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.
This work supported by NIH grants U41-RR019703, P41-RR13218, R01-MH050740, and R01-MH074794. DTI data courtesy of Dr. Susumu Mori, Johns Hopkins University, supported by NIH R01-AG20012-01 and P41-RR15241-01A1.
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Kindlmann, G., San José Estépar, R., Niethammer, M., Haker, S., Westin, CF. (2007). Geodesic-Loxodromes for Diffusion Tensor Interpolation and Difference Measurement. In: Ayache, N., Ourselin, S., Maeder, A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007. MICCAI 2007. Lecture Notes in Computer Science, vol 4791. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75757-3_1
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DOI: https://doi.org/10.1007/978-3-540-75757-3_1
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