[Paper Review] Eigenfaces vs. Fisherfaces - Recognition Using Class Specific Linear Projection

The main contribution of this work should be the application of Fisher Linear Discriminant method to face recognition. The idea of FLD(or more conveniently, LDA) is quite simple: as our objective is to classify the input into several categories and we are going to compress the dimensions, why not choose a dimension-reduction mapping that best favors this purpose. This is in contrary to methods like SVM where the data are projected to a higher dimensional space for better separation.

Since FLD is designed for classification purpose, it is no wonder it can outperform pure PCA as the later has no such special intention. Just like what is shown in the paper, PCA aims to retain the most scatter of data points only, so the resulting axes may just mix up the originally isolating groups. As FLD tries to maximize the ratio of between-class distance to within-class distance during optimization, it may not suffer from these kinds of chaos. Nevertheless, one can find a projection subspace such that the within-class distance become zero due to the large difference between the observation's dimension and the number of observations. Thus, a pre-processing PCA is still required.

Another observation in the paper is based on the fact that the reflectance of a Lambertian surface is solely determined by the light source direction, the surface normal and the albedo of the object. As the later two are already determined, the real appearance of each pixel(ignoring shadow and self-reflectance etc.) lies on a 3D space spanned by the the positions of the light source. Although this might be a common sense in the rendering field, it seems rather interesting to me.

One thing that also interests me is the glasses recognition by FLD. In fact, I have read one work that attacks a similar problem by explicitly building a subspace that accounts for the appearance variation from layered objects. The result of their method on glasses removal looks like that(images from the paper):



This picture perfectly underlines the value of class-aware subspace projection.