Eigenfaces 2 Face Recognition and Biometric Systems Plan

Eigenfaces (2) Face Recognition and Biometric Systems

Plan of the lecture PCA – repeated Back projection Feature vectors comparison Methods based on the Eigenfaces Face Recognition and Biometric Systems

Eigenfaces Feature extraction method Redundant information reduction (dimensionality reduction) Two stages: n n training projection (feature extraction) Possibility of back projection Face Recognition and Biometric Systems

Eigenfaces: training C 00. . . C 0 n. . Cn 0. . . Cnn Normalised images Covariance matrix Eigenfaces Face Recognition and Biometric Systems

Eigenfaces: laboratory Input data: n normalised images, number and size Implementation: n n n covariance matrix eigenvalues and eigenvectors (Open. CV) output buffer – eigenvectors / eigenfaces Testing: n dimensionality reduction Face Recognition and Biometric Systems

Eigenfaces: feature extraction K 1 K 2 K 3. . . Scalar products between normalised image and eigenvectors . . . Feature vector Face Recognition and Biometric Systems

Eigenfaces: feature extraction matrix can be cut to reduce dimensions ’ ’’ Feature vector element is a scalar product: Feature vector – cut projected vector x’ Face Recognition and Biometric Systems

Back projection: example 2 -dimensional space: n eigenvectors: n average vector [0, 0] Vectors projection: n [3; 1], [-2; -2], [10, 9] Back projection Face Recognition and Biometric Systems

Back projection Feature vector -> face image Projection error – difference between original and recovered image Face Recognition and Biometric Systems

Back projection: 2 D Face Recognition and Biometric Systems

Back projection: 2 D Face Recognition and Biometric Systems

Back projection: 2 D Face Recognition and Biometric Systems

Back projection: 2 D Face Recognition and Biometric Systems

Back projection: face image Feature vector – face description n information reduction Back projection: face image recovered from feature vector n reduced information are lost Projection error: n n n depends on similarity to the training set 2 D example face images Face Recognition and Biometric Systems

Face Recognition and Biometric Systems

Face Recognition and Biometric Systems

Back projection: detection Back projection of images: n n face -> slightly modified face image flower -> image similar to a face Back projection error is higher for non -face images Can be used as a verifier n threshold of accepted projection error Face Recognition and Biometric Systems

Feature vectors comparison Similarity based on distance metric n n n Euclidean distance (norm L 2) Mahalanobis distance angle between vectors Classifier-based similarity n SVM, ANN Face Recognition and Biometric Systems

Feature vectors comparison Euclidean distance (L 2 norm) n distance between two points in Euclidean space Face Recognition and Biometric Systems

Feature vectors comparison Mahalanobis distance n variance normalised in all directions (a. k. a. whitening) - eigenvalue Face Recognition and Biometric Systems

Feature vectors comparison Weak whitening: Eigenvalue filter: Face Recognition and Biometric Systems

Feature vectors comparison Based on cosine of the angle n feature vector length not taken into consideration Face Recognition and Biometric Systems

Feature vectors comparison Classifiers n n n single vector can be classified two or more classes long training stage One person – one class n training necessary when gallery is changed Similarity between any two vectors n n universal training two vectors -> one vector Face Recognition and Biometric Systems

K 11 K 12. . . K 1 n K 21 K 22 SVM The same class Different classes . . . K 2 n Face Recognition and Biometric Systems

K 11 - K 21 K 12 - K 22. . . K 1 n - K 2 n SVM The same class Different classes Face Recognition and Biometric Systems

Feature vectors comparison Training set for classifiers: 1. 2. 3. 4. 5. classified samples intra-personal pairs extra-personal pairs differences within each pair training with two sets: intra-personal and extra-personal Face Recognition and Biometric Systems

Feature vectors comparison A pair of feature vectors: n n many metrics, various results metric as a separate feature extraction method Metrics fusion n n weighted mean of single results classifiers again Testing necessary Face Recognition and Biometric Systems

Eigenfaces – improvements Main drawbacks: n n 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: n n Error function minimisation Methods derived from Eigenfaces Face Recognition and Biometric Systems