Dot Product of Tensor Characteristic Polynomials: A Diffusion Tensor Imaging Segmentation Approach

The development of quantitative measurements from DTI may have important clinical and biological applications, helping doctors to infer microstructural characteristics that was undetectable using other techniques as well as pathological changes in the microstructure of the tissue. Such measures will enable the study of normal development of the anatomical connections of the human brain, its natural variations, and the structural impact resulting from degenerative and demyelinating diseases.

We propose a new intervoxel measure that may uses the whole tensor information in its formulation. Towards this goal, we will assess measures of similarity between tensors that highlight the edges of the white matter tracts. Among these measures we have the Log-Euclidean distance and a new measure that we will call Polynomial Inverse Transformation as it represents the transformation between the tensors matrices and their inverses. These measures can be used to build functions that form the basis for the evolution of deformable surfaces that will enable the segmentation of white matter fascicles using diffusion tensor imaging.