A Riemannian scalar measure for diffusion tensor images

Authors:
Laura Astola;Andrea Fuster;Luc Florack
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, Den Dolech 2, 5600 MB Eindhoven, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, Den Dolech 2, 5600 MB Eindhoven, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, Den Dolech 2, 5600 MB Eindhoven, The Netherlands
Venue:
Pattern Recognition
Year:
2011

Citing 8
Cited 1

New Approaches to Estimation of White Matter Connectivity in Diffusion Tensor MRI: Elliptic PDEs and Geodesics in a Tensor-Warped Space

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
Finsler Active Contours

IEEE Transactions on Pattern Analysis and Machine Intelligence
Front-End Vision and Multi-Scale Image Analysis: Multi-scale Computer Vision Theory and Applications, written in Mathematica

Front-End Vision and Multi-Scale Image Analysis: Multi-scale Computer Vision Theory and Applications, written in Mathematica
Finsler Geometry on Higher Order Tensor Fields and Applications to High Angular Resolution Diffusion Imaging

SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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 crossing detector based on the structure tensor

ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging

Journal of Mathematical Imaging and Vision

Finsler Streamline Tracking with Single Tensor Orientation Distribution Function for High Angular Resolution Diffusion Imaging

Journal of Mathematical Imaging and Vision

Quantified Score

Hi-index	0.04

Visualization

Abstract

We study a well-known scalar quantity in Riemannian geometry, the Ricci scalar, in the context of diffusion tensor imaging (DTI), which is an emerging non-invasive medical imaging modality. We derive a physical interpretation for the Ricci scalar and explore experimentally its significance in DTI. We also extend the definition of the Ricci scalar to the case of high angular resolution diffusion imaging (HARDI) using Finsler geometry. We mention that the Ricci scalar is not only suitable for tensor valued image analysis, but it can be computed for any mapping f:R^n-R^m(m@?n).