Approximate Viterbi decoding for 2D-hidden Markov models

While one-dimensional Hidden Markov Models have been very successfully applied to numerous problems, their extension to two dimensions has been shown to be exponentially complex, and this has very much restricted their usage for problems such as image analysis. In this paper we propose a novel algorithm which is able to approximate the search for the best state path (Viterbi decoding) in a 2D HMM. This algorithm makes certain assumptions which lead to tractable computations, at a price of loss in full optimality. We detail our algorithm, its implementation, and present some experiments on handwritten character recognition. Because the Viterbi algorithm serves as a basis for many applications, and 1D HMMs have shown great exibility in their usage, our approach has the potential to make 2D HMMs as useful for 2D data as 1D HMMs are for 1D data such as speech.