Cluster Analysis of Diffusion Tensor Fields with Application to the Segmentation of the Corpus Callosum

Accurate segmentation of the Corpus Callosum (CC) is an important aspect of clinical medicine and is used in the diagnosis of various brain disorders. In this paper, we propose an automated method for two and three dimensional segmentation of the CC using diffusion tensor imaging. It has been demonstrated that Hartigan's K-means is more efficient than the traditional Lloyd algorithm for clustering. We adapt Hartigan's K-means to be applicable for use with the metrics that have a f -mean (e.g. Cholesky, root Euclidean and log Euclidean). Then we applied the adapted Hartigan's K-means, using Euclidean, Cholesky, root Euclidean and log Euclidean metrics along with Procrustes and Riemannian metrics (which need numerical solutions for mean computation), to diffusion tensor images of the brain to provide a segmentation of the CC. The log Euclidean and Riemannian metrics provide more accurate segmentations of the CC than the other metrics as they present the least variation of the shape and size of the tensors in the CC for 2D segmentation. They also yield a full shape of the splenium for the 3D segmentation.