MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
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
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
A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging
Journal of Mathematical Imaging and Vision
A Riemannian scalar measure for diffusion tensor images
Pattern Recognition
CUDA-accelerated geodesic ray-tracing for fiber tracking
Journal of Biomedical Imaging - Special issue on Parallel Computation in Medical Imaging Applications
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We study three dimensional volumes of higher order tensors, using Finsler geometry. The application considered here is in medical image analysis, specifically High Angular Resolution Diffusion Imaging (HARDI) [1] of the brain. We want to find robust ways to reveal the architecture of the neural fibers in brain white matter. In Diffusion Tensor Imaging (DTI), the diffusion of water is modeled with a symmetric positive definite second order tensor, based on the assumption that there exists one dominant direction of fibers restricting the thermal motion of water molecules, leading naturally to a Riemannian framework. HARDI may potentially overcome the shortcomings of DTI by allowing multiple relevant directions, but invalidates the Riemannian approach. Instead Finsler geometry provides the natural geometric generalization appropriate for multi-fiber analysis. In this paper we provide the exact criterion to determine whether a field of spherical functions has a Finsler structure. We also show a fiber tracking method in Finsler setting. Our model also incorporates a scale parameter, which is beneficial in view of the noisy nature of the data. We demonstrate our methods on analytic as well as real HARDI data.