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
A Riemannian Scalar Measure for Diffusion Tensor Images
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
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
Journal of Mathematical Imaging and Vision
Approximating Symmetric Positive Semidefinite Tensors of Even Order
SIAM Journal on Imaging Sciences
Morphological and Linear Scale Spaces for Fiber Enhancement in DW-MRI
Journal of Mathematical Imaging and Vision
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We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358---1372, 2004) of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the variety of existing techniques, we wish to add novel approaches that exploit differential geometry and tensor calculus.In Diffusion Tensor Imaging (DTI), the diffusion of water is modeled by a symmetric positive definite second order tensor, leading naturally to a Riemannian geometric framework. A limitation is that it is based on the assumption that there exists a single dominant direction of fibers restricting the thermal motion of water molecules. Using HARDI data and higher order tensor models, we can extract multiple relevant directions, and Finsler geometry provides the natural geometric generalization appropriate for multi-fiber analysis. In this paper we provide an exact criterion to determine whether a spherical function satisfies the strong convexity criterion essential for a Finsler norm. We also show a novel fiber tracking method in Finsler setting. Our model incorporates a scale parameter, which can be beneficial in view of the noisy nature of the data. We demonstrate our methods on analytic as well as simulated and real HARDI data.