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

• Published in: IEEE transactions on image processing Vol. 18; no. 6; pp. 1304 - 1313
• Main Authors: Xiang Ma, Schonfeld, D., Khokhar, A.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation; Classification; Classification algorithms; Coding, codes; Computation; Computational modeling; Computer simulation; Distributed computing; Exact sciences and technology; Hidden Markov model (HMM); Hidden Markov models; Image classification; Image processing; Image segmentation; Information, signal and communications theory; Mathematical models; Miscellaneous; Motion analysis; motion trajectory analysis; Multidimensional systems; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Speech recognition; Studies; Telecommunications and information theory; video classification; Viterbi algorithm; Performance evaluation; Probabilistic approach; Image processing; motion trajectory analysis; Updating; Distributed computing; Computational complexity; Viterbi code; Image segmentation; Hidden Markov model (HMM); Accuracy; Simulation; Hidden Markov models; Multidimensional model; Signal processing; video classification; Causality; Approximate solution; Multidimensional system; EM algorithm; Learning algorithm; Motion analysis; Image classification
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2009.2017166

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.