[Insight-users] how to calculate the derivatons of images in DeformableRegistration4?

[Luis Ibanez]

Hi shengzhouxu,

We computer (or rather, "estimate") the derivatives of an image,
by using finite differences methods.

The simplest of which is to compute the difference in intensity
between two adjacent pixels and divide that value by the spacing
(physical distance) between the two pixels.

In practice, this is already implemented in the filters:

http://www.itk.org/Insight/Doxygen/html/classitk_1_1DerivativeImageFilter.html
http://www.itk.org/Insight/Doxygen/html/classitk_1_1GradientRecursiveGaussianImageFilter.html

and in the functions:

http://www.itk.org/Insight/Doxygen/html/classitk_1_1GaussianDerivativeImageFunction.html
http://www.itk.org/Insight/Doxygen/html/classitk_1_1GaussianDerivativeOperator.html
http://www.itk.org/Insight/Doxygen/html/classitk_1_1DerivativeOperator.html


You may want to get familiar with
http://en.wikipedia.org/wiki/Image_gradient



    Regards,


       Luis


------------------
shengzhouxu wrote:
> Hi All,
>  
> 
> In the example DeformableRegistration4.cxx, the 
> itkMeanSquaresImageToImageMetric is used as the metric method, and the 
> optimization method is LBFGS, and in the LBFGS the derivations have to 
> be calculated to obtain the Hessian matrix. Generally the derivation is 
> easy to calculate, such as f(x)= x^2 , f’(x)=2x, but how to calculate 
> the derivatons of images?  because I don’t know the expression of the 
> function, and how we explain the derivations of images? would anyone 
> please explain this? Thanks every much!
> 
>  
> 2009-03-07
> ------------------------------------------------------------------------
> shengzhouxu
> 
> 
> ------------------------------------------------------------------------
> 
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