[Insight-users] why using GetJacobian in every trasformation class to Calculate derivatives

[Luis Ibanez]

Hi Xiahai Zhuang,

The Jacobian is not used for computing derivatives of the
image intensities.

The Jacobian is used for computing the derivative of
Image Metrics with respect to the Transform Parameters.

You can better observe that if you manually write the
expressions for the MeanSquared derivatives with respect
to the Transform parameters.

You will find that the derivatives of the Metrics always
depend at some point on the product of

              ImageDerivative X TransformJacobian

because that express the chain rule of derivation involving
the variations of image intensities with respect to variations
of transform parameters.

Note also that this is not the typical Jacobian that you would
find in differential calculus. This jacobian is not relating
the variations of the output coordinate to variations of the
input coordinates. Instead, this Jacobian is the one relating
the variations of output coordinates with respect to variations
of the Transform parameters.



    Regards,


       Luis


-----------------------------------------
庄吓海(Xiahai Zhuang) wrote:

>  why using GetJacobian in every trasformation class to
>  Calculate derivatives of the image intensity with respect
>   to the transform parmeters.
> 
> 
> 
> 　　　　　　　　致
> 礼！
>  				
> 
> 　　　　　　　　庄吓海(Xiahai Zhuang)
> 　　　　　　　　arhye at 163.com
> 　　　　　　　　　　2005-04-15     
> 
> 
> 
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