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Eigenfaces (2)

Eigenfaces (2). Plan of the lecture. PCA – repeated Back projection Feature vectors comparison Methods based on the Eigenfaces. Eigenfaces. Feature extraction method Redundant information reduction (dimensionality reduction) Two stages: training projection (feature extraction)

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Eigenfaces (2)

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  1. Eigenfaces (2) Face Recognition and Biometric Systems

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

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

  4. Eigenfaces: training C00 ... C0n ... ... ... Cn0 ... Cnn Normalised images Covariance matrix Eigenfaces Face Recognition and Biometric Systems

  5. 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

  6. Eigenfaces: feature extraction K1 K2 K3 ... ... Scalar products between normalised image and eigenvectors Feature vector Face Recognition and Biometric Systems

  7. ’ ’’ 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

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

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

  10. Back projection: 2D Face Recognition and Biometric Systems

  11. Back projection: 2D Face Recognition and Biometric Systems

  12. Back projection: 2D Face Recognition and Biometric Systems

  13. Back projection: 2D Face Recognition and Biometric Systems

  14. 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

  15. 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 images • Can be used as a verifier • threshold of accepted projection error Face Recognition and Biometric Systems

  16. Feature vectors comparison • Similarity based on distance metric • Euclidean distance (norm L2) • Mahalanobis distance • angle between vectors • Classifier-based similarity • SVM, ANN Face Recognition and Biometric Systems

  17. Feature vectors comparison • Euclidean distance (L2 norm) • distance between two points in Euclidean space Face Recognition and Biometric Systems

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

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

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

  21. 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 Face Recognition and Biometric Systems

  22. K11 K12 ... The same class K1n SVM Different classes K21 K22 ... K2n

  23. K11 - K21 The same class K12 - K22 SVM Different classes ... K1n - K2n

  24. Feature vectors comparison • Training set for classifiers: • 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

  25. 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

  26. 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

  27. Example Face Recognition and Biometric Systems

  28. Example: PCA Face Recognition and Biometric Systems

  29. Example: PCA not helpful Face Recognition and Biometric Systems

  30. Example: Linear Discriminant Analysis Face Recognition and Biometric Systems

  31. Thank you for your attention! • Next time: • Error function minimisation • Methods derived from Eigenfaces Face Recognition and Biometric Systems

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