Pseudo-linear scale space on diffusion tensor images of brain white matter: A Mathematica 6.0 package for computing and visualizing pseudo-linear scale space on symmetric positive tensor fields

In this paper we discuss a scale space approach for the geometric analysis of diffusion tensor images, and show some examples of how Mathematica 6.0 is useful in such an analysis. Diffusion tensor imaging (DTI) is a relatively new noninvasive in-vivo medical imaging modality that is suited in inferring the anatomical structure of inhomogeneous tissue such as brain white matter or muscle. The standard DTI method provides a probabilistic model for the Brownian motion of water in the tissue by assigning a symmetric positive definite (SPD) 3 by 3 matrix (tensor) to each voxel (volume element) in the image. We are specifically interested in the connectivity of the subregions in the tissue, e.g. how different areas of brain cortex are connected to each other. As any other imaging method DTI is also sensitive to noise. Here we particularily want to address the effect of noise on connectivity analysis and present novel methods to alleviate this problem. For simplicity we illustrate these methods in dimension two