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In this paper, we propose a novel multi-dimensional distributed hidden Markov model (DHMM) framework. We first extend the theory of 2D hidden Markov models (HMMs) to arbitrary causal multi-dimensional HMMs and provide the classification and training algorithms for this model. The proposed extension of causal multi-dimensional HMMs allows state transitions in arbitrary causal directions and neighbors. We subsequently generalize this framework further to non-causal models by distributing the non-causal models into multiple causal multi-dimensional HMMs. The proposed training and classification process consists of the extension of three fundamental algorithms to multi-dimensional causal systems, i.e. (1) expectation-maximization (EM) algorithm; (2) general forward-backward (GFB) algorithm; and (3) Viterbi algorithm. Simulation results performed using real-world images and videos demonstrate the superior performance, higher accuracy rate and promising applicability of the proposed DHMM framework.