Hidden Markov Multiresolution Texture Segmentation

A texture segmentation algorithm is developed, utilizing a wavelet-based multi-resolution analysis of general imagery. The wavelet analysis yields a set of quadtrees, each composed of highhigh (HH), high-low (HL) and low-high (LH) wavelet coefficients. Hidden Markov trees (HMTs) are designed for the quadtree HH, HL and LH wavelet coefficients. Many textures have intricate structure, extending beyond the support of a single quadtree. Therefore, for a given texture we define a set of states, each characterized by unique statistics. The state occupied by a given quadtree is “hidden”, and a hidden Markov model (HMM) is developed to characterize the statistics of a given quadtree with respect to the statistics of surrounding quadtrees. Each HMM state is characterized by a unique set of HMTs (one each for the HH, HL and LH wavelet coefficients). An HMM-HMT model is developed for each texture of interest, with which texture segmentation is achieved. Several numerical examples are presented to demonstrate the model, with comparisons to alternative approaches.