A New Approach to Probabilistic Image Modeling with Multidimensional Hidden Markov Models

Abstract

This paper presents a novel multi-dimensional hidden Markov model approach to tackle the complex issue of image modeling. We propose a set of efficient algorithms that avoids the exponential complexity of regular multidimensional HMMs for the most frequent algorithms (Baum-Welch and Viterbi) due to the use of a random dependency tree (DT-HMM). We provide the theoretical basis for these algorithms, and we show that their complexity remains as small as in the uni-dimensional case. A number of possible applications are given to illustrate the genericity of the approach. Experimental results are also presented in order to demonstrate the potential of the proposed DTHMM for common image analysis tasks such as object segmentation, and tracking.