[Insight-users] Finding saddle points in a 2D image

[Luis Ibanez]

Hi Roman,

You can find Saddle-like points by using
the Hessian image filter:

http://www.itk.org/Doxygen/html/classitk_1_1HessianRecursiveGaussianImageFilter.html

and then computing Eigen analysis for the
Hessian matrices at every pixels.

Whenever you find that your two eigen values
have opposite signs, then you are in a Saddle-like
point.


You can compute the Eigen analysis at every
pixel by using the class
http://www.itk.org/Doxygen/html/classitk_1_1SymmetricEigenAnalysis.html

or you can generate a full image by using the class
http://www.itk.org/Doxygen/html/classitk_1_1SymmetricEigenAnalysisImageFilter.html

The first option will require less memory.


     Regards,


           Luis


---------------------------------------------------------------------------------------
On Thu, Apr 22, 2010 at 10:09 AM, Roman Grothausmann <
roman.grothausmann at helmholtz-berlin.de> wrote:

> Dear Richard,
>
>
> Many thanks for Your answers. Recommending the watershed filter for this
> was a great hint. I hadn't realized (since I was not looking for a
> segmentation) that the borderline of the watershed of the inverted image
> is exactly what I'm looking for.
>
> Still I'm wondering how I could find the saddle points (not the regional
> minima) of a 2D image (eg. point 0,0 of the plot of the function
> x*x-y*y). If I'm not mistaken those are the points where a watershed
> border starts when two basins meet. So kind of the origins of the
> watershed borderlines.
>
> Many thanks again.
> Roman
>
> Richard Beare wrote:
>
>> Hi,
>> I'm not entirely sure what problem you are trying to solve, but there
>> may be a simple approach if you outline it in more detail. The
>> discussion of gradient descent makes me wonder whether you might be
>> interested in watershed approaches, which are sometimes discussed in
>> terms of gradient descent but are  more usefully implemented as
>> gradient ascent.. They are likely to be useful if you have a
>> segmentation problem.
>>
>> Anyhow - regional minima can be found using a number of filters -
>> search for RegionalMinima in documentation.
>>
>>
>> On 4/22/10, Roman Grothausmann <roman.grothausmann at helmholtz-berlin.de>
>> wrote:
>>
>>> Dear mailing list members,
>>>
>>>
>>> How can I find saddle points and image border pixels with minimum
>>> gradient in a 2D image? I need those as starting points for tracing the
>>> gradient decent (as is done in the Random access iteration example in
>>> the user guide) because I want to detect valley traces in a 2D image
>>> that originate from saddle points (for no border pixels) or pixels with
>>> minimum gradient (for image border pixels).
>>> Is there a way to find these two types of special points with ITK?
>>>
>>> Any help is very much appreciated
>>> Roman
>>>
>>> --
>>> Roman Grothausmann
>>>
>>> Helmholtz-Zentrum Berlin für Materialien und Energie GmbH
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>>
>>
> --
> Roman Grothausmann
>
> Helmholtz-Zentrum Berlin für Materialien und Energie GmbH
> Bereich Funktionale Materialien
> Institut für angewandte Materialforschung
> Hahn-Meitner-Platz 1
> D-14109 Berlin
>
> Tel.: +49-(0)30-8062-2816
> Fax.: +49-(0)30-8062-3059
>
> Vorsitzender des Aufsichtsrats: Prof. Dr. Dr. h.c. mult. Joachim Treusch
> Stellvertretende Vorsitzende: Dr. Beatrix Vierkorn-Rudolph
> Geschäftsführer: Prof. Dr. Anke Rita Kaysser-Pyzalla, Prof. Dr. Dr. h.c.
> Wolfgang Eberhardt, Dr. Ulrich Breuer
> Sitz der Gesellschaft: Berlin
> Handelsregister: AG Charlottenburg, 89 HRB 5583
>
>
> _____________________________________
> Powered by www.kitware.com
>
> Visit other Kitware open-source projects at
> http://www.kitware.com/opensource/opensource.html
>
> Kitware offers ITK Training Courses, for more information visit:
> http://www.kitware.com/products/protraining.html
>
> Please keep messages on-topic and check the ITK FAQ at:
> http://www.itk.org/Wiki/ITK_FAQ
>
> Follow this link to subscribe/unsubscribe:
> http://www.itk.org/mailman/listinfo/insight-users
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