Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
Spherical Diffusion for 3D Surface Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Control Theory and Fast Marching Techniques for Brain Connectivity Mapping
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
IEEE Transactions on Pattern Analysis and Machine Intelligence
Riemannian Framework for Estimating Symmetric Positive Definite 4th Order Diffusion Tensors
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Ternary quartic approach for positive 4th order diffusion tensors revisited
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Measures for pathway analysis in brain white matter using diffusion tensor images
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
ODF maxima extraction in spherical harmonic representation via analytical search space reduction
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Higher Order Positive Semidefinite Diffusion Tensor Imaging
SIAM Journal on Imaging Sciences
International Journal of Computer Vision
A Riemannian scalar measure for diffusion tensor images
Pattern Recognition
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We introduce a new framework based on Riemann-Finsler geometry for the analysis of 3D images with spherical codomain, more precisely, for which each voxel contains a set of directional measurements represented as samples on the unit sphere (antipodal points identified). The application we consider here is in medical imaging, notably in High Angular Resolution Diffusion Imaging (HARDI), but the methods are general and can be applied also in other contexts, such as material science, et cetera, whenever direction dependent quantities are relevant. Finding neural axons in human brain white matter is of significant importance in understanding human neurophysiology, and the possibility to extract them from a HARDI image has a potentially major impact on clinical practice, such as in neuronavigation, deep brain stimulation, et cetera. In this paper we introduce a novel fiber tracking method which is a generalization of the streamline tracking used extensively in Diffusion Tensor Imaging (DTI). This method is capable of finding intersecting fibers in voxels with complex diffusion profiles, and does not involve solving extrema of these profiles. We also introduce a single tensor representation for the orientation distribution function (ODF) to model the probability that a vector corresponds to a tangent of a fiber. The single tensor representation is chosen because it allows a natural choice of Finsler norm as well as regularization via the Laplace-Beltrami operator. In addition we define a new connectivity measure for HARDI-curves to filter the most prominent fiber candidates. We show some very promising results on both synthetic and real data.