Image segmentation and classification based on a 2D distributed hidden Markov model

In this paper, we propose a two-dimensional distributed hidden Markov model (2D-DHMM), where dependency of the state transition probability on any state is allowed as long as causality is preserved. The proposed 2D-DHMM model is result of a novel solution to a more general non-causal two-dimensional hidden Markov model (2D-HMM) that we proposed. Our proposed models can capture, for example, dependency among diagonal states, which can be critical in many image processing applications, for example, image segmentation. A new sets of basic image patterns are designed to enrich the variability of states, which in return largely improves the accuracy of state estimations and segmentation performance. We provide three algorithms for the training and classification of our proposed model. A new Expectation-Maximization (EM) algorithm suitable for estimation of the new model is derived, where a novel General Forward-Backward (GFB) algorithm is proposed for recursive estimation of the model parameters. A new conditional independent subset-state sequence structure decomposition of state sequences is proposed for the 2D Viterbi algorithm. Application to aerial image segmentation shows the superiority of our model compared to the existing models.