I want to calculate the orientation distance between two tensors.
Tensor A = [4, 0, 0, 4, 0, 4] i.e., perfect sphere.
Tensor B = [10, 0, 0, 1, 0, 1] i.e., linear shape tensor.
My expectation is that if a tensor is compared with a sphere tensor, the orientation should be 0.
tenInterpDistanceTwo_d can give me a value very close to 0.
But if I change B to [1, 0, 0, 10, 0, 1] or [1, 0, 0, 1, 0, 10], the function returns a very large orientation distance value. But B is still a linear shaped tensor. This is not what I expect.
What is the reason behind this?
Furthermore, in the paper Geodesic-Loxodromes for Diﬀusion Tensor Interpolation and Diﬀerence Measurement, page 6, it says ''there is little orientation change between isotropic and anisotropic
tensors of comparable size".
In this case, B is very anisotropic tensor and A is a perfect isotropic tensor and both have exactly the same trace (=12, i.e., the size in the context), why it returns a large value far from 0.
Thank you very much.
Ph.D candidate in Computer Graphics and Visualization section