# Neighborhood Cross Correlation

**URL:** <https://discourse.itk.org/t/neighborhood-cross-correlation/443>\
**Category:** Algorithms\
**Created:** [November 21, 2017, 6:08pm UTC](https://discourse.itk.org/t/neighborhood-cross-correlation/443 "2017-11-21T18:08:58Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Ray](https://discourse.itk.org/letter_avatar_proxy/v4/letter/r/e9a140/32.png) [@Ray](https://discourse.itk.org/u/Ray)\
**Post date:** [November 21, 2017, 6:08pm UTC](https://discourse.itk.org/t/neighborhood-cross-correlation/443/1 "2017-11-21T18:08:58Z")

</div>

This is a function in itkANTSNeighborhoodCorrelationImageToImageMetricv4GetValueAndDerivativeThreader.hxx to compute cross correlation in a local window. I think if fabs(sFixedFixed\_sMovingMoving) \< NumericTraits\< LocalRealType \>::epsilon(), localCC should not be one (which means perfect correlation). For example, [0, 0, 0] and [1, 2, 3] are actually not correlated, but this function will give localCC the value of one.

template \< typename TDomainPartitioner, typename TImageToImageMetric, typename TNeighborhoodCorrelationMetric \>  
void  
ANTSNeighborhoodCorrelationImageToImageMetricv4GetValueAndDerivativeThreader\< TDomainPartitioner, TImageToImageMetric, TNeighborhoodCorrelationMetric \>  
::ComputeMovingTransformDerivative( const ScanIteratorType &, ScanMemType &scanMem, const ScanParametersType &, DerivativeType &deriv, MeasureType &localCC, const ThreadIdType threadId) const  
{  
MovingImageGradientType derivWRTImage;  
localCC = NumericTraits::OneValue();

typedef InternalComputationValueType LocalRealType;

LocalRealType sFixedFixed = scanMem.sFixedFixed;  
LocalRealType sMovingMoving = scanMem.sMovingMoving;  
LocalRealType sFixedMoving = scanMem.sFixedMoving;  
LocalRealType fixedI = scanMem.fixedA;  
LocalRealType movingI = scanMem.movingA;

LocalRealType sFixedFixed\_sMovingMoving = sFixedFixed \* sMovingMoving;

if ( fabs(sFixedFixed\_sMovingMoving) \> NumericTraits\< LocalRealType \>::epsilon() )  
{  
localCC = sFixedMoving \* sFixedMoving / (sFixedFixed\_sMovingMoving);  
}

if( this-\>m\_ANTSAssociate-\>GetComputeDerivative() )  
{  
const MovingImageGradientType movingImageGradient = scanMem.movingImageGradient;

```
if ( ! (sFixedFixed > NumericTraits<LocalRealType>::epsilon() && sMovingMoving > NumericTraits<LocalRealType>::epsilon() ) )
  {
  deriv.Fill( NumericTraits<DerivativeValueType>::ZeroValue() );
  return;
  }

for (ImageDimensionType qq = 0; qq < TImageToImageMetric::VirtualImageDimension; qq++)
  {
  derivWRTImage[qq] = 2.0 * sFixedMoving / (sFixedFixed_sMovingMoving) * (fixedI - sFixedMoving / sMovingMoving * movingI) * movingImageGradient[qq];
  }

/* Use a pre-allocated jacobian object for efficiency */
typedef JacobianType & JacobianReferenceType;
JacobianReferenceType jacobian = this->m_GetValueAndDerivativePerThreadVariables[threadId].MovingTransformJacobian;
JacobianReferenceType jacobianPositional = this->m_GetValueAndDerivativePerThreadVariables[threadId].MovingTransformJacobianPositional;

/** For dense transforms, this returns identity */
this->m_Associate->GetMovingTransform()->
  ComputeJacobianWithRespectToParametersCachedTemporaries(scanMem.virtualPoint,
                                                          jacobian,
                                                          jacobianPositional);

NumberOfParametersType numberOfLocalParameters = this->m_Associate->GetMovingTransform()->GetNumberOfLocalParameters();

for (NumberOfParametersType par = 0; par < numberOfLocalParameters; par++)
  {
  deriv[par] = NumericTraits<DerivativeValueType>::ZeroValue();
  for (ImageDimensionType dim = 0; dim < TImageToImageMetric::MovingImageDimension; dim++)
    {
    deriv[par] += derivWRTImage[dim] * jacobian(dim, par);
    }
  }
}

```

}