问题描述：
英语翻译
Due to the difficulty of estimating the number of pixel
classes (or clusters),unsupervised algorithms often assume
that this parameter is known a priori [4,5].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.Basically,there
are two approaches in the literature.One of them is an
exhaustive search of the combined parameter space [6,7]:
segmentations and parameter estimates are obtained via
an iterative algorithm by alternately sampling the label
field based on the current estimates of the parameters.
Then the maximum likelihood estimates of the parameter
values are computed using the current labeling.The resulting
estimates are then applied to a model fitting criterion to
select the optimum number of classes.Another approach
consists of a two step approximation technique [1,8]:the
first step is a coarse segmentation of the image into the
most likely number of regions.Then the parameter values
are estimated from the resulting segmentation and the final
result is obtained via a supervised segmentation.
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 [9],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 RJMCMC
algorithm is used to sample from the whole posterior distribution
in order to obtain a MAP estimate via simulated
annealing [9].Until now,RJMCMC has been applied to
univariate Gaussian mixture identification [10] and its
applications in different areas like inference in hidden Markov
models [11],intensity-based image segmentation [12],
and computing medial axes of 2D shapes [13].The novelty
of our approach is twofold:first,we extend the ideas in
[10,12] and propose a RJMCMC method for identifying
multi-variate Gaussian mixtures.Second,we apply it to
unsupervised color image segmentation.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 for clarity of presentation we will concentrate
on the case of three-variate Gaussians,it is straightforward
to extend the equations to higher dimensions.
Due to the difficulty of estimating the number of pixel
classes (or clusters),unsupervised algorithms often assume
that this parameter is known a priori [4,5].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.Basically,there
are two approaches in the literature.One of them is an
exhaustive search of the combined parameter space [6,7]:
segmentations and parameter estimates are obtained via
an iterative algorithm by alternately sampling the label
field based on the current estimates of the parameters.
Then the maximum likelihood estimates of the parameter
values are computed using the current labeling.The resulting
estimates are then applied to a model fitting criterion to
select the optimum number of classes.Another approach
consists of a two step approximation technique [1,8]:the
first step is a coarse segmentation of the image into the
most likely number of regions.Then the parameter values
are estimated from the resulting segmentation and the final
result is obtained via a supervised segmentation.
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 [9],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 RJMCMC
algorithm is used to sample from the whole posterior distribution
in order to obtain a MAP estimate via simulated
annealing [9].Until now,RJMCMC has been applied to
univariate Gaussian mixture identification [10] and its
applications in different areas like inference in hidden Markov
models [11],intensity-based image segmentation [12],
and computing medial axes of 2D shapes [13].The novelty
of our approach is twofold:first,we extend the ideas in
[10,12] and propose a RJMCMC method for identifying
multi-variate Gaussian mixtures.Second,we apply it to
unsupervised color image segmentation.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 for clarity of presentation we will concentrate
on the case of three-variate Gaussians,it is straightforward
to extend the equations to higher dimensions.
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