/
itkRatioVarianceImageToImageMetric.txx
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itkRatioVarianceImageToImageMetric.txx
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#ifndef __itkRatioVarianceImageToImageMetric_txx
#define __itkRatioVarianceImageToImageMetric_txx
#include "itkRatioVarianceImageToImageMetric.h"
#include "itkImageRegionConstIteratorWithIndex.h"
namespace itk
{
/**
* Constructor
*/
template <class TFixedImage, class TMovingImage>
RatioVarianceImageToImageMetric< TFixedImage, TMovingImage >
::RatioVarianceImageToImageMetric()
{
}
/**
* Get the match Measure
*/
template <class TFixedImage, class TMovingImage>
typename RatioVarianceImageToImageMetric< TFixedImage, TMovingImage >::MeasureType
RatioVarianceImageToImageMetric< TFixedImage, TMovingImage >
::GetValue( const TransformParametersType& parameters ) const
{
// if moving image voxel values are m(i) and fixed image f(i) and the ratio
// x(i) = m(i) / f(i), then the registration metric being calculated is
// the variance of all x(i). The variance of a sample of n values can be
// estimated using
// M = (1 / (n - 1)) * ( sum(x(i)*x(i)) - (1/n)*sum(x(i))*sum(x(i)) )
// ratios_sum = sum(x(i)) and ratios2_sum = sum(x(i)*x(i))
// where i is an index of fixed image voxels
itkDebugMacro("GetDerivative( " << parameters << " ) ");
FixedImageConstPointer fixedImage = this->m_FixedImage;
if ( !fixedImage )
{
itkExceptionMacro( << "Fixed image has not been assigned" );
}
typedef itk::ImageRegionConstIteratorWithIndex<FixedImageType> FixedIteratorType;
FixedIteratorType ti( fixedImage, this->GetFixedImageRegion() );
typedef typename NumericTraits< MeasureType >::AccumulateType AccumulateType;
AccumulateType ratios_sum = NumericTraits< AccumulateType >::Zero;
AccumulateType ratios2_sum = NumericTraits< AccumulateType >::Zero;
this->m_NumberOfPixelsCounted = 0;
this->SetTransformParameters( parameters );
// loop through all pixels in fixed image, finding ratio of pixel values
// at each, and adding to accumulators
ti.GoToBegin();
while ( !ti.IsAtEnd() )
{
typename FixedImageType::IndexType index = ti.GetIndex();
// get physical point in fixed image corresponding to index
InputPointType inputPoint;
fixedImage->TransformIndexToPhysicalPoint( index, inputPoint );
// reject points outside fixed image mask, if mask is present
if ( this->m_FixedImageMask && !this->m_FixedImageMask->IsInside( inputPoint ) )
{
++ti;
continue;
}
// reject points which have a fixed image pixel value of zero, to
// prevent divide by zero problems when calculating ratios
const RealType fixedValue = ti.Get();
if ( fixedValue == NumericTraits< RealType >::Zero )
{
++ti;
continue;
}
// get physical point in moving image correspnoding to index using transform
OutputPointType transformedPoint = this->m_Transform->TransformPoint( inputPoint );
// reject points outside moving image mask, if mask is present
if ( this->m_MovingImageMask && !this->m_MovingImageMask->IsInside( transformedPoint ) )
{
++ti;
continue;
}
// if point is in masks and inside interpolator buffer, add the ratio of
// pixel values to accumulators
if ( this->m_Interpolator->IsInsideBuffer( transformedPoint ) )
{
// get moving value and calculate ratio between moving and fixed
// fixed values at current index
const RealType movingValue = this->m_Interpolator->Evaluate( transformedPoint );
const RealType ratio = movingValue / fixedValue;
// add ratio and ratio squared to accumulators
ratios_sum += ratio;
ratios2_sum += ratio*ratio;
this->m_NumberOfPixelsCounted++;
}
++ti;
}
const unsigned long& n = this->m_NumberOfPixelsCounted;
// abort if no data with which to calculate variance
if( !n )
{
itkExceptionMacro( << "All the points mapped to outside of the moving image");
}
// use intermediate sums to calculate variance of ratios of pixel values.
if ( n > 1 )
{
// simple variance calculation for sample of data
MeasureType measure = (ratios2_sum - (ratios_sum * ratios_sum / n)) / (n - 1.0);
return measure;
}
// default if only one pixel value ratio found
return NumericTraits< MeasureType >::Zero;
}
/**
* Get the Derivative Measure
*/
template < class TFixedImage, class TMovingImage>
void
RatioVarianceImageToImageMetric< TFixedImage, TMovingImage >
::GetDerivative( const TransformParametersType& parameters,
DerivativeType& derivative ) const
{
// (as above...)
// if moving image voxel values are m(i) and fixed image f(i) and the ratio
// x(i) = m(i) / f(i)
// then the registration metric being calculated is the variance of all
// x(i). The variance of a sample of n values can be estimated using
// M = (1 / (n - 1)) * ( sum(x(i)*x(i)) - (1/n)*sum(x(i))*sum(x(i)) )
// where
// ratios_sum = sum(x(i)) and ratios2_sum = sum(x(i)*x(i))
// where i is an index of fixed image voxels
//
// the derivative of M with respect to a transformation parameter T is:
// dM/dT = (2 / (n - 1)) * ( sum(x(i)*dx(i)/dT) - (1/n)*sum(x(i))*sum(dx(i)/dT) )
// where, because the moving image changes with the transform,
// dx(i)/dT = (d/dT)( m(i) / f(i) ) = (1/f(i)) * dm(i)/dT
//
// if
// f(i) = f(p(i))
// where p(i) is the physical point corresponding to the point in the fixed
// image f with index i, and
// q(i) = S(p(i), T)
// where q(i) is the physical point in the moving image that the transform
// S maps physical point p when the transform parameter T is specified, and
// m(i) = m(q(i)) = m(S(p(i), T))
// then
// dm(i)/dT = (d/dT)(m(i)) = (d/dT)(m(S(p(i), T)))
// = (dm(S(p(i), T))/dS) * (dS(p(i), T)/dT)
// = (dm(q(i))/dq) * (dS(p(i), T)/dT)
// where dm(q(i))/dq is the derivative of the moving image voxel value as
// the physical point in that image that is being sampled changes, or the
// gradient of m, and
// where dS(p(i), T)/dT is the vector of how the physical point q in the
// moving image that corresponds to the fixed image physical point p is
// changing as the transform parameter T is changed, or the Jacobian of the
// transform S
//
// so,
// dx(i)/dT = (1/f(i)) * [ Grad(m) (dot) Jacobian(S) ]
// where the Gradient of m and Jacobian component for each transform
// parameter are evaluated for each spatial dimension of f (and m) and summed
itkDebugMacro("GetDerivative( " << parameters << " ) ");
if ( !this->GetGradientImage() )
{
itkExceptionMacro( << "The gradient image is null, maybe you forgot to call Initialize()");
}
FixedImageConstPointer fixedImage = this->m_FixedImage;
if ( !fixedImage )
{
itkExceptionMacro( << "Fixed image has not been assigned" );
}
typedef itk::ImageRegionConstIteratorWithIndex<FixedImageType> FixedIteratorType;
FixedIteratorType ti( fixedImage, this->GetFixedImageRegion() );
typedef typename NumericTraits< MeasureType >::AccumulateType AccumulateType;
AccumulateType ratios_sum = NumericTraits< AccumulateType >::Zero;
this->m_NumberOfPixelsCounted = 0;
this->SetTransformParameters( parameters );
const unsigned int ParametersDimension = this->GetNumberOfParameters();
derivative = DerivativeType( ParametersDimension );
derivative.Fill( NumericTraits<ITK_TYPENAME DerivativeType::ValueType>::Zero );
DerivativeType derivative_sums = DerivativeType( ParametersDimension );
derivative_sums.Fill( NumericTraits<ITK_TYPENAME DerivativeType::ValueType>::Zero );
DerivativeType derivative_product_sums = DerivativeType( ParametersDimension );
derivative_product_sums.Fill( NumericTraits<ITK_TYPENAME DerivativeType::ValueType>::Zero );
// loop through all pixels in fixed image, finding ratio of pixel values
// and derivatives of ratios with respect to transform parameters at each
ti.GoToBegin();
while ( !ti.IsAtEnd() )
{
typename FixedImageType::IndexType index = ti.GetIndex();
// get physical point in fixed image corresponding to index
InputPointType inputPoint;
fixedImage->TransformIndexToPhysicalPoint( index, inputPoint );
// reject points outside fixed image mask, if mask is present
if ( this->m_FixedImageMask && !this->m_FixedImageMask->IsInside( inputPoint ) )
{
++ti;
continue;
}
// reject points which have a fixed image pixel value of zero, to
// prevent divide by zero problems when calculating ratios
const RealType fixedValue = ti.Get();
if ( fixedValue == NumericTraits< RealType >::Zero )
{
++ti;
continue;
}
// get physical point in moving image correspnoding to index using transform
OutputPointType transformedPoint = this->m_Transform->TransformPoint( inputPoint );
// reject points outside moving image mask, if mask is present
if ( this->m_MovingImageMask && !this->m_MovingImageMask->IsInside( transformedPoint ) )
{
++ti;
continue;
}
// if point is in masks and inside interpolator buffer, add the ratio of
// pixel values to accumulators
if ( this->m_Interpolator->IsInsideBuffer( transformedPoint ) )
{
// get moving value and calculate ratio between moving and fixed
// fixed values at current index
const RealType movingValue = this->m_Interpolator->Evaluate( transformedPoint );
const RealType ratio = movingValue / fixedValue;
this->m_NumberOfPixelsCounted++;
const TransformJacobianType& jacobian = this->m_Transform->GetJacobian( inputPoint );
// Get the gradient by NearestNeighboorInterpolation:
// which is equivalent to round up the point components.
typedef typename OutputPointType::CoordRepType CoordRepType;
typedef ContinuousIndex<CoordRepType, MovingImageType::ImageDimension> MovingImageContinuousIndexType;
MovingImageContinuousIndexType tempIndex;
this->m_MovingImage->TransformPhysicalPointToContinuousIndex( transformedPoint, tempIndex );
typename MovingImageType::IndexType mappedIndex;
mappedIndex.CopyWithRound( tempIndex );
const GradientPixelType gradient = this->GetGradientImage()->GetPixel( mappedIndex );
// add ratio to accumulator...
ratios_sum += ratio;
// for each transform parameter, find contributions to derivative
for (unsigned int par = 0; par < ParametersDimension; par++)
{
for (unsigned int dim = 0; dim < FixedImageType::ImageDimension; dim++)
{
const RealType ratio_derivative = jacobian( dim, par ) * gradient[dim] / fixedValue;
derivative_sums[par] += ratio_derivative;
derivative_product_sums[par] += ratio * ratio_derivative;
}
}
}
++ti;
}
const unsigned long& n = this->m_NumberOfPixelsCounted;
// abort if no data with which to calculate variance
if ( !n )
{
itkExceptionMacro( << "All the points mapped to outside of the moving image");
}
// use intermediate sums to calculate derivatives of variance of ratios of
// pixel values with respect to transformation parameters
if ( n > 1 )
{
for (unsigned int par = 0; par < ParametersDimension; par++)
{
derivative[par] = 2.0 / (n - 1.0) * ( derivative_product_sums[par] - ((ratios_sum * derivative_sums[par]) / n) );
}
}
// if n == 1, return derivatives of 0, which are the default since
// derivative is initialized to all NumericTraits< MeasureType >::Zero
}
/*
* Get both the match Measure and theDerivative Measure
*/
template < class TFixedImage, class TMovingImage >
void
RatioVarianceImageToImageMetric< TFixedImage, TMovingImage >
::GetValueAndDerivative( const TransformParametersType& parameters,
MeasureType& value, DerivativeType& derivative) const
{
itkDebugMacro("GetDerivative( " << parameters << " ) ");
if ( !this->GetGradientImage() )
{
itkExceptionMacro( << "The gradient image is null, maybe you forgot to call Initialize()");
}
FixedImageConstPointer fixedImage = this->m_FixedImage;
if ( !fixedImage )
{
itkExceptionMacro( << "Fixed image has not been assigned" );
}
typedef itk::ImageRegionConstIteratorWithIndex<FixedImageType> FixedIteratorType;
FixedIteratorType ti( fixedImage, this->GetFixedImageRegion() );
typedef typename NumericTraits< MeasureType >::AccumulateType AccumulateType;
AccumulateType ratios_sum = NumericTraits< AccumulateType >::Zero;
AccumulateType ratios2_sum = NumericTraits< AccumulateType >::Zero;
this->m_NumberOfPixelsCounted = 0;
this->SetTransformParameters( parameters );
const unsigned int ParametersDimension = this->GetNumberOfParameters();
derivative = DerivativeType( ParametersDimension );
derivative.Fill( NumericTraits<ITK_TYPENAME DerivativeType::ValueType>::Zero );
DerivativeType derivative_sums = DerivativeType( ParametersDimension );
derivative_sums.Fill( NumericTraits<ITK_TYPENAME DerivativeType::ValueType>::Zero );
DerivativeType derivative_product_sums = DerivativeType( ParametersDimension );
derivative_product_sums.Fill( NumericTraits<ITK_TYPENAME DerivativeType::ValueType>::Zero );
// loop through all pixels in fixed image, finding ratio of pixel values
// and derivatives of ratios with respect to transform parameters at each
ti.GoToBegin();
while ( !ti.IsAtEnd() )
{
typename FixedImageType::IndexType index = ti.GetIndex();
// get physical point in fixed image corresponding to index
InputPointType inputPoint;
fixedImage->TransformIndexToPhysicalPoint( index, inputPoint );
// reject points outside fixed image mask, if mask is present
if ( this->m_FixedImageMask && !this->m_FixedImageMask->IsInside( inputPoint ) )
{
++ti;
continue;
}
// reject points which have a fixed image pixel value of zero, to
// prevent divide by zero problems when calculating ratios
const RealType fixedValue = ti.Get();
if ( fixedValue == NumericTraits< RealType >::Zero )
{
++ti;
continue;
}
// get physical point in moving image correspnoding to index using transform
OutputPointType transformedPoint = this->m_Transform->TransformPoint( inputPoint );
// reject points outside moving image mask, if mask is present
if ( this->m_MovingImageMask && !this->m_MovingImageMask->IsInside( transformedPoint ) )
{
++ti;
continue;
}
// if point is in masks and inside interpolator buffer, add the ratio of
// pixel values to accumulators
if ( this->m_Interpolator->IsInsideBuffer( transformedPoint ) )
{
// get moving value and calculate ratio between moving and fixed
// fixed values at current index
const RealType movingValue = this->m_Interpolator->Evaluate( transformedPoint );
const RealType ratio = movingValue / fixedValue;
this->m_NumberOfPixelsCounted++;
const TransformJacobianType& jacobian = this->m_Transform->GetJacobian( inputPoint );
// Get the gradient by NearestNeighboorInterpolation:
// which is equivalent to round up the point components.
typedef typename OutputPointType::CoordRepType CoordRepType;
typedef ContinuousIndex<CoordRepType, MovingImageType::ImageDimension> MovingImageContinuousIndexType;
MovingImageContinuousIndexType tempIndex;
this->m_MovingImage->TransformPhysicalPointToContinuousIndex( transformedPoint, tempIndex );
typename MovingImageType::IndexType mappedIndex;
mappedIndex.CopyWithRound( tempIndex );
const GradientPixelType gradient = this->GetGradientImage()->GetPixel( mappedIndex );
// add ratio to accumulator...
ratios_sum += ratio;
ratios2_sum += ratio*ratio;
// for each transform parameter, find contributions to derivative
for (unsigned int par = 0; par < ParametersDimension; par++)
{
for (unsigned int dim = 0; dim < FixedImageType::ImageDimension; dim++)
{
const RealType ratio_derivative = jacobian( dim, par ) * gradient[dim] / fixedValue;
derivative_sums[par] += ratio_derivative;
derivative_product_sums[par] += ratio * ratio_derivative;
}
}
}
++ti;
}
const unsigned long& n = this->m_NumberOfPixelsCounted;
// abort if no data with which to calculate variance
if ( !n )
{
itkExceptionMacro( << "All the points mapped to outside of the moving image");
}
// use intermediate sums to calculate derivatives of variance of ratios of
// pixel values with respect to transformation parameters
if ( n > 1 )
{
for (unsigned int par = 0; par < ParametersDimension; par++)
{
derivative[par] = 2.0 / (n - 1.0) * ( derivative_product_sums[par] - ((ratios_sum * derivative_sums[par]) / n) );
}
// simple variance calculation for sample of data
value = (ratios2_sum - (ratios_sum * ratios_sum / n)) / (n - 1.0);
} else {
// leave derivatives = 0, which are the default since derivative is
// initialized to all NumericTraits< MeasureType >::Zero
value = NumericTraits< MeasureType >::Zero;
}
}
/**
* PrintSelf
*/
template < class TFixedImage, class TMovingImage >
void
RatioVarianceImageToImageMetric< TFixedImage, TMovingImage >
::PrintSelf(std::ostream& os, Indent indent) const
{
Superclass::PrintSelf(os, indent);
}
} // end namespace itk
#endif