[Insight-developers] Suggestion: Tensors and Tensor Image Filters

[Gunnar Farneback]

Torsten wrote:
> Are those tensors you mentioned also symmetric? It seems that for 
> diffusion imaging, one can conveniently represent the tensors as compact 
> coefficient vectors by linearizing the upper right half of the tensor 
> (including the diagonal). Is the same true for the tensors you 
> mentioned?

Yes, they are always symmetric. Ideally they are also positive
semidefinite, although there are estimation methods which occasionally
yield tensors with a negative eigenvalue.

> Can you think of applications where the symmetry constraint would be
> a problem?

I can't give actual applications but I'm aware of research involving
asymmetric tensors, complex tensors, and higher-order tensors.

There are many optimizations that can be done for tensors with certain
properties, and we probably want to take advantage of those, but I
agree with Carl-Fredrik that it would be good if the design at least
at least leaves an opening for various generalizations.

/Gunnar