The finite mixture (FM) model is the most commonly used model for statistical segmentation
of brain magnetic resonance (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 levels of noise;
unfortunately, this is often not the the case due to artifacts such as partial volume
effect and bias field distortion. Under these 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 MRF whose state sequence cannot
be observed directly but which can be indirectly estimated 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 neighboring sites. Although MRF modeling 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. To fit the
HMRF model, an 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. More importantly, 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 (1997) can be incorporated into this framework to achieve a three-dimensional
fully automated approach for brain MR image segmentation.