Geodesic-loxodromes for diffusion tensor interpolation and difference measurement

Kindlmann G, Estepar RSJ, Niethammer M, Haker S, Westin C-F. Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. Med Image Comput Comput Assist Interv 2007;10(Pt 1):1-9.
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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.
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