Utilizing scatter for pixel subspace selection

Measures of scatter are used in statistical pattern recognition to identify and select important features, computed as linear combinations of the given features. Examples include principal components and linear discriminants. The classic computational procedures require eigenvector decomposition of large matrices, and in the case of images they are only practical for identifying a low dimensional feature subspace. We investigate the case in which the selected features are required to be a subset of the given features. It is shown that the same scatter measures used in the general case can also be used in this discrete selection case, but the computational procedure no longer involves matrix eigenvector decomposition. Instead, the selection of pixels that optimize scatter measures can be accomplished by a very simple and efficient discrete optimization technique that runs in linear time regardless of the subspace size. Applications to clustering and content based indexing are discussed.