[Insight-users] HessianRecursiveGaussianImageFilter

[Luis Ibanez]

Hi Ivan,

Thanks for entering the bug report regarding this filter.

There seems to be a duplicate report, and an ITK versioning issue
involved.

As we just mentioned to Won-Ki:

    This problem was pointed out by Andreas Keil in the
    users list on April 2007:

http://public.kitware.com/pipermail/insight-users/2007-April/022019.html

    We entered in the Bug tracker as Bug # 4934
http://public.kitware.com/Bug/bug.php?op=show&bugid=4934

    and committed a fix in the CVS repository on April 27th 2007:
http://www.itk.org/cgi-bin/viewcvs.cgi/Code/BasicFilters/itkHessianRecursiveGaussianImageFilter.txx?root=Insight&sortby=date&r2=1.5&r1=1.4




What version of ITK did you use for this recent test ?

Was it a CVS version posterior to April 27th 2007 ?


   Please let us know,


      Thanks





-------------------
Iván Macía wrote:
> Hi Won-Ki,
> 
> Regarding Q1 you are right, the filter computes in the 3D case the six
> possible gaussian second order derivatives. Note that the filter uses
> itk::RecursiveGaussianImageFilter internally.
> 
> Regarding Q2 I think you are also right. When computing second orderivative
> (G*I)xx the filter applies recursive gaussian smoothing with first order
> derivative twice in the x direction, but the number of smoothing filter is
> fixed in the static member NumberOfSmoothingFilters = ImageDimension-2, so
> in the 3D case there is only a single smoothing filter.
> 
> I made a small test with a 3D MRI image, applied HessianRecursiveGaussian
> filter with sigma = 5.0 and extracted the six components of the hessian
> tensor. The attached image shows an slice of the original image and the
> sixth component (G*I)zz of the hessian matrix of the same slice. It seems
> like there is smoothing in x but no smoothing in y (see the narrow
> horizontal lines).
> 
> I made a Bug entry in the bug tracker with ID 5292
> http://www.itk.org/Bug/bug.php?op=show&bugid=5292
> 
> Best regards
> 
> Ivan
> 
> 
> -----Mensaje original-----
> De: insight-users-bounces+imacia=vicomtech.es at itk.org
> [mailto:insight-users-bounces+imacia=vicomtech.es at itk.org] En nombre de
> Won-Ki Jeong
> Enviado el: lunes, 02 de julio de 2007 21:26
> Para: Insight-users at itk.org
> Asunto: [Insight-users] HessianRecursiveGaussianImageFilter
> 
> Hi all
> 
> I have some questions about the HessianRecursiveGaussianImageFilter.
> 
> Q1. Is this filter (theoretically) same as applying Gaussian smoothing
> and compute derivatives to the input image? For example, let G be a
> Gaussian kernel and I be the input image, then is the filter compute
> (G*I)xx, (G*I)xy, (G*I)xz, (G*I)yy, (G*I)yz, (G*I)zz (subscript means
> partial derivative along that axis)?
> 
> Q2. If so, the implementation is not correct because, for example
> (G*I)xx, the filter applies 1D recursive Gaussian order-1 derivative
> filter twice along x and applies 1D recursive Gaussian filter along y,
> that means along x the Gaussian is applied twice but there is no
> Gaussian for z direction. Can somebody clarify this?
> 
> The implementation is in void GenerateData(void) in
> itkHessianRecursiveGaussianImageFilter.txx.
> 
> Thanks a lot!
> 
> Won-Ki
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