Unifying Statistical Texture Classification Frameworks

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].