[ITK-users] How to Calculate Hessian Matrix from Gradient Image?

[Bradley Lowekamp]

Hello,

I don't think there is going to be anything turnkey to do what you want.

I'd looking to writing a custom filter for this specialized task. You can either base it off the the HessianRecursiveGaussianImageFilter [1] , which utilizes filters per-component and adaptors.

Or do a discrite approach along the lines of something I have done here [2]. 

Hope that helps,
Brad

[1] https://github.com/InsightSoftwareConsortium/ITK/blob/1ce0e5dd3b2d9c7a7a9353dfb8b728ada8d71320/Modules/Filtering/ImageFeature/include/itkHessianRecursiveGaussianImageFilter.hxx#L187-L368
[2] https://github.com/blowekamp/itkLocalDiscreteHessian/blob/30aa775494c20eaf9e085781ae233e0511773758/include/itkHessianImageFilter.hxx#L132-L174

On Mar 27, 2015, at 10:16 AM, Thomas Seidel <seidel at cvrti.utah.edu> wrote:

> Hi all,
> 
> I would like to calculate the hessian matrix and get an output of type SymmetricSecondRankTensor pixel from a gradient image.
> 
> The irk HessianRecursiveGaussianImageFilter uses as input an intensity image.
> However, I would like to implement a method for vessel detection based on the following algorithm:
> 
> 1. GradientImageFilter
> 2. GradientVectorFlowImageFilter
> 3. get the hessian Matrix from 2. (this is my problem)
> 4. Hessian3DToVesselnessImageFilter
> 
> 
> How can I get from the vector field in 2. to the hessian matrix I need for 3.?
> 
> Thanks for your help,
> Thomas
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