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

[Roman Grothausmann]

Dear Luis,

Thanks a lot, that's what I need.

Many Thanks
Roman

Luis Ibanez wrote:
> 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

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