[Insight-users] Computing the gradient of a vector image

[David Doria]

On Fri, Dec 10, 2010 at 5:44 AM, Luis Ibanez <luis.ibanez at kitware.com> wrote:
> Hi David,
>
> The gradient of a vector image could have different interpretations...
>
> The Gradient of a scalar image will be an image of covariant vectors.
>
> The Gradient of a vector image will be an image of Tensors
> one of whose indices will be covariant and the other contravariant.
>
> Are you looking for a filter that will produce an image of
> tensors as output ?

Say there is a pixel like this (a itk::Image<itk::CovariantVector<int, 3>, 2> )

           (0,0,0)
(1,1,1) (3,3,3)

(pixel of interest is (3,3,3) and its top and left neighbor are shown).

If we used only these two neighbors to compute the gradient (backwards
differencing), couldn't the gradient at the pixel of interested be
computed/interpreted as:

{ (2,2,2), (3,3,3) }

That is, a 2-vector of 3-vectors describing
{ the change in the the gradient vector moving along dimension 0, the
change in the gradient vector moving along dimenson 1}

?

Thanks,

David