Kindlmann G, Estepar RSJ, Niethammer M, Haker S, Westin CF. Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. Med Image Comput Comput Assist Interv. 2007;10(Pt 1):1–9.
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.Last updated on 02/24/2023