[Insight-users] Gaussian Derivative Operators & Hessian & Eigenvalue solver

[Karthik Krishnan]

Bitter, Ingmar (NIH/CC/DRD) wrote:

>Hi All,
>
>Am I right that there is not currently an implementation of
>
>a) a Gaussian derivative operator that can compute 2nd degree symmetric and
>asymmetric derivatives along a compete 3D neighborhood
>
>  
>
HessianRecursiveGaussianImageFilter
http://www.itk.org/cgi-bin/viewcvs.cgi/Code/BasicFilters/itkHessianRecursiveGaussianImageFilter.h?rev=1.5&root=Insight&view=markup

Does exactly what you just mentioned...

>b) and consequently no easy way to compute a 3D Hessian matrix for each
>voxel
>  
>
Can't get easier...
This filter returns an image with pixels of type 
SymmetricSecondRankTensor... ie an image of with each pixel being a 3x3 
symmetric matrix


>c) and also no solver for eigenvalues of symmetric 3x3 matrices?
>
>  
>
Yes... There are two options here..

the thread safe and recommended one being...

Code/Common/itkSymmetricEigenAnalysis.h

And a filter that uses this class to compute an image of eigen values 
from an image of 3x3 tensors:

Code/BasicFilters/itkSymmetricEigenAnalysisImageFilter


Please do not use Code/Numerics/itkSymmetricEigenSystem as it is not 
threadsafe

HTH
-karthik

PS:
If you need example usage for all these filters, look at 
InsightApplications/Curves3DExtractor ...
(This extracts curves from MRA images)

>Ingmar Bitter
>_______________________________________________
>Insight-users mailing list
>Insight-users at itk.org
>http://www.itk.org/mailman/listinfo/insight-users
>
>  
>