The finite mixture (FM) model is the most commonly used model for
statistical segmentation of brain MR images because of its simple
mathematical form and the piecewise constant nature of ideal brain
MR images. However, being a histogram-based model, the FM has an
intrinsic limitation - no spatial information is taken into
account. This causes the FM model to work only on well-defined
images with low noise level; unfortunately, this is often not the
the case due to artifacts such as partial volume effect and bias
field distortion. Under such conditions, FM model-based methods
produce unreliable results. In this paper, we propose a novel
hidden Markov random field (HMRF) model, which is a stochastic
process generated by a Markov random field whose state sequence
cannot be observed directly but which can be observed through
observations. Mathematically, it can be shown that the FM model is
a degenerate version of the HMRF model. The advantage of the HMRF
model derives from the way in which the spatial information is
encoded through the mutual influences of neighbouring sites.
Although MRF modelling has been employed in MR image segmentation
by other researchers, most reported methods are limited to using
MRF as a general prior in an FM model-based approach. Moreover,
they either lack a proper parameter estimation step to fit the FM
model [
14,
16] or the parameter estimation procedure
they use, such as ML or EM [
33,
27,
20],
suffers greatly from the limitation of the FM model mentioned
above. To fit the HMRF model, an expectation-maximization (EM)
algorithm is used. We show that by incorporating both the HMRF
model and the EM algorithm into a HMRF-EM framework, an accurate
and robust segmentation can be achieved. Moreover, the HMRF-EM
framework can easily be combined with other techniques. As an
example, we show how the bias field correction algorithm of
Guillemaud and Brady [
13] can be incorporated into
this framework. A three-dimensional fully automated approach for
brain MR image segmentation is achieved and significant
improvement is obtained compared to the Guillemaud-Brady
algorithm.
