multivariate poisson hidden markov models for analysis of spatial ...

egularity constraints on the underlying classes of an observed image, which allow
Bayesian optimization of the classification. However, the computing time is often
prohibitive with this approach. A substantially quicker alternative is to use a hidden
Markov model (HMM), which can be adapted to two-dimensional analysis through
different types of scanning methods (e.g. Line Scan, Hilbert-Peano scan etc.). Markov
random field models can only be used for small neighbourhoods in the image, due to the
computational complexity and the modeling problems posed by large neighbourhoods
(Aas et al., 1999). Leroux and Puterman (1992) used maximum–penalized likelihood
estimation to estimate the independent and the Markov-dependent mixture model
parameters. In their analysis, they focus on the use of Poisson mixture models assuming
independent observations and Markov-dependent models (or hidden Markov Models)
for a set of univariate fetal movement counts. Extending this idea, for a set of
multivariate Poisson counts, a novel multivariate Poisson hidden Markov model
(Markov-dependent multivariate Poisson finite mixture model) is introduced. These
counts can be considered as a stochastic process, generated by a Markov chain whose
state sequence cannot be observed directly but which can be indirectly estimated
through observations. Zhang et al. (2001) described that the finite mixture model is a
degenerate version of the hidden Markov random field model. Fjφrtoft (2003) explained
that the classification accuracy of hidden Markov random fields and hidden Markov
models were not differing very much. Hidden Markov models are much faster than the
ones based on the Markov random fields (Fjφrtoft et al., 2003). The advantage of hidden
Markov models compared to the Markov random field models is the ability to combine
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