[Insight-users] Structure Tensor in ITK

[Jeff Donner]

No, the Hessian is the partial applied first with respect to one
variable, then the other variable:
      http://en.wikipedia.org/wiki/Hessian_matrix#Mixed_derivatives_and_symmetry_of_the_Hessian

The structure tensor is the PRODUCT of the partial wrt one var, with
the partial wrt the other var:

Straightforward equations:
http://github.com/JDonner/gabbleduck/blob/master/report/structure-tensor.png

Wikipedia says the same (as Ghassan mentioned:)
http://en.wikipedia.org/wiki/Structure_tensor

Note that as it says: "... where Ix denotes the partial derivative of
image I along the x-axis."

But I too wasted time being similarly confused.

On Fri, Jun 4, 2010 at 11:01 AM, Cory Quammen <cquammen at cs.unc.edu> wrote:
> Forgive me for my possible ignorance, but isn't the structure tensor
> simply a Hessian matrix? ITK has HessianRecursiveGaussianImageFilter
> which can compute a Hessian image:
> http://www.itk.org/Doxygen318/html/classitk_1_1HessianRecursiveGaussianImageFilter.html
>
> Cory
>
> On Fri, Jun 4, 2010 at 9:04 AM, Sergio Vera <sergio.vera at alma3d.com> wrote:
>> Thanks for the contributions
>>
>> I'll try to implement it and if the result is half decent, the idea was to
>> publish it at the insight journal indeed
>>
>> Regards
>>
>> On Fri, Jun 4, 2010 at 2:47 PM, Jeff Donner <jeffrey.donner at gmail.com>
>> wrote:
>>>
>>> On Fri, Jun 4, 2010 at 8:18 AM, Sergio Vera <sergio.vera at alma3d.com>
>>> wrote:
>>> > I'm in need of calculating the structure tensor (also called second
>>> > moment
>>> > matrix) of an image, and it seems that there is not a filter to compute
>>> > it
>>> > in ITK.
>>> > I've seen the class itk::TensorRelativeAnisotropyImageFilter and I'm not
>>> > sure if it may be related to the structure tensor?
>>>
>>> I found that there was no structure tensor filter in ITK; perhaps
>>> someone could point one out, it was a while since I used ITK. But, in
>>> the meantime I hand-rolled my own (plain code, not filter):
>>>
>>>  http://github.com/JDonner/gabbleduck
>>>
>>> in gaussian.cpp and pipeline.cpp.
>>>
>>> It's really too messy to actually recommend to anyone but, it exists
>>> if you want to look at it. The names of things should be reasonable at
>>> least.
>>>
>>> Jeff
>>
>>
>>
>> --
>> Sergio Vera
>>
>> Alma IT Systems
>> C/ Vilana, 4B, 4º 1ª
>> 08022 Barcelona
>> T. (+34) 932 380 592
>> www.alma3d.com
>>
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>
>
>
> --
> Cory Quammen
> Center for Computer Integrated Systems for Microscopy and Manipulation (CISMM)
> Department of Computer Science
> University of North Carolina at Chapel Hill
> http://www.cs.unc.edu/~cquammen
> _____________________________________
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