[Insight-users] Structure Tensor in ITK

[Cory Quammen]

Ah ha, I didn't look carefully enough at the notation. Thanks for
clarifying my confusion.

Cory

On Fri, Jun 4, 2010 at 11:49 AM, Jeff Donner <jeffrey.donner at gmail.com> wrote:
> ... 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
>>> _____________________________________
>>> Powered by www.kitware.com
>>>
>>> Visit other Kitware open-source projects at
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>>> Kitware offers ITK Training Courses, for more information visit:
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>>> Please keep messages on-topic and check the ITK FAQ at:
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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