[Insight-developers] GaussianFilter::NormalizeAcrossScale not good for scale space analysis

[Jim Miller]

Luca, 

Is this the same bug you mentioned to me in Rotterdam?  You had patched something related to scale space and Hessian calculations shortly after our discussion.

Jim


On Nov 17, 2010, at 11:19 AM, Bradley Lowekamp wrote:

> Hello,
> 
> I can not find that rational for the scaling factors applied to the gaussian filter when NormalizeAcrossScale is enabled:
> http://www.itk.org/Doxygen/html/classitk_1_1RecursiveGaussianImageFilter.html#a042f38140c124e1f4a9b0461ef720982
> 
> Is there a reference for the logic and motivation for this scaling?
> 
> I have been working on a multi-scale laplacian blob detector, so this scaling is critical for this to be working correctly. However for a 3D Laplacian, the normalization does not match any know rational I can find. Specifically for the 3D case the laplacian is normalized with sigma^3 not sigma^2. ( Side Note: standard scale space notation of L(x;t) where t=sigma^2, would indicate that the normalized laplacian = t(L_xx+L_yy+L_zz) )
> 
> 
> From my recent readings there is a "natural coordinates" or "dimensionless spatial units" which are frequently used for this analysis. The conclusion I reach from this analysis is that the correct scaling factor should be sigma^n where n is the order of the differentiating for the separated convolutions. ( Not the current constant sigma ).
> 
> This issue was also noticed with the Hessian filter:
> http://public.kitware.com/Bug/view.php?id=10599
> 
> However the solution was filter specific:
> git show 49e7362fc295033e5e6594b1325a5c7997d9bb95 -- Code/BasicFilters/itkHessianRecursiveGaussianImageFilter.txx
> 
> I see two solutions:
> 
> 1 ) Change RecursiveGaissianImageFilter to scale according to sigma^n. This is my preferred solution as I believe it's correct.
> 
> 2) Hack the set of Recursive Gaussian Filter to perform the correct scaling for their specific operation and not use RecursiveGaissianImageFilter::NormalizeAcrossScale.
> 
> 
> Any thoughts on this issue?
> 
> Brad 
> 
> BTW: I have been reading "Scale-Space Theory in Computer Vision" by Tony Lindeberg as my main reference.
> 
> ========================================================
> Bradley Lowekamp  
> Lockheed Martin Contractor for
> Office of High Performance Computing and Communications
> National Library of Medicine 
> blowekamp at mail.nih.gov
> 
> 

Jim Miller
Senior Scientist
GE Research 
Interventional and Therapy

GE imagination at work

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