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

[Torsten Rohlfing]

Carl-Fredrik,

thanks for your comments. I agree that generality is a good idea, but 
once you want to support higher-rank tensors, that adds a whole lot of 
extra complexity to the class interface. To beign with, we would need a 
dimensions array of rank size, instead of row and column count.

What do you think about a dual approach that supports general tensors of 
arbitrary rank, but at the same time provides a separate class for 
symmetric tensors in a compact representation? If the general tensor 
class and the compact symmetric tensor class define the same essential 
member functions, we should be able to use either type of tensor 
representation in filter classes by means of templating.

What do you think?
  Torsten

Carl-Fredrik Westin wrote:

> Torsten and Gunnar,
> Thanks for your inputs on a new tensor class in itk. We need this and 
> there is an ongoing discussion how to go about this. I agree with 
> Gunnar that we should be  general. The structure tensor and the 
> diffusion tensor have similar constrains (symmetric, real eigenvalues 
> in the ideal case, etc). However, my experience is that we should not 
> try to be as efficient as possible, that is to use the fact that the 
> tensor is symmetric, positive semi-definite  etc. With a wider tensor 
> class, we can host other tensors as well,  such as the stress, the 
> strain, and the deformation gradient tensor (common in nonlinear 
> registration). Further, when we start differentiating these tensors, 
> and get higher order tensors, it would be great to have structure in 
> ITK to accommodate for this.
>
> In summary, let's be as general defining a tensor class that we can 
> afford to be, without complicating the use of them in applications 
> such as DTMRI or local structure estimation. My suggestion is to not 
> exploit the symmetry to begin with.
>
> C-F
>
> -- 
> Dr. Carl-Fredrik Westin
> Director, Laboratory of Mathematics in Imaging (LMI)
> Assistant Professor of Radiology, Harvard Medical School
> Brigham and Women's Hospital, 75 Francis St., Boston, MA 02115
>
> Phone: (+1) 617-278-0639, Fax: (+1) 617-582-6033
> Email:  westin at bwh.harvard.edu, Office: Thorn Building 323
> http://lmi.bwh.harvard.edu/~westin



-- 
--
Torsten Rohlfing, PhD           SRI International, Neuroscience Program
 Research Scientist              333 Ravenswood Ave
  torsten at synapse.sri.com         Menlo Park, CA 94025
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     "Though this be madness, yet there is a method in't"