Comparison between fourth and second order DT-MR image segmentations

A second order tensor is usually used to describe the diffusion of water for each voxel within a Diffusion Tensor Magnetic Resonance (DT-MR) images. However, a second order tensor approximation fails to accurately represent complex local tissue structures such as crossing fibers. Therefore, higher order tensors are used to represent more complex diffusivity profiles. In this work we examine and compare segmentations of both second order and fourth order DT-MR images using the Random Walker segmentation algorithm with the emphasis of pointing the shortcomings of second order tensor model in segmenting regions with complex fiber structures. We first adopt the Random Walker algorithm for segmenting diffusion tensor data by using appropriate tensor distance metrics and then demonstrate the advantages of performing segmentation on higher order DT-MR data. The approach proposed takes advantage of all the information provided by the tensors by using suitable tensor distance metrics. The distance metrics used are: the Log-Euclidean for the second order tensors and the normalized L2 distance for the fourth order tensors. The segmentation is carried out on a weighted graph that represents the image where, the tensors are the nodes and the edge weights are computed using the tensor distance metrics. Applying the approach to both synthetic and real DT-MRI data yields segmentations that are both robust and qualitatively accurate.