Unsupervised Image Segmentation with Spatial Triplet Markov Trees

Hidden Markov Trees (HMTs) are successful probabilistic models [1] [2] [3] in image segmentation or genetic analysis for example. They offer a good compromise between the random variables that can be modeled and the tractability of the inference within these models. Indeed, the inference procedures can be conducted in a direct, exact fashion [4]. However the conditional independence restrictions in HMTs can be too simplistic with respect to the interactions we wish to model, particularly in the task of natural image segmentation. In this article we study an extension of HMTs called Spatial Triplet Markov Trees (STMTs) which is designed to greatly increase the correlations of the random variables while keeping the possibility of direct and exact inference procedures. The STMT model is tested and compared to other unsupervised segmentation techniques in the case of unsupervised image segmentation. Numerical experiments show that STMTs outperform HMTs and present rich spatial dependencies which are crucial for image segmentation.