[Insight-users] Gradient of Vector Image

[Bing Jian]

Yes. Luis, You are right. I think both us are talking about same
thing. The Jacobian of the gradient vector image is same as the
Hessian matrix of orginal image. Here I am using Jacobian
because I expect a general filter to calculate the gradient
(Jacobian) of a general vector function which may not have to be a
gradient output. Hope it's clear.

-- 
Best wishes,
Bing Jian
bjian at cise . ufl . edu


On Thu, 2 Oct 2003, Luis Ibanez wrote:

>
> Hi Bing,
>
>
>    No, you cannot provide a vector image as
>    input to the Gradient filter.  This filter
>    is expecting a scalar image.
>
>    You may want to double check on the math of
>    what you would expect from this operation.
>    The gradient of the gradient will not give
>    you a Jacobian, but the Hessian matrix of
>    the image.
>
>
>    Assumming that the image is a function
>
>              I = f(x,y,z)
>
>    the Hessian matrix will have the second
>    derivatives
>
>         df/dxdx  df/dxdy   df/dxdz
>         df/dydx  df/dydy   df/dydz
>         df/dzdx  df/dxdy   df/dzdz
>
>
>     You can get this matrix using the Recursive
>     Gaussian filters.  Please look at the
>     demo application:
>
>       InsightApplications/Curve2DExtraction
>
>     which computes the Hessian of the input
>     image. Note that this applications uses
>     2D images, but the concept is scalable
>     in dimension.
>
>     http://www . itk . org/HTML/Curve2DExtraction . htm
>
>
>
>       Regards,
>
>
>          Luis
>
>
> --------------------------
> Bing Jian wrote:
> > Hi, Here is a question about gradient image.
> >
> > Suppose I have a vector image which is obtained from
> > the output of gradientfilter applied on a scalar 3D
> > image. Now the dimension of vector is 3. Can I take
> > this vector image as input to the gradientfilter again?
> > My expected output image should be a 3d vector image.
> > And here the dimension of the vector should be 3*3=9,
> > as the Jacobian of the original gradient image.
> >
> > Thanks in advance!
> >
>
>
>
>
>