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

[Roman Grothausmann]

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
>> Bereich Funktionale Materialien
>> Institut für angewandte Materialforschung
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>>
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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