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

[Siddharth Vikal]

Well, there is a jacobian filter available in ITK that calculates the
jacobian of displacement field (vector) image volume:
http://www.itk.org/Doxygen/html/classitk_1_1DisplacementFieldJacobianDeterminantFilter.html

It returns the jacobin determinant, but one can easily modify it to return
the Jacobian matrix, and then do the eigen value analysis on top of that.

Cheers

On Tue, Oct 6, 2015 at 7:09 AM, Jakob Weiss <weissj at in.tum.de> wrote:

> Thank you a lot Matheus, this has been very helpful!
>
> As to the question of using the Jacobian: Since the Hessian s the same as
> the Jacobian of the Gradient, this just another equal formulation of the
> same problem. I could not find any filter for computing the Jacobian on a
> vector volume either, so not really a solution. For example [1] applies a
> scheme to make these matrices symmetric.
>
> Cheers,
> J
>
> [1] Goch, Caspar J., et al. "Liver vessel segmentation using gradient
> vector
> flow." Bildverarbeitung für die Medizin 2011. Springer Berlin Heidelberg,
> 2011. 104-108.
>
>
>
> --
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