An Approximate Bayes Rule for Texture Classification Based on Filter Marginals.

• Activity Number: 137
• Type: Topic Contributed
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing*
• Author(s): Elizaveta Levina*+ and Peter Bickel
• Affiliation(s): University of California, Berkeley and University of California, Berkeley
• Keywords: texture classification ; Bayes rule ; manifold projection ; Mallows distance

Abstract

Textures are commonly represented by marginal distributions of filter responses and compared via some distance on probability distributions. We take a different approach and construct a non-parametric approximation to the likelihood ratio of distributions of filter marginals. We create a training set of texture patches from each class and estimate the classification error by leave-one-out cross-validation. Each filter marginal is approximated by the empirical distribution over the sample image. Class distributions are in turn approximated by nearest neighbor density estimation using the training data. This rule performs uniformly better, and for small texture patches the error is reduced by more than 20%, as compared to a commonly used distance on distributions. We beleive this method works well because the data concentrate on a much lower-dimensional subspace. When a filter marginal is projected to a ten-dimensional manifold, the classification results remain almost as good. We also show how this Bayes rule relates to the Mallows metric and suggest a modification to this metric which improves its performance for texture classification.