We propose three original approaches for the segmentation of three-dimensional fields of probability density functions. This presents a wide range of applications in medical image processing, in particular for diffusion magnetic resonance imaging where each voxel is assigned with a function describing the average motion of water molecules. Being able to automatically extract relevant anatomical structures of the white matter, such as the corpus callosum, would dramatically improve our current knowledge of the cerebral connectivity as well as allow for their statistical analysis. Our first approach involves the use of a multivariate Gaussian law to approximate the distribution of the components of diffusion tensors for each sub-region of a DTI volume. The second technique relies on the use of the symmetrized Kullback-Leibler distance and on the modelization of its distribution over the subsets of interest in the volume. The third technique considers the 6-dimensional statistical manifold defined by the parameters of the diffusion tensors and proposes a segmentation algorithm by rigorously defining the geodesic distance and the intrinsic mean on this Riemannian manifold. The variational formulations of the problems yield three differents level-set evolutions converging towards the respective optimal segmentation. We validate these approaches on synthetical data and show promising results on the extraction of the corpus callosum and of the lateral brain ventricles from a real dataset.
