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 [Int. J. Comput. Vis. 43 (2001) 29], Cula and Dana [Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2001) 1041], and Varma and Zisserman [Proceedings of the Seventh European Conference on Computer Vision 3 (2002) 255], and the Bayesian framework most closely represented by the work of Konishi and Yuille [Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2000) 125]. (C) 2004 Elsevier B.V. All rights reserved.