
The same class
Differentclasses
SVM
The sameclass
Different classes
K11 - K21
...
K12 - K22
K1n - K2n
Face Recognition and Biometric Systems
Feature vectors comparison
Training set for classifiers:1. classified samples2. intra-personal pairs3. extra-personal pairs4. differences within each pair5. training with two sets:
intra-personal and extra-personal
Face Recognition and Biometric Systems
Feature vectors comparison
A pair of feature vectors: many metrics, various results metric as a separate feature
extraction method
Metrics fusion weighted mean of single results classifiers again
Testing necessary
Face Recognition and Biometric Systems
Eigenfaces – improvements
Main drawbacks: holistic method face topology not taken into
account statistical analysis of differences
between images in the training set character of differences not taken
into account
Face Recognition and Biometric Systems
Example
Face Recognition and Biometric Systems
Example: PCA
Face Recognition and Biometric Systems
Example: PCA not helpful
Face Recognition and Biometric Systems
Example: Linear Discriminant Analysis
Face Recognition and Biometric Systems
Thank you for your attention!
Next time: Error function minimisation Methods derived from Eigenfaces