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. Author manuscript; available in PMC: 2009 Oct 8.
Published in final edited form as: IEEE Trans Med Imaging. 2007 Nov;26(11):1537–1546. doi: 10.1109/TMI.2007.903195

Fig. 1.

Fig. 1

(a) Tangent space of the manifold M of diffusion tensors at point p1. The tangent vector X points to the direction of geodesic γ(t) between the points p1 and p2. (b) A cubic tensor spline S(t), that approximates pis of a 1-D tensor field. The given points pi and the points of the tensor spline S(t) are SPD matrices, elements of the Riemannian manifold M. Seven control points ci and 11 knots ti are required. The association between basis functions Ni,4(t), knots ti and given data points pi is displayed in this figure.