[Insight-developers] An implementation question in ITK

[Luis Ibanez]

Hi Hua,


1) In the case of the MeanSquaresImageMetric,
    the Gradient of the moving image is interpolated using
    NearestNeighborhood interpolation.

    See lines: 210-217 of

    Insight/Code/Algorithms/itkMeanSquaresImageToImageMetric.txx


2) In the case of the SymmetricForcesDemonsRegistration
    the gradient of the moving image is computed *after*
    mapping the moving image to the coordinate system of
    the fixed image.

    See lines: 188-220 of

     Insight/Code/Algorithms/
       itkSymmetricForcesDemonsRegistrationFunction.txx

    Note that in this case, this is done "on-demand",
    that is, on a pixel-by-pixel basis.



3) In the case of the
    itkFastSymmetricForcesDemonsRegistrationFunction

    The gradient is also computed by finite differences
    *after* mapping the moving image to the coordinate
    system of the fixed image, but this time is not done
    on-demand, but the entire moving image is warped
    first, and the resulting warped image is used for
    computing the gradient.

    See lines: 196  and  151-157  of


     Insight/Code/Algorithms/
       itkFastSymmetricForcesDemonsRegistrationFunction.txx

     Note that there is a difference between computing the
     gradient of the moving image in the coordinate system
     of the moving image, and then mapping that back to the
     coordinate system of the fixed image,  and mapping the
     moving image to the coordinate system of the fixed image
     and then computing the gradient with respect to the
     coordinate system of the fixed image.




    Regards,


        Luis



---------------------
Hua-mei Chen wrote:
> Sorry. I forgot to change the subject of my previous email. Here I 
> re-send it again.
> 
> ====================================================================
> 
> Dear ITK Users and Developers,
> 
>         In deformable image registration, it is very common to find the 
> image gradient at non-grid positions. For example, to obtain the driving 
> force by taking the derivative of SSD similarity measure. I am wondering 
> how this procedure is implemented in ITK. I used to construct a 
> continuous image based on Bspline model and then find the derivitive at 
> non-grid positions. However, I recently found a MATLAB code which 
> resamples the image based on the current deformation field and then find 
> the gradient at the resampled image. In this way, there is no need to 
> find the gradient at non-grid positions. Afterwards, the gradient 
> information is used to construct the update of the deformation field and 
> the new deformation field is obtained by ADDING the update to the 
> original deformation field. Is this a common practice to implement 
> deformable image registration algorithms like demons, fluid, and FFD in 
> ITK? Any response is appreciated.
> 
> Chen