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# Eigenfaces

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### Eigenfaces

1. 1. EIGENFACES FOR RECOGNITON Paper: EigenFaces For Recognition, 1991 Authors: Matthew Turk and Alex Pentland Presenter: Semih Korkmaz 1/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
2. 2. EIGENFACES FOR RECOGNITON Left: Prof. Dr. Matthew Turk, currently working at UC Santa Barbara University(http://transliteracies.english.ucsb.edu) Right :Prof. Dr. Alex Pentland, Currently working at MIT. (http://ticsp.cs.tut.fi) 2/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
3. 3. EIGENFACES FOR RECOGNITON Contents • Overview of the method • Principal Component Analysis • Recognition Process • Acquiring Images • Calculating EigenFaces • Training the system • Additional Capabilities • Conclusion and Recent Work EigenFaces For Recognition, 91 3/24 Presenter: Semih Korkmaz
4. 4. EIGENFACES FOR RECOGNITON Overview • Acquire training images. • Calculate Eigenfaces. • Project them to face space. • Project test image to face space. • Calculate the Euclidean distance and make a decision. 4/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
5. 5. EIGENFACES FOR RECOGNITON Principal Component Analysis Find the dimensions of data with highest variance http://web.media.mit.edu/ EigenFaces For Recognition, 91 5/24 Presenter: Semih Korkmaz
6. 6. EIGENFACES FOR RECOGNITON Principal Component Analysis Finding patterns in many dimensions is hard. Mapping to a simpler domain is desirable. 𝑛 → 𝑘 | 𝑘≪ 𝑛 𝑛, 𝑘 number dimensions Invented in 1901, by Karl Pearson. 6/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
7. 7. EIGENFACES FOR RECOGNITON Acquire Training Images Get 𝑀 training samples with variances … 𝐼1 𝐼2 𝐼3 𝐼4 … 𝐼 𝑀−1 𝐼𝑀 (Olivetti - Att – ORL dataset, ‘94) Images are in same size and equivalently framed. 7/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
8. 8. EIGENFACES FOR RECOGNITON Calculate EigenFaces • Convert all the images in vector form. 25 55 8 200 180 70 𝐼𝑖 = 40 65 Γ𝑖 ′ = 18 25 40 55 8 200 180 70 65 18 𝑁2 𝑁 × 𝑁 • Calculate the mean . (Average Face) 1 Ψ= 𝑀 EigenFaces For Recognition, 91 𝑀 Γ𝑛 𝑛=1 8/24 Presenter: Semih Korkmaz
9. 9. EIGENFACES FOR RECOGNITON Calculate EigenFaces • Normalize vectors. Φ𝑖 = Γ 𝑖 − Ψ • Form the covariance matrix 𝐴 = [Φ1 , Φ2 , . . , Φ 𝑚 ] 1 𝐶= 𝑀 𝑀 𝑇 Φ 𝑛 Φ 𝑛 = 𝐴𝐴 𝑇 𝑛=1 EigenFaces For Recognition, 91 9/24 Presenter: Semih Korkmaz
10. 10. EIGENFACES FOR RECOGNITON Calculate EigenFaces • We calculate the Eigen vectors of Covariance Matrix 𝐶 = 𝐴𝐴 𝑇 → 𝑁 2 × 𝑀 . 𝑀 × 𝑁 2 → 𝑵 𝟐 × 𝑵 𝟐 • Do we need so many eigenvectors anyway ? No, we don’t ! Calculate eigenvectors of the Covariance matrix with reduced dimensionality. 10/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
11. 11. EIGENFACES FOR RECOGNITON Calculate EigenFaces 𝐶 = 𝐴 𝑇 𝐴 → 𝑀 × 𝑁2. 𝑁2 × 𝑀 → 𝑴 × 𝑴 𝑣 𝑖 is an eigenvector of 𝐴 𝑇 𝐴 𝜇 𝑖 is an eigenvector of 𝐴 𝐴 𝑇 (Eigen Face) 𝜇 𝑖 = 𝐴𝑣 𝑖 (𝐴 𝑇 𝐴)𝑣 𝑖 = 𝜆 𝑖 𝑣 𝑖 𝐴𝐴 𝑇 𝐴𝑣 𝑖 = 𝜆 𝑖 (𝐴𝑣 𝑖 ) Calculate 𝑘 eigenvectors and associate remaining to 0. 11/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
12. 12. EIGENFACES FOR RECOGNITON Training the system Ψ = 𝜇1 * 𝜔1 + 6 eigenfaces case + 𝜇2 ∗ 𝜔2 + 𝜇3 ∗ 𝜔3 + 𝜇4 ∗ 𝜔4 + 𝜇5 ∗ 𝜔5 + 𝜇6 ∗ 𝜔6 12/24 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
13. 13. EIGENFACES FOR RECOGNITON Training the system • Images projected to face space. 𝜔 𝑘 = 𝜇 𝑘𝑇 (Γ − Ψ) • Images projected to face space. Ω𝑖 = 𝜔1 𝜔2 𝜔3 … 𝜔𝑘 𝑀′ Φ𝑓 = 𝜔𝑖 𝜇𝑖 𝑖=1 13/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
14. 14. EIGENFACES FOR RECOGNITON Training the system Testing a face has two cases: • Find the nearest face with designated threshold 𝜃 𝜖 𝜖2 = ( Ω − Ω 𝑘) 𝑘 2 compare with 𝜃 𝜖 • Normalize and find out if it is a face according to𝜃 𝜖 2 𝜖 = ( Φ − Φ 𝑓) 2 compare with 𝜃 𝜖 14/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
15. 15. EIGENFACES FOR RECOGNITON Additional Capabilities Detection and Tracking • Check around every pixel for an image • Try to classify faces using spatiotemporal filtering for a video • Both methods can be combined 15/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
16. 16. EIGENFACES FOR RECOGNITON Additional Capabilities Relation to Neural Networks • Model the system as Neural Network. Φ Ω Φ𝑓 16/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
17. 17. EIGENFACES FOR RECOGNITON Additional Capabilities Increasing Robustness • Multiply around the face with Gaussian for attenuating the effects of background. • Try different scales of eigenfaces, estimate head pose. • Up to 45 𝜊 turned faces with profile might be interpolated. 17/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
18. 18. EIGENFACES FOR RECOGNITON Summary 1. Acquire a set images with variations 2. Calculate eigenfaces and choose M’ of them associated with highest eigenvalues. 3. By projecting each indivual’s images to face space, train the system. 4. Given a test image; project it to face space and make decision according to threshold. 18/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
19. 19. EIGENFACES FOR RECOGNITON Results Percentage results for Recognition from AT&T dataset, equal number of training and test images. 96 90 94 85 92 80 EigenFaces 90 75 Fisher Faces 88 LBP 86 70 10 Faces 50 Faces 100 Faces EigenFaces For Recognition, 91 84 r:1 n:8 r:2 n:8 r:1 n:8 nx:8 nx:8 nx:4 19/23 ny:8 ny:8 ny:4 Presenter: Semih Korkmaz
20. 20. EIGENFACES FOR RECOGNITON Results Speed of Eigenfaces, 200 images for training and testing. Eigenfaces Training+Test Test 10 0.52 seconds 0.02 seconds 50 0.7 0.11 100 0.92 0.25 20/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
21. 21. EIGENFACES FOR RECOGNITON Results (Caltech Face Dataset,’99) Selection of 150 images from Caltech Faces(Converted to Grayscale); 45 Training, 105 test and 10 eigenfaces selected. Eigenfaces used directly and.. Only 7 (!) are correctly classified. EigenFaces For Recognition, 91 21/23 Presenter: Semih Korkmaz
22. 22. EIGENFACES FOR RECOGNITON References [1]Matthew Turk and Alex Pentland. 1991. Eigenfaces for recognition. J. Cognitive Neuroscience 3, 1 (January 1991), 71-86. DOI=10.1162/jocn.1991.3.1.71 http://dx.doi.org/10.1162/jocn.1991.3.1.71 [2]L. Sirovich and M. Kirby, Low-dimensional Procedure for the Characterization of Human Faces, Journal of the Optical Society of America A, 4:519--524, 1987 [3]Belhumeur, P.N.; Hespanha, J.P.; Kriegman, D., "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.19, no.7, pp.711,720, Jul 1997 doi: 10.1109/34.598228 22/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
23. 23. EIGENFACES FOR RECOGNITON References [4] Anil K. Jain and Stan Z. Li. 2005. Handbook of Face Recognition. SpringerVerlag New York, Inc., Secaucus, NJ, USA. 23/23 EigenFaces For Recognition, 91 Presenter: Semih Korkmaz
24. 24. EIGENFACES FOR RECOGNITON Thank you for listening Questions ? EigenFaces For Recognition, 91 Presenter: Semih Korkmaz