HARDI Segmentation via Fourth-Order Tensors and Anisotropy Preserving Similarity Measures

Abstract

In this work, we discuss the higher-order tensors appearing in high angular resolution diffusion tensor imaging, and we have tested two segmentation methods, the Riemannian spectral clustering and the deformable models, using several projections of the fourth-order tensors to the second-order ones, and diverse similarity measures on them. High angular resolution diffusion imaging has proved its effectiveness in modeling white matter brain structures along with the fiber intersection regions, which is of high importance in brain research. Along with other known projections, we observe that the diagonal components of the flattened fourth-order tensors also live in the well-known Riemannian symmetric space of symmetric positive-definite matrices. We discuss and compare several natural approximations of the distance on the latter space to be used in clustering and segmentation algorithms. The results show that some of the projections unfold the geometry of the higher-order tensors very well, and we also propose the exploitation of the spherical linear interpolation spectral quaternion metric, which proves to be very effective. The latter claims are supported by experimental comparison of the effectiveness of our algorithms with the more usual logarithmic Euclidean and spectral quaternionic metrics, in particular in the presence of noise. Our methods allow to distinguish individual objects in complex structures with high curvatures and crossings.