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

[C Boydev]

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

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