[Insight-users] HessianRecursiveGaussianImageFilter

Wed Jul 4 12:42:50 EDT 2007

Hi again,

As I use this class frequently I tried and finally I was able to fix the
issue. Now it seems to work correctly (see image compared to previous).
Patched files are attached to this email and also in the bug tracker
http://www.itk.org/Bug/bug.php?op=show&bugid=5292

Could you check if the implementation is correct now please?

Best regards

Ivan

-----Mensaje original-----
De: Iván Macía [mailto:imacia at vicomtech.es] 
Enviado el: miércoles, 04 de julio de 2007 17:28
Para: 'Won-Ki Jeong'; 'Insight-users at itk.org'
Asunto: RE: [Insight-users] HessianRecursiveGaussianImageFilter

Forgot to attach the images :)

-----Mensaje original-----
De: Iván Macía [mailto:imacia at vicomtech.es] 
Enviado el: miércoles, 04 de julio de 2007 17:25
Para: 'Won-Ki Jeong'; 'Insight-users at itk.org'
Asunto: RE: [Insight-users] HessianRecursiveGaussianImageFilter

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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