DTI Segmentation Using Anisotropy Preserving Quaternion Based Distance Measure

Abstract

In brain research, the second order tensor model of the diffusion tensor imaging (DTI) encodes diffusion of water molecules in micro-structures of tissues. These tensors are real matrices lying in a non-linear space enjoying the Riemannian symmetric space structure. Thus, there are natural intrinsic metrics there, together with their extrinsic approximations. The effective implementations are based on the extrinsic ones employing their vector space structure. In processing DTI, the Log-Euclidean (LogE) metric is most popular, though very far from optimal. The spectral decomposition approach yields the distance measures which respect the anisotropy much better. In the present work, we propose to use the spherical linear interpolation (slerp-SQ) which performs much better than the LogE one and provides better interpolation of geodesics than the spectral-quaternion one. We have implemented the localized active contour segmentation method for these metrics, providing much better handling of the inhomogeneity of the data than global counterpart.