MantisBT - ITK
http://public.kitware.com/pipermail/insight-users/2007-July/022770.html [^]
when computing second order derivatives in the same direction twice, 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. The same applies for (G*I)yy and (G*I)zz in 3D.
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 where there should by two for computing (G*I)xx
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).
MRI_HessianGzz_Slice44.zip (29,570) 1969-12-31 19:00https://public.kitware.com/Bug/file/1060/MRI_HessianGzz_Slice44.zip
itkHessianRecursiveGaussianImageFilter.txx (7,244) 1969-12-31 19:00https://public.kitware.com/Bug/file/1061/itkHessianRecursiveGaussianImageFilter.txx
itkHessianRecursiveGaussianImageFilter.h (6,441) 1969-12-31 19:00https://public.kitware.com/Bug/file/1062/itkHessianRecursiveGaussianImageFilter.h
MRI_HessianGzz_Slice44_Fixed.jpg (8,719) 1969-12-31 19:00https://public.kitware.com/Bug/file/1063/MRI_HessianGzz_Slice44_Fixed.jpg
