A Variational, Non-Parametric Approach to the Fuzzy Segmentation of Diffusion Tensor Images

This paper presents a novel variational approach for the segmentation of diffusion tensor images (DTI). After a certain fiber bundle has been tracked by means of an arbitrary fiber tracking algorithm, we suggest to use the DTI segmentation algorithm to better determine the true borders of the fiber bundle. Specifically, we perform kernel density estimations of the probability density functions (PDFs) of the principal diffusion directions in the foreground to be segmented and the background. Thus, we choose a non-parametric approach and do not make any assumption on the distribution of the underlying data. The estimated PDFs are employed to construct a novel energy functional to be minimized. The energy functional contains a fuzzy membership function and a regularization term, to guarantee the smoothness of the resulting segmentation. A robust and efficient two-phase method is used to minimize the energy functional and simultaneously update the density functions. The algorithm is validated on both simulated DTI phantoms and real data.