Following brain/non-brain segmentation, tissue-type segmentation can be performed, that is, classification of each voxel into grey, white, or CSF (cerebro-spinal fluid) and possibly pathology (e.g., lesion). It is common to segment purely on the basis of voxel intensity, once intensity thresholds have been found to optimally distinguish between the different tissue classes. This can be considered as an analysis of the image histogram, where the different classes appear (ideally) as separate peaks, which have a spread caused by factors such as image noise, motion artefacts, partial-volume effect, bias field (intensity fluctuations across the image caused by inhomogeneities in the radio-frequency field) and true within-class variation. This spread can cause serious mislabelling of voxels, particularly if the bias field is strong.
A central problem is that robust and accurate estimation of the bias field ideally requires perfect knowledge of the segmentation, whilst obtaining a perfect segmentation requires that the bias field be known and corrected. This circularity of dependence means that a sensible approach to both problems is to solve the two problems together, in practise iterating between estimating the segmentation and the bias field, until convergence. This is the approach taken in FAST (FMRIB's Automated Segmentation Tool) [45]. The histogram is modelled as a mixture of Gaussians (one for each class), giving each class's mean (and variance) intensity. Each voxel is then labelled by taking into account not just its intensity with respect to the estimated class means, but also the labelling of its local neighbours - a Markov random field (MRF) is placed on the labelling, causing spatial regularisation (i.e., smoothness of segmentation). This greatly reduces the effect of noise on the segmentation. The segmentation allows an idealised reconstruction of the image; subtracting this from the real image (and smoothing) gives an estimate of the bias field. This whole process is then iterated several times.
If required, FAST also models the partial volume effect (PVE) at each voxel. The voxel's intensity with respect to the global class mean and variance intensities is used to estimate the PVE, and this is augmented with an MRF on the PVE to spatially regularise with local voxels.
The above approach easily generalises to ``multi-channel segmentation'', i.e. if more than one input modality (image type) is available. For example, if both T1-weighted and proton density images are available, the input can be thought of as a vector image instead of just a scalar. FAST allows for two or more input images, which can give improved results, for example, in the deep grey structures where T1-only segmentation often has problems due to the intermediate (between white and cortical grey) intensities of some subcortical ``grey'' mattter.
FAST does not use segmentation priors (images in standard space of the expected distribution of the tissue types, averaged over many subjects) by default, as the prior segmentation images tend to be very blurred, and therefore not very informative. However, this option can be turned on, for example, to aid the initial segmentation in the case of very bad bias field.