Relative anatomical location for statistical non-parametric brain tissue classification in MR images

We propose a statistical non-parametric classification of brain tissues from an MR image based on the voxel intensities and on the relative anatomical location of the different tissues. Classically, the overlap of the tissue probability distribution functions for voxel intensities can be reduced by using multi-component (T1w,T2w,Pd,...) MR images, but at a much higher cost for image acquisition. Instead, we generate an artificial image component as the distance from the edges of the segmented brain. The non-parametric k-Nearest Neighbors rule (k-NN) is used since it requires no a priori on the probability distribution of this distance component. The k-NN rule is also tested using different metrics (Euclidean, weighted Euclidean, Mahalanobis) in the classification space to define what ”nearest neighbors” are. The results are twofold: firstly we show that all metrics perform well in ideal conditions, but that the Mahalanobis (and to some extent the weighted Euclidean) metric is more robust in case of under-training of the classifier. Secondly we show that using the relative anatomical location in combination with the intensity information improves the classification of the tissues.