Multi-Dimensional Dependency-Tree Hidden Markov Models

In this paper, we propose a new type of multi-dimensional hidden Markov model based on the idea of dependency tree between positions. This simplification leads to an efficient implementation of the re-estimation algorithms, while keeping a mix of horizontal and vertical dependencies between positions. We explain DT-HMM and we present the formulas for the maximum likelihood re-estimation. We illustrate the algorithm by training a 2-dimensional model on a set of coherent images