Due to the difficulty of estimating the number of pixel classes (or clusters), unsupervised algorithms often assume that this parameter is known a priori. When the number of pixel classes is also being estimated, the unsupervised segmentation problem may be treated as a model selection problem over a combined model space.
Our approach consists of building a Bayesian color image model using a
first order MRF. The observed image is represented by a mixture of
multivariate Gaussian distributions while inter-pixel interaction
favors similar labels at neighboring sites. In a Bayesian framework,
we are interested in the posterior distribution of the unknowns
given the observed image. Herein, the unknowns comprise the hidden
label field configuration, the Gaussian mixture parameters, the MRF
hyperparameter, and the number of mixture components (or
classes). Then a MCMC algorithm is used to sample from the whole
posterior distribution in order to obtain a MAP estimate via simulated
annealing. However, classical MCMC methods are restricted to problems
where the dimensionality of the parameter vector is fixed. Therefore,
the estimation of the number of mixture components is not
possible. Recently, a novel method, called Reversible Jump MCMC
(RJMCMC), has been proposed by P. Green. This method makes it possible
to construct reversible Markov chain samplers that jump between
parameter subspaces of different dimensionality. It has also been
applied to univariate Gaussian mixture identification, intensity based
image segmentation, and computing medial axes of 2D shapes. Herein,
RJMCMC allows us the direct sampling of the whole posterior
distribution defined over the combined model space thus reducing the
optimization process to a single simulated annealing run. Another
advantage is that no coarse segmentation neither exhaustive search
over a parameter subspace is required. Although we present the model
in the case of 3 dimensional observations, it is straightforward to
extend it to higher dimensions.