Textures and wavelet-domain joint statistics

This paper presents an empirical study of the joint wavelet statistics for textures and other random imagery. There is a growing realization that modeling wavelet coefficients as independent, or at best correlated only across scales, assuming independence within a scale, may be a poor assumption. While recent developments in wavelet-domain Hidden Markov Models (notably HMT-3S) account for within-scale dependencies, we find empirically that wavelet coefficients exhibit within- and across-subband neighborhood activities which are orientation dependent. Surprisingly these structures are not considered by the state-of-the-art wavelet modeling techniques. In this paper we describe possible choices of the wavelet statistical interactions by examining the joint-histograms, correlation coefficients, and the significance of coefficient relationships.