The PUB-MRF algorithm uses a Markov Random Field model to update the label probabilities obtained with a multi-atlas registration method. In particular, the algorithm has been tested extensively with MAGeT-Brain.

PUB-MRF starts by subdividing the stereotaxic space into a high-confidence and a low-confidence region. A voxel is included in the low-confidence region if and only if for any label, the percentage of votes at that voxel does not exceed a given threshold. Then, PUB-MRF iterates through the voxels in the low-confidence region. At each voxel, a local Markov Random Field is defined. We consider that the set of all labels which receive at least one vote on a given voxel is a partition of the sample space.

The doubleton potentials are estimated using the segmentation votes at the voxel itself, and in an immediate 26-voxel neighborhood. The singleton potential for each label is estimated using the local intensity values in the brain scan, under the assumption that with a large number of voxels, this will approximately correspond to a normal distribution. For any voxel in the low-confidence region, the final label is the argmin of the Markov Random Field energies, which corresponds to the argmax of the updated label probabilities. In the high-confidence region, the output labels are obtained using majority vote.

Threshold
Let N be the number of labels which receive at least one at voxel v. Then v is in the low-confidence region if and only if, for any label l, P(L(v) = l) < (1.0/N + self.threshold)

Patch Length
At each low-confidence voxel v, the region used to compute the singleton potential is a cube with edge length (2*self.patch_length + 1) centered at v.

Alpha
Corresponds to the relative weight of the doubleton potential with respect to the singleton potential in the MRF energy computation.

Beta
The weights in the 26-voxel neighborhood for the doubleton potential are evaluated with an expotential decay function with parameter self.beta, with respect to the Euclidian norm.

(C) Charles Lagace, Nikhil Bhagwat, Chakravarty Lab
http://www.douglas.qc.ca/researcher/mallar-chakravarty?locale=en