Tracking Lines in Higher Order Tensor Fields

Abstract

While tensors occur in many areas of  science and engineering, little has been done to visualize tensors with order higher than two. Tensors of higher orders can be used for example to describe complex diffusion patterns in magnetic resonance imaging (MRI). Recently, we presented a method for tracking lines in higher order tensor fields that is a generalization of methods known from first order tensor fields (vector fields) and symmetric second order tensor fields. Here, this method is applied to magnetic resonance imaging where tensor fields are used to describe diffusion patterns for example of hydrogen in the human brain. These patterns align to the internal structure and can be used to analyze interconnections between different areas of the brain, the so called tractography problem. The advantage of using higher order tensor lines is the ability to detect crossings locally, which is not possible in second order tensor fields. In this paper, the theoretical details will be extended and tangible results will be given on MRI data sets.