Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.
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.
Kindlmann
Gordon
G
Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, USA. gk@bwh.harvard.edu
Estépar
Raúl San José
RS
Niethammer
Marc
M
Haker
Steven
S
Westin
Carl-Fredrik
CF
D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity