On the Choice of a Tensor Distance for DTI White Matter Segmentation

The segmentation of anatomical structures within the white matter of the brain from DTI is an important task for white matter analysis, and has therefore received considerable attention in the literature during the last few years. Any segmentation method relies on the choice of a tensor dissimilarity measure, which should be small between tensors belonging to the same region and large between tensors belonging to different structures. Many different tensor distances have been proposed in the literature (Frobenius, Kullback-Leibler, Geodesic, Log-Euclidean, Hybrid…) for segmentation or other purposes, and there exist reasons (either theoretical or empirical) to justify the choice of any of them. Thus, determining which is the most appropriate tensor distance for a specific segmentation problem has become an extremely difficult decision. In this chapter we present a study on different tensor dissimilarity measures and their performance for white matter segmentation. The study is based on the use of two different DTI atlases of human brain, which provide a ground truth upon which the distances can be fairly compared. In order for the comparison to be independent of the segmentation method employed, it has been performed in terms of the separability of the different clases. Results show the Hybrid distance to perform better than other traditional tensor dissimilarity measures in terms of separability between classes, while the Frobenius, Kullback-Leibler, Geodesic and Log-Euclidean distances perform similarly.