[Insight-users] Structure Tensor in ITK

[Jeff Donner]

... wrt notation it's the difference between:

    fxfy

and

    fxy

On Fri, Jun 4, 2010 at 11:46 AM, Jeff Donner <jeffrey.donner at gmail.com> wrote:
> 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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>> Visit other Kitware open-source projects at
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>