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

[Torsten Rohlfing]

Gunnar:

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

Thanks!
  Torsten

Gunnar Farneback wrote:

>Torsten wrote:
>  
>
>>Also, can anyone think of a reason why the tensor dimension (i.e., the 
>>tensor matrix size) should be a template parameter (as opposed to fixed 
>>3x3)? My current state of mind is that tensor image dimensions should 
>>definitely be templated to allow processing of 2D slices, whereas the 
>>tensors themselves really don't seem to make much sense in anything 
>>other than 3D.
>>    
>>
>
>If your aim is strictly Diffusion Tensor MRI, I don't think anything
>but 3x3 is meaningful. However, it's also possible to represent the
>orientation and structure of local features in an intensity image with
>tensors, usually called orientation tensors or structure tensors.
>These are in general NxN for N-dimensional images and at least 2x2,
>3x3, and 4x4 tensors are in common use. 
>
>The properties of these tensors are very similar to diffusion tensors
>and many of the same operations on the tensors are relevant, so it
>would be useful with a more general tensor class.
>
>I can provide further explanation and references on request.
>
>/Gunnar
>  
>


-- 
--
Torsten Rohlfing, PhD           SRI International, Neuroscience Program
 Research Scientist              333 Ravenswood Ave
  torsten at synapse.sri.com         Menlo Park, CA 94025
   Phone: ++1 (650) 859-3379       Fax: ++1 (650) 859-2743

     "Though this be madness, yet there is a method in't"