One of the beginner topics in a computer vision class is face recognition. Given some assumptions, it is now a solved problem in the AI community – or at-least one which has been given sufficient amount of attention that there are numerous methods that work well at scale in a lot of scenarios.

As part of an effort at maintaining and growing my knowledge-base, I am in the process of spending some amount of time in reviewing course materials that I’d once wisely stored away for posterity. I’ve re-begun with CS231a – the Stanford University course on Computer Vision.

The first lecture discussed two popular methods for face recognition – the first being EigenFaces – a seminal method developed at MIT – http://www.face-rec.org/algorithms/PCA/jcn.pdf. The gist of it is finding the eigen-vectors of the aggregate vectorized image patch training sets – thus significantly reducing the dimensionality of the problem. Given a new image patch vector, find its projection in the lower-dimensional sub-space and run an OTS classifier on it to tell which one of the trained image patch classes (or faces) it is closest too. Nearest neighbor etc. should be sufficient. The eigenvector formulation ensures dimensionality-reduction while preserving the dimensions of maximum variance so that, in a sense, an image patch, say 90×90 (or a vector or length 8100), is compressed to, say, 20 dimensions, such that these 20 dimensions represent most of the variance that exists in image patches of faces. “PCA projection is optimal for reconstruction from a low-dimensional basis but may not be optimal for discrimination”.

The second method discussed was FischerFaces – which improved face recognition significantly over EigenFaces. http://www.cs.columbia.edu/~belhumeur/journal/fisherface-pami97.pdf. The motivation for the method is that EigenFaces, which doing well on dimensionality-reduction, does not preserve between-class separation as a result of doing PCA. This is nicely illustrated on page 4 of the paper in a diagram. It shows through a toy example how choosing the principal component causes a complete loss in separability between classes.

A lot of paper-reading lies ahead…

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