We can optionally use prior information by applying a Hidden Markov Random Field (HMRF) model. Using this model we introduce spatial constraints based on neighbouring voxels of a 3x3x3 cube. The center voxel has 26 neighbours and we can calculate MRF energy by counting the number of neighbours. Neighboring voxels are expected to have the same class labels. The prior probability of the class and the likelihood probability of the observation is combined to estimate the Maximum a posteriori (MAP). Prior probability can be weighted between 0 (no HMRF) and 1 (maximum HMRF for very noisy data) to cover different levels of noise. Parts of this version are based on an implementation of a Gaussian Hidden Markov Random Field (GHMRF) approach by Meritxell Bach Cuadra et al. (2005).
The idea is to remove isolated voxels of one tissue class which are unlikely to be member of this tissue type. It also closes holes in a cluster of connected voxels of one tissue type. In the resulting segmentation the noise level will be minimized.
Depending on your scanner and the used MR sequence your T1-images will contain at least 3% noise level. Hence, I would recommend for most images a medium HMRF weighting of 0.3. If your images are affected by more noise level you can choose a larger HMRF weighting.
The resulting files are indicated by the term “_HMRF” at the end of the filename.
Use of MRF prior probability
Effect of noise reduction
Comparison with segmentation without MRF approach