Thursday, March 6, 2008

[Reading] Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection

This paper formally classify the variation of the facial appearance into different classes. The variation can be due to different persons, different expressions, or different lighting conditions. For face identification, we hope the variations due to different expressions and lightings can be reduced by processing while the variation due to different persons are preserved. The author find that a linear projection obtained by LDA can efficiently achieve this goal. This result is very important since the projection does not only reduce the computation for matching, but also minimize the effect of the facial and lighting variation to the face recognition.

One thing should be noted is that this paper is very clear. It is maybe the best document I've ever read that explains LDA best. One interesting problem is that finding the optimal projection here is a generalized eigenvalue problem: Ax = \lambda Bx, where B and A are n-by-n matrices which could be very large for big images. Though the paper does not discuss the method to compute this, I believe a trick similar to the one used eigenface should be applied here, and I will make another post after I find it. (or if someone tell me directly :P)

Since both eigenface and fisherface are very old, I can't know the state-of-the-art in face recognition. However, these two papers are both very good at showing the applications of dimension reduction techniques.


AcmeChimera said...

I think the author detours the problem by a pre-PCA on the data?

Chia-Kai Liang said...

Yeah I noted it. But what I want to know is what if the number of class is large and there is no way to perform a PCA before LDA?