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Eigenfaces for Face Recognition ECE 533 Final Project, Fall ‘03

Eigenfaces for Face Recognition ECE 533 Final Project, Fall ‘03. Min Luo, Dept. of Biomedical Engineering Yuwapat Panitchob, Dept. of Electrical & Computer Engineering. OUTLINE. Overview Eigenfaces for Recognition-- Algorithm Eigenfaces for Recognition-- Implementation

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Eigenfaces for Face Recognition ECE 533 Final Project, Fall ‘03

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  1. Eigenfaces for Face Recognition ECE 533 Final Project, Fall ‘03 Min Luo, Dept. of Biomedical Engineering Yuwapat Panitchob, Dept. of Electrical & Computer Engineering

  2. OUTLINE • Overview • Eigenfaces for Recognition--Algorithm • Eigenfaces for Recognition--Implementation • Experiment Result • Conclusion

  3. Overview • Face Representation -- Template-based approaches -- Feature-based approaches -- Appearance-based approaches • Face Detection -- Utilization of elliptical shape of human head (applicable only to front views ) [5] -- Manipulation of images in “face space” [1] • Face Identification -- Performance affected by scale, pose, illumination, facial expression, and disguise, etc.

  4. OUTLINE • Overview • Eigenfaces for Recognition--Algorithm • Eigenfaces for Recognition--Implementation • Experiment Result • Conclusion

  5. Eigenfaces Approach • In the language of information theory…… -- Efficient encoding followed by comparing one face encoding with a database of models encoded similarly • In mathematical terms……. -- Find the principal components of the face distribution, or the eigenvectors of the covariance matrix of the set of face images, called eigenfaces -- Eigenfaces are a set of features that characterize the variation between face images -- Each training face image can be represented in terms of a linear combination of the eigenfaces, so can the new input image -- Compare the feature weights of the new input image with those of the known individuals

  6. Eigenfaces Approach(Contd.) • Major Steps 1. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space 2. Given an image to be recognized, calculate a set of weights of the M eigenfaces by projecting it onto each of the eigenfaces 3. Determine if the image is a face at all by checking if the image is sufficiently close to the face space 4. If it is a face, classify the weight pattern as either a known person of as unknown 5. (Optional) If the same unknown face is seen several times, update the eigenfaces / weight patterns, calculate its characteristic weight pattern and incorporate into the known faces

  7. Calculating Eigenfaces • Set of training images ( is a column vector of size ) Average face of the training set: Each training image differs from the average face by: • A total number of pairs of eigenvectors and eigenvalues of the covariance matrix (C: matrix) Eq. (1) where (A: matrix) Computationally Intractable!

  8. Calculating Eigenfaces (Contd.) • For Computational Feasibility -- Only M-1 eigenvectors are meaningful ( ) Eigenvectors and associated eigenvalues of : Eq. (2) Therefore, are the eigenvalues of , are the associated eigenvalues Eq. (3) The associated eigenvalues allow us to rank the eigenvectors according to their usefulness in characterizing the variation among the images

  9. Using Eigenfaces for Identification • Construction of Known Individuals’ Face Classes -- Images of known individuals are projected onto “face space” by a simple operation , wherei=1, 2, ……, M represents the ith individual, and k=1, 2, ……, M’ represents the weight coefficient of eigenvector . The pattern vector of the ith individual -- If an individual has more than one image, take the average of the pattern vectors of this person • Given a new image -- Project onto face space, and get its pattern vector -- Determine whether is a face image: Eq. (4) If < a predefined threshold , it is a face image; otherwise, not -- Classify either as a known individual or as unknown: Eq. (5) If < a predefined threshold , is identified as the k’th face class; otherwise, it is identified as unknown

  10. Summary of Eigenfaces Recognition Procedure • Collect a set of training images of known individuals. The set may have a number of images for each person, with some variation in expression and in the lighting (say four images of ten people each, so M=40) • Calculate the (40 x 40) matrix L, find its eigenvectors and eigenvalues, and choose the M’ eigenvectors with the highest associated eigenvalues. (Let M’=10 in this example.) • Combine the normalized training set of images according to Eq. (3) to produce the (M’=10) eigenfaces • For each known individual, calculate the class vector by averaging the eigenface pattern vectors [from Eq. (5)] calculated from the original (four) images of the individual. Choose a threshold that defines the maximum allowable distance from any face class, and a threshold that defines the maximum allowable distance from face space [according to Eq. (4)].

  11. Summary of Eigenfaces Recognition Procedure (Contd.) • For each new face image to be identified, calculate its pattern vector , the distance to each known class, and the distance to face space. If the minimum distance , and the distance , classify the input face as the individual associated with class vector ; if the minimum distance , but , then the image may be classified as “unknown”, and optionally used to begin a new face class 6. If the new image is classified as a known individual, this image may be added to the original set of familiar face images, and the eigenfaces may be recalculated (steps 1-4). This gives the opportunity to modify the face spaces as the system encounters more instances of known faces.

  12. OUTLINE • Overview • Eigenfaces for Recognition--Algorithm • Eigenfaces for Recognition--Implementation • Experiment Result • Conclusion

  13. System Structure LoadImages trainingimages.mat eigenfaces.mat ConstructEigenfaces Arrow pointing to a file: file being created/modified Arrow pointing from a file: file being loaded ClassifyNewface faceclasses.mat undoUpdateEigenfaces note_eigenfaces.mat Functional block File containing intermediate data: for the ease of communication between functional blocks

  14. OUTLINE • Overview • Eigenfaces for Recognition--Algorithm • Eigenfaces for Recognition--Implementation • Experiment Results • Conclusion

  15. Training Images Training images: (1) full head scale (2) head-on lighting (3) upright head tilt

  16. Average Face Image & Eigenfaces

  17. Recognition with Different Head Tilts • Total number of test images: 24 -- each person in the training set has two test images -- one test image with head left-oriented, the other with head right-oriented • Recognition results -- true-positive’s: 11 -- false-positive’s: 13 -- false-negative’s (identified as unknown): 0 training image test image 1 test image 2

  18. d a  Recognition with Different Head Tilts(True-positive examples) david irfan b • training image • test image 1 • test image 2 e • training image • test image 1 c

  19. a c Recognition with Different Head Tilts(False-positive examples) foof WRONG!  b d b & d: test images a: b’s corresponding training image c: d’s corresponding training image

  20. Recognition with Varying Illuminance • Total number of test images: 24 -- each person in the training set has two test images -- one test image with 45 degree lighting, the other with 90 degree lighting • Identification results -- true-positive’s: 21 -- false-positive’s: 3 -- false-negative’s (identified as unknown): 0 training image test image 1 test image 2

  21. a b c Recognition with Varying Illuminance (Contd.)  True-positive example: stan  False-positive example: ming • training image, head-on lighting • test image, light moved by 45 degrees d c. training image, head-on lighting d. test image, light moved by 90 degrees

  22. Recognition with Varying Head Scale • Total number of test images: 24 -- each person in the training set has two test images -- one test image has a medium head scale, the other has a small one • Recognition results -- true-positive’s: 7 -- false-positive’s: 17 -- false-negative’s (identified as unknown): 0 training image test image 1 test image 2

  23. a d Recognition with Varying Head Scale (Contd.) True-positive example: stan  b c • training image, full head scale • test image 1, medium head scale • test image 2, small head scale False-positive example: ming  d. training image, full head scale e. test image, medium head scale e

  24. Experiment Result Summary • From the experiments performed -- fairly good recognition rate with varying illuminance: 21/24 -- acceptable recognition rate with different head tilts: 11/24 -- poor identification with varying head scale: 7/24 • Large case study needs carrying out before a general conclusion can be drawn -- large training set: large group of people + a number of face images for each individual -- numerous testing: face images of people who are or aren’t in the training set -- combination of condition changes: e.g. head scale change + lighting change • Thresholding issue -- no false-negative identification in the experiment, because is set to be large -- tradeoff between false-negative and false-positive identification rates: they cannot be reduced simultaneously; optimal choice of could well balance them

  25. OUTLINE • Overview • Eigenfaces for Recognition--Algorithm • Eigenfaces for Recognition--Implementation • Experiment Result • Conclusion

  26. Advantages & Limitations of Eigenfaces Recognition Algorithm • Advantages 1. Ease of implementation 2. No knowledge of geometry or specific feature of the face required 3. Little preprocessing work • Limitations 1. Sensitive to head scale 2. Applicable only to front views 3. Good performance only under controlled background (not including natural scenes)

  27. Further Improvement • To reduce false-positive rate, return a number of candidates from existing face classes instead of a single face class • Regarding the pattern vector representing a face class, make each face class consist of several pattern vectors, each constructed from a face image of the same individual taken under a certain condition, instead of taking the average of these pattern vectors to represent the face class • To be discovered…

  28. References • “Eigenfaces for recognition”, M. Turk and A. Pentland, Journal of Cognitive Neuroscience, vol.3, No.1, 1991 • “Face recognition using eigenfaces”, M. Turk and A. Pentland, Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 586-591, 1991 • “Face recognition for smart environments”, A. Pentland and T. Choudhury, Computer, Vol.33 Iss.2, Feb. 2000 • “Face recognition: Features versus templates”, R. Brunelli and T. Poggio, IEEE Trans. Pattern Analysis and Machine Intelligence, 15(10): 1042-1052, 1993 5. “Human face segmentation and identification”, S. A. Sirohey, Technical Report CAR-TR-695, Center for Automation Research, University of Maryland, College Park, MD, 1993

  29. References (Contd.) 6. “Human and machine recognition of faces: A survey”, R. Chellappa, C. L. Wilson, and S. Sirohey, Proc. of IEEE, volume 83, pages 705-740, 1995 7. “Eigenfaces vs. fisherfaces: Recognition using class specific linear projection”, P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, IEEE Trans. Pattern Analysis and Machine Intelligence, 19(7):711-720, 1997 8. “Illumination cones for recognition under variable lighting: Faces”, A. S. Georghiades, D. J. Kriegman, and P. N. Belhumeur, Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 52-59, 1998 • “Automatic recognition and analysis of human faces and facial expressions: A survey”, A. Samal and P. A. Iyengar, Pattern Recognition, 25(1): 65-77, 1992 • ftp://whitechapel.media.mit.edu/pub/images/

  30. & Min Luo Yuwapat Panitchob Thank you!

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