Geodesic-loxodromes for diffusion tensor interpolation and difference measurement

Authors:
Gordon Kindlmann;Raúl San José Estépar;Marc Niethammer;Steven Haker;Carl-Fredrik Westin
Affiliations:
Department of Radiology, Brigham and Women's Hospital, Harvard Medical School;Department of Radiology, Brigham and Women's Hospital, Harvard Medical School;Department of Psychiatry, Brigham and Women's Hospital, Harvard Medical School;Department of Radiology, Brigham and Women's Hospital, Harvard Medical School;Department of Radiology, Brigham and Women's Hospital, Harvard Medical School
Venue:
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Year:
2007

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Abstract

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.