[Insight-users] HessianRecursiveGaussianImageFilter

[Won-Ki Jeong]

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