In this paper, we propose a novel distributed causal multi-dimensional hidden Markov model (DHMM). The proposed
model can represent, for example, multiple motion trajectories of objects and their interaction activities in
a scene; it is capable of conveying not only dynamics of each trajectory, but also interactions information between
multiple trajectories, which can be critical in many applications. We firstly provide a solution for non-causal,
multi-dimensional hidden Markov model (HMM) by distributing the non-causal model into multiple distributed
causal HMMs. We approximate the simultaneous solution of multiple HMMs on a sequential processor by an
alternate updating scheme. Subsequently 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. The new model can be applied to many other areas such as
image segmentation and image classification. Simulation results in classification of multiple interacting trajectories
demonstrate the superior performance and higher accuracy rate of our distributed HMM in comparison to
previous models.
In this paper, we propose a two-dimensional distributed hidden Markovmodel (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 Markovmodel (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.
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