1. Face Recognition and Detection Using Eigenfaces
Based on: M.A. Turk and A. P. Pentland,“Face Recognition Using Eigenfaces,”Proc. IEEE Conf. on CVPR, Maui, HI, USA, pp , Jun
Kohsia Huang
ECE 285 Class Presentation
Prof. Mohan Trivedi
Winter, 2001
Department of Electrical and Computer Engineering
University of California, San Diego

2. Background Works Detecting individual face features
- Difficult to extend to non-frontal views
- Insufficient representation for face identification
Neural network approaches
Multiresolution template matching
Other methods:
- A. Pentland and T. Choudhury, “Face Recognition for Smart Environments,” IEEE Comp. Mag., pp , Feb
- P. Penev and J. Atick, “Local Feature Analysis: A General Statistical Theory for Object Representation,” Network: Compu. in Neural Syst. 7, pp , Mar

3. Interpretations of Eigenface
Information Theory: Extract relevant information in face images, encode face images efficiently, and compare individual face images.
Linear Algebra: Find principle components of the distribution of faces, which is the eigenvectors of the covariance matrix of the training faces. Principle components = Features = Eigenfaces.

4. Eigenface Algorithm
Dimension reduction: Face images can be represented as a linear combination of the eigenfaces.
Approximation: The feature space or eigenface space can be approximated by the eigenfaces associated with the largest eigenvalues.

5. Eigenface Example

6. Procedure
Initialization: Obtain training faces and calculate the eigenfaces.
Operating: Calculate a set of weights by projecting the test face into eigenface space.
Face detection: If the image is close to the face space, it is a face image.
Recognition: If the test face is close to a certain training face, it is recognized.

7. Formulation Eigenface Recognition Algorithm Training Face Vectors
Correlation Matrix
Singular Value Decomposition
Eigenface Representation

8. Face Detection
Face Space
Error
Projection
Face Image
The error is the difference between the original image and its projection image onto eigenface space.
If the error is within a threshold, the image is detected as a face image.
Efficient calculation available.

9. Face Recognition
Face Space
Face Image
Projection
Error
Class B
Class A
Class C
If the projection of face image onto eigenface space is close to one training face, it is identified as that training face.
Distance measure can be Euclidian distance.

10. Classification Summary
Four possible patterns of an input image:
Near face space and its projection is near a face class  Recognized.
Near face space but its projection is distant from all face classes  Unknown face.
Distant from face space but its projection is near a face class  Not a face image.
Distant from face space and its projection is distant from all face classes  Not a face image.

11. Compare with Projection Vectors of Training Faces
Implementation
Projection into
Eigenface Space
Snapshot
Image Processing
& Face Extraction
Projection Vector
Face Image
Compare with Projection Vectors of Training Faces
Classification
Person ID & Facing Angle
Near Y N
Not a Face Image

12. Accuracy
2500 face images:
Infinite thresholds: 96% correct on lighting variation, 85% on face orientation variation, 64% on size (zooming) variation.
Limited thresholds: Adjust unknown rate to 20%, the above correct rates becomes 100%, 94%, and 74%, respectively.
25 face images:
74% correct rate for controlled conditions.

13. Accuracy (Cont.) FERET Competition: Standardized testing criteria.
Not accurate enough for lower dimension eigenface spaces.
Needs approximately 120 dimensions to compete with local feature analysis.