Nonlinear models for the statistics of adaptive wavelet packet coefficients of texture

Probabilistic adaptive wavelet packet models of texture provide new insight into texture structure and statistics by focusing the analysis on significant structure in frequency space. In very adapted subbands, they have revealed new bimodal statistics, corresponding to the structure inherent to a texture, and strong dependencies between such bimodal subbands, related to phase coherence in a texture. Existing models can capture the former but not the latter. As a first step towards modelling the joint statistics, and in order to simplify earlier approaches, we introduce a new parametric family of models capable of modelling both bimodal and unimodal subbands, and of being generalized to capture the joint statistics. We show how to compute MAP estimates for the adaptive basis and model parameters, and apply the models to Brodatz textures to illustrate their performance.