Multiresolution Morphodynamic Diffusion Tensor Imaging

We have proposed and developed a new multiresolution morphological reconstruction approach for diffusion tensor imaging. Our strategy solves simultaneously the segmentation and fusion problem (Verschmelzung/Sonderung duality). Our point of departure is a precise multiresolution statistical interpretation of a three-dimensional variational approach to segmentation that incorporates recursive procedures for computing estimates of inhomogeneous Gaussian Markov random fields. The diffusion tensor is based on a regularized shape operator of the evolving level sets that preserves geometric features by a multiresolution anisotropic curvature evolution. Our geodesic following algorithm is formulated in the mathematically most natural manner - as a nonlinear eigenvalue minimization problem on Stiefel manifold - allowing computation directly right on the surface. This results a computationally efficient and optimal 3D level set reconstruction that can yet generate error statistics, as desired.