Video Event Classification and Image Segmentation Based on Noncausal Multidimensional Hidden Markov Models

In this paper, we propose a novel solution to an arbitrary noncausal, multidimensional hidden Markov model (HMM) for image and video classification. First, we show that the noncausal model can be solved by splitting it into multiple causal HMMs and simultaneously solving each causal HMM using a fully synchronous distributed computing framework, therefore referred to as distributed HMMs. Next we present an approximate solution to the multiple causal HMMs that is based on an alternating updating scheme and assumes a realistic sequential computing framework. The parameters of the distributed causal HMMs are estimated by extending the classical 1-D training and classification algorithms to multiple dimensions. The proposed extension to arbitrary causal, multidimensional HMMs allows state transitions that are dependent on all causal neighbors. We, thus, extend three fundamental algorithms to multidimensional causal systems, i.e., 1) expectation-maximization (EM), 2) general forward-backward (GFB), and 3) Viterbi algorithms. In the simulations, we choose to limit ourselves to a noncausal 2-D model whose noncausality is along a single dimension, in order to significantly reduce the computational complexity. Simulation results demonstrate the superior performance, higher accuracy rate, and applicability of the proposed noncausal HMM framework to image and video classification.