[ITK-users] Computation of the derivative of normalized cross correlation

[C Boydev]

Hi everyone,

I finally understood the derivations (I forgot to derive the denominator 
in the formula of the normalized cross correlation). There is an article 
published in The InsightJournal that explains how to compute the 
derivative of the normalized cross corralation:

http://www.insight-journal.org/browse/publication/87

Sorry for that,
Christina


Le 19/06/2014 16:16, C Boydev a écrit :
> Hi everyone,
>
> I'm trying to understand the implementation of 
> itkNormalizedCorrelationImageToImageMetric. I understand the use of 
> the jacobian and the gradient of the moving image to calculate the 
> differential but I don't see why we don't have
> derivative[i] = derivativeF[i]  / denom instead of derivative[i] = ( 
> derivativeF[i] - ( sfm / smm ) * derivativeM[i] ) / denom in the final 
> loop:
>
>
> if( this->m_NumberOfPixelsCounted > 0 && denom != 0.0 )
>     {
>     for( unsigned int i = 0; i < ParametersDimension; i++ )
>       {
>       derivative[i] = ( derivativeF[i] - ( sfm / smm ) * 
> derivativeM[i] ) / denom;
>       }
>     }
>
>
> I must be missing something - where does the term ( sfm / smm ) * 
> derivativeM[i] come from?
>
> Thank you very much for your help,
> Christina
>