[Insight-developers] Re: Recursive Gaussian : ITK Release 1.10

[Luis Ibanez]

Hi Gunnar,


1) Yes, I agree with you in that this normalization is image dependent.
    The test is usually done with an input image that has a single pixel
    On, which is the equivalent of a discrete Dirac Delta.



2) Yeap, that's the reason why the test is done with a single pixel ON
    at the input.




3) Yes, please look at the example:

            Insight/Examples/Filtering/
                     ScaleSpaceGenerator2D.cxx


    This example takes a 2D image as input and produces its
    ScaleSpace image, which is a 3D image, where "scale" is
    the 3rd coordinate.  Scale space analysis usually involves
    to track isosurfaces of the 3D image in order to identify
    image features that are stable across scale.

    An interesting exercise is to generate the 3D ScaleSpace
    of a 2D image, then load it in to ParaView, VolView or
    Slicer and generate isosurfaces on the scale.




    Regards,



        Luis



----------------------
Gunnar Farneback wrote:

>>The purpose of the normalization across scale is to configure
>>the filter in such a way that the maximum value of an image will
>>remain the same after filtering it with the Gaussian filter.
> 
> 
> Um, there's no way you can do that by an image-independent
> normalization of the filter, unless you restrict the images under
> consideration to some specific class.
> 
> 
>>That's the reason why the test takes one image, and smooth it
>>with two different sigma values. It is expected in that case
>>that the pixel that we are sampling will have the same value,
>>given that is the pixel with the maximum value in the image.
> 
> 
> That test only checks that the central value of the impulse response
> is the same. Try by setting three pixels to 1000.0 instead of only one
> and you will get a different result. Or set all 21 pixels to 1000.0
> and you will get a constant maximum value if you turn off
> normalization across scale but a result that is proportional to sigma
> if you turn it on.
> 
> 
>>This mode of the filter permits to process N-D images with
>>multiple sigmas in order to generate a (N+1)-D image in scale
>>space. The normalization makes possible to search for isovalues
>>in that (N+1)-D space.
> 
> 
> Is there an example somewhere which shows how this works in practice?
> 
> /Gunnar
> 
>