Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Statistical variability in nonlinear spaces: application to shape analysis and dt-mri
Statistical variability in nonlinear spaces: application to shape analysis and dt-mri
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution
Journal of Mathematical Imaging and Vision
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Large deformation diffeomorphic metric mapping of orientation distribution functions
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Diffeomorphism invariant riemannian framework for ensemble average propagator computing
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Nonnegative definite EAP and ODF estimation via a unified multi-shell HARDI reconstruction
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Anisotropy Preserving DTI Processing
International Journal of Computer Vision
Hi-index | 0.01 |
Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy $H_{\frac{1}{2}}$ of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.