Definition of Gradient Magnitude

ParaView Support
1

Hello,

using the gradient filter on a vector fields yields the nine components of the gradient tensor and also a scalar magnitude. It is my understanding that the gradient filter computes the gradient as an Image gradient via this script: https://gitlab.kitware.com/vtk/vtk/blob/master/Imaging/General/vtkImageGradient.cxx
Unfortunately, I can’t work out the exact definition of the magnitude and how it is computed (having some trouble interpreting the above script). Can anyone perhaps help me and point out which definition of a matrix norm is used?

2

You can use the calculator filter over the gradient filter, and do the sqrt(Component_0Component_0+Component_iComponent_i…). This is equivalent to the Frobenius norm, which is what is used by default.

3

I was guessing it was the Frobenius norm. Thank you very much!