Title: Eigenfaces for recognition
Author: M Turk, A Pentland
Year: Journal of Cognitive Neuroscience, 1991
[ Target ]
from training faces, try to find principal dimensions that map the faces into it. Find the significant,characteristic and representative faces (eigenface) from data, then the faces are linear combination of this principal vectors,which can easily compute the similarity.[ Summary ]
we need the following steps to compute the eigenface,1. from training images (N*N), each is a N*N vector. First compute the average vector and subtract all images with average.
2. compute the covariance matrix between them (has been averaged).
3. find eigenvector and eigenvalue of C. The dimension of AA^T is (N^2 x N^2) which will be computationally expensive step. because the data is always smaller than dimension ( M << N^2 ), the rank of A is at most M which means AA^T at most M rank. We just expect to find M-1 meaningful eigenvector, which transform the problem to:
5. Now each face in the training set can be represented as a linear combination of these Eigenvectors:
We can now compute the weight of each training face by eigenfaces.
omega i: the pattern in this basis.
6. [AP- Face Identification]
1) for test face, first subtract from average vector,use this vector for following computation.
2) project onto face space , computing the weight by eigenfaces
3) Determine whether it is a face image by the distance between the face space (original zero-mean face feature v.s projected face feature )
1. Sensitive to head scale
2. Applicable only to front views
3. Good performance only under controlled background (not including natural scenes)
4. how to efficiently decide the threshold?!
[ Meaning ]
1. eigenvector: are the directions in which the images differ from the mean image.2. reduces the dimensionality of the training set, leaving only those features that are critical for face recognition
[ Reference ]
- Good Tutorial by Shubhendu Trivedi
- Eigenface@wiki
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