The objective of this paper is to examine statistical approaches to
the classification of textured materials from a single image obtained
under unknown viewpoint and illumination. The approaches investigated
here are based on the joint probability distribution of filter
responses.

We review previous work based on this formulation and make two
observations. First, we show that there is a correspondence between
the two common representations of filter outputs - textons and binned
histograms. Second, we show that two classification methodologies,
nearest neighbour matching and Bayesian classification, are equivalent
for particular choices of the distance measure. We describe the pros
and cons of these alternative representations and distance measures,
and illustrate the discussion by classifying all the materials in the
Columbia-Utrecht (CUReT) texture database.

These equivalences allow us to perform direct comparisons between the
texton frequency matching framework, best exemplified by the
classifiers of Leung and Malik [IJCV 2001], Cula and Dana [CVPR 2001],
and Varma and Zisserman [ECCV 2002], and the Bayesian framework most
closely represented by the work of Konishi and Yuille [CVPR 2000].