Linear invariant tensor interpolation applied to cardiac diffusion tensor MRI

Authors:
Jin Kyu Gahm;Nicholas Wisniewski;Gordon Kindlmann;Geoffrey L. Kung;William S. Klug;Alan Garfinkel;Daniel B. Ennis
Affiliations:
Department of Radiological Sciences, UCLA, CA, USA, Department of Computer Science, UCLA, CA;Department of Medicine (Cardiology), UCLA, CA;Computer Science Department, University of Chicago, Chicago, IL;Department of Radiological Sciences, UCLA, CA;Department of Mechanical and Aerospace Engineering, UCLA, CA;Department of Medicine (Cardiology), UCLA, CA;Department of Radiological Sciences, UCLA, CA
Venue:
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Year:
2012

Citing 5
Cited 0

A Riemannian Framework for Tensor Computing

International Journal of Computer Vision
Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing

Journal of Mathematical Imaging and Vision
Riemannian geometry for the statistical analysis of diffusion tensor data

Signal Processing
Geodesic-loxodromes for diffusion tensor interpolation and difference measurement

MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Interpolating 3D diffusion tensors in 2D planar domain by locating degenerate lines

ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

Purpose: Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods: Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results: EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion: GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost.