#include <itkCorrelationImageToImageMetricv4.h>

Inheritance diagram for itk::CorrelationImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >:

Collaboration diagram for itk::CorrelationImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >:

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef Superclass::DerivativeType	DerivativeType
typedef Superclass::FixedImageGradientType	FixedImageGradientType
typedef Superclass::FixedImagePixelType	FixedImagePixelType
typedef Superclass::FixedImagePointType	FixedImagePointType
typedef Superclass::JacobianType	JacobianType
typedef Superclass::MeasureType	MeasureType
typedef Superclass::MovingImageGradientType	MovingImageGradientType
typedef Superclass::MovingImagePixelType	MovingImagePixelType
typedef Superclass::MovingImagePointType	MovingImagePointType
typedef Superclass::MovingTransformType	MovingTransformType
typedef SmartPointer< Self >	Pointer
typedef CorrelationImageToImageMetricv4	Self
typedef ImageToImageMetricv4 < TFixedImage, TMovingImage, TVirtualImage >	Superclass
typedef Superclass::VirtualImageType	VirtualImageType
typedef Superclass::VirtualIndexType	VirtualIndexType
typedef Superclass::VirtualPointSetType	VirtualPointSetType
typedef Superclass::VirtualPointType	VirtualPointType
Public Types inherited from itk::ImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >
typedef Superclass::CoordinateRepresentationType	CoordinateRepresentationType
typedef GradientRecursiveGaussianImageFilter < FixedImageType, FixedImageGradientImageType >	DefaultFixedImageGradientFilter
typedef GradientRecursiveGaussianImageFilter < MovingImageType, MovingImageGradientImageType >	DefaultMovingImageGradientFilter
typedef DerivativeType::ValueType	DerivativeValueType
typedef Superclass::DimensionType	DimensionType
typedef FixedImageType::ConstPointer	FixedImageConstPointer
typedef FixedImageGradientCalculatorType::Pointer	FixedImageGradientCalculatorPointer
typedef FixedImageGradientFilterType::Pointer	FixedImageGradientFilterPointer
typedef ImageToImageFilter < FixedImageType, FixedImageGradientImageType >	FixedImageGradientFilterType
typedef FixedImageType::IndexType	FixedImageIndexType
typedef FixedImageMaskType::ConstPointer	FixedImageMaskConstPointer
typedef FixedImageMaskType::Pointer	FixedImageMaskPointer
typedef SpatialObject < itkGetStaticConstMacro(FixedImageDimension) >	FixedImageMaskType
typedef FixedImageType::Pointer	FixedImagePointer
typedef TFixedImage	FixedImageType
typedef Superclass::FixedInputPointType	FixedInputPointType
typedef FixedInterpolatorType::Pointer	FixedInterpolatorPointer
typedef InterpolateImageFunction < FixedImageType, CoordinateRepresentationType >	FixedInterpolatorType
typedef Superclass::FixedOutputPointType	FixedOutputPointType
typedef FixedImagePixelType	FixedPixelType
typedef FixedSampledPointSetType::ConstPointer	FixedSampledPointSetConstPointer
typedef FixedSampledPointSetType::Pointer	FixedSampledPointSetPointer
typedef PointSet< typename FixedImageType::PixelType, itkGetStaticConstMacro(FixedImageDimension)>	FixedSampledPointSetType
typedef Superclass::FixedTransformJacobianType	FixedTransformJacobianType
typedef Superclass::FixedTransformParametersType	FixedTransformParametersType
typedef Superclass::FixedTransformPointer	FixedTransformPointer
typedef Superclass::FixedTransformType	FixedTransformType
typedef Superclass::GradientSourceType	GradientSourceType
typedef Superclass::DimensionType	ImageDimensionType
typedef Superclass::InternalComputationValueType	InternalComputationValueType
typedef CovariantVector < MovingRealType, itkGetStaticConstMacro(MovingImageDimension) >	MovingGradientPixelType
typedef MovingImageType::ConstPointer	MovingImageConstPointer
typedef MovingImageGradientCalculatorType::Pointer	MovingImageGradientCalculatorPointer
typedef MovingImageGradientFilterType::Pointer	MovingImageGradientFilterPointer
typedef ImageToImageFilter < MovingImageType, MovingImageGradientImageType >	MovingImageGradientFilterType
typedef MovingImageGradientImageType::Pointer	MovingImageGradientImagePointer
typedef Image < MovingGradientPixelType, itkGetStaticConstMacro(MovingImageDimension) >	MovingImageGradientImageType
typedef MovingImageType::IndexType	MovingImageIndexType
typedef MovingImageMaskType::ConstPointer	MovingImageMaskConstPointer
typedef MovingImageMaskType::Pointer	MovingImageMaskPointer
typedef SpatialObject < itkGetStaticConstMacro(MovingImageDimension) >	MovingImageMaskType
typedef MovingImageType::Pointer	MovingImagePointer
typedef MovingImageType::RegionType	MovingImageRegionType
typedef TMovingImage	MovingImageType
typedef Superclass::MovingInputPointType	MovingInputPointType
typedef MovingInterpolatorType::Pointer	MovingInterpolatorPointer
typedef InterpolateImageFunction < MovingImageType, CoordinateRepresentationType >	MovingInterpolatorType
typedef Superclass::MovingOutputPointType	MovingOutputPointType
typedef MovingImagePixelType	MovingPixelType
typedef NumericTraits < MovingImagePixelType > ::RealType	MovingRealType
typedef Superclass::MovingTransformJacobianType	MovingTransformJacobianType
typedef Superclass::MovingTransformParametersType	MovingTransformParametersType
typedef Superclass::MovingTransformPointer	MovingTransformPointer
typedef Superclass::NumberOfParametersType	NumberOfParametersType
typedef Superclass::ParametersType	ParametersType
typedef Superclass::ParametersValueType	ParametersValueType
typedef Superclass::VirtualDirectionType	VirtualDirectionType
typedef CovariantVector < CoordinateRepresentationType, itkGetStaticConstMacro(VirtualImageDimension) >	VirtualImageGradientType
typedef Superclass::VirtualImagePointer	VirtualImagePointer
typedef Superclass::VirtualPointType	VirtualOriginType
typedef Superclass::VirtualPixelType	VirtualPixelType
typedef Superclass::VirtualPointSetPointer	VirtualPointSetPointer
typedef Superclass::VirtualSizeType	VirtualRadiusType
typedef Superclass::VirtualRegionType	VirtualRegionType
typedef Superclass::VirtualSizeType	VirtualSizeType
typedef Superclass::VirtualSpacingType	VirtualSpacingType
typedef NumericTraits < FixedImagePixelType > ::RealType	FixedRealType
typedef CovariantVector < FixedRealType, itkGetStaticConstMacro(FixedImageDimension) >	FixedGradientPixelType
typedef Image < FixedGradientPixelType, itkGetStaticConstMacro(FixedImageDimension) >	FixedImageGradientImageType
typedef FixedImageGradientImageType::Pointer	FixedImageGradientImagePointer
typedef ImageFunction < FixedImageType, CovariantVector< double, itkGetStaticConstMacro(FixedImageDimension)> , CoordinateRepresentationType >	FixedImageGradientCalculatorType
typedef ImageFunction < MovingImageType, CovariantVector< double, itkGetStaticConstMacro(MovingImageDimension)> , CoordinateRepresentationType >	MovingImageGradientCalculatorType
Public Types inherited from itk::ObjectToObjectMetric< TFixedImage::ImageDimension, TMovingImage::ImageDimension, TVirtualImage >
typedef DisplacementFieldTransform < CoordinateRepresentationType, itkGetStaticConstMacro(MovingDimension) >	MovingDisplacementFieldTransformType
typedef VirtualImageType::ConstPointer	VirtualImageConstPointer
Public Types inherited from itk::ObjectToObjectMetricBase
Public Types inherited from itk::SingleValuedCostFunctionv4
Public Types inherited from itk::CostFunction
Public Types inherited from itk::Object
Public Types inherited from itk::LightObject

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual const char *	GetNameOfClass () const
Public Member Functions inherited from itk::ImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >
virtual void	GetDerivative (DerivativeType &) const
virtual const FixedImageType *	GetFixedImage ()
virtual const FixedImageGradientImageType *	GetFixedImageGradientImage ()
virtual const FixedInterpolatorType *	GetFixedInterpolator ()
virtual const MovingImageType *	GetMovingImage ()
virtual const MovingImageGradientImageType *	GetMovingImageGradientImage ()
virtual const MovingInterpolatorType *	GetMovingInterpolator ()
SizeValueType	GetNumberOfDomainPoints () const
virtual const SizeValueType &	GetNumberOfSkippedFixedSampledPoints ()
virtual ThreadIdType	GetNumberOfThreadsUsed () const
virtual SizeValueType	GetNumberOfValidPoints () const
virtual MeasureType	GetValue () const
virtual void	GetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const
virtual const VirtualPointSetType *	GetVirtualSampledPointSet ()
virtual void	Initialize (void) throw ( itk::ExceptionObject )
virtual void	SetFixedImage (const FixedImageType *_arg)
virtual void	SetFixedInterpolator (FixedInterpolatorType *_arg)
virtual void	SetMovingImage (const MovingImageType *_arg)
virtual void	SetMovingInterpolator (MovingInterpolatorType *_arg)
virtual bool	SupportsArbitraryVirtualDomainSamples (void) const
virtual void	SetMovingImageMask (MovingImageMaskType *_arg)
virtual void	SetMovingImageMask (const MovingImageMaskType *_arg)
virtual const MovingImageMaskType *	GetMovingImageMask ()
virtual void	SetFixedImageMask (FixedImageMaskType *_arg)
virtual void	SetFixedImageMask (const FixedImageMaskType *_arg)
virtual const FixedImageMaskType *	GetFixedImageMask ()
virtual void	SetFixedSampledPointSet (FixedSampledPointSetType *_arg)
virtual void	SetFixedSampledPointSet (const FixedSampledPointSetType *_arg)
virtual const FixedSampledPointSetType *	GetFixedSampledPointSet ()
virtual void	SetUseFixedSampledPointSet (bool _arg)
virtual const bool &	GetUseFixedSampledPointSet ()
virtual void	UseFixedSampledPointSetOn ()
virtual void	UseFixedSampledPointSetOff ()
virtual void	SetFixedImageGradientFilter (FixedImageGradientFilterType *_arg)
virtual FixedImageGradientFilterType *	GetFixedImageGradientFilter ()
virtual void	SetMovingImageGradientFilter (MovingImageGradientFilterType *_arg)
virtual MovingImageGradientFilterType *	GetMovingImageGradientFilter ()
virtual void	SetFixedImageGradientCalculator (FixedImageGradientCalculatorType *_arg)
virtual FixedImageGradientCalculatorType *	GetFixedImageGradientCalculator ()
virtual void	SetMovingImageGradientCalculator (MovingImageGradientCalculatorType *_arg)
virtual MovingImageGradientCalculatorType *	GetMovingImageGradientCalculator ()
virtual void	SetUseFixedImageGradientFilter (bool _arg)
virtual const bool &	GetUseFixedImageGradientFilter ()
virtual void	UseFixedImageGradientFilterOn ()
virtual void	UseFixedImageGradientFilterOff ()
virtual void	SetUseMovingImageGradientFilter (bool _arg)
virtual const bool &	GetUseMovingImageGradientFilter ()
virtual void	UseMovingImageGradientFilterOn ()
virtual void	UseMovingImageGradientFilterOff ()
virtual void	SetMaximumNumberOfThreads (const ThreadIdType threads)
virtual ThreadIdType	GetMaximumNumberOfThreads () const
virtual void	SetUseFloatingPointCorrection (bool _arg)
virtual const bool &	GetUseFloatingPointCorrection ()
virtual void	UseFloatingPointCorrectionOn ()
virtual void	UseFloatingPointCorrectionOff ()
virtual void	SetFloatingPointCorrectionResolution (DerivativeValueType _arg)
virtual DerivativeValueType	GetFloatingPointCorrectionResolution () const
Public Member Functions inherited from itk::ObjectToObjectMetric< TFixedImage::ImageDimension, TMovingImage::ImageDimension, TVirtualImage >
OffsetValueType	ComputeParameterOffsetFromVirtualIndex (const VirtualIndexType &index, const NumberOfParametersType &numberOfLocalParameters) const
OffsetValueType	ComputeParameterOffsetFromVirtualPoint (const VirtualPointType &point, const NumberOfParametersType &numberOfLocalParameters) const
virtual const FixedTransformType *	GetFixedTransform ()
virtual const MovingTransformType *	GetMovingTransform ()
virtual NumberOfParametersType	GetNumberOfLocalParameters () const
virtual NumberOfParametersType	GetNumberOfParameters () const
virtual const ParametersType &	GetParameters () const
const MovingTransformType *	GetTransform ()
VirtualDirectionType	GetVirtualDirection (void) const
virtual const TimeStamp &	GetVirtualDomainTimeStamp (void) const
virtual const VirtualImageType *	GetVirtualImage ()
VirtualOriginType	GetVirtualOrigin (void) const
const VirtualRegionType &	GetVirtualRegion (void) const
VirtualSpacingType	GetVirtualSpacing (void) const
virtual bool	HasLocalSupport () const
virtual void	SetFixedTransform (FixedTransformType *_arg)
virtual void	SetMovingTransform (MovingTransformType *_arg)
virtual void	SetParameters (ParametersType &params)
void	SetTransform (MovingTransformType *transform)
void	SetVirtualDomain (const VirtualSpacingType &spacing, const VirtualOriginType &origin, const VirtualDirectionType &direction, const VirtualRegionType &region)
virtual void	UpdateTransformParameters (const DerivativeType &derivative, ParametersValueType factor)
void	SetVirtualDomainFromImage (VirtualImageType *virtualImage)
void	SetVirtualDomainFromImage (const VirtualImageType *virtualImage)
bool	IsInsideVirtualDomain (const VirtualPointType &point) const
bool	IsInsideVirtualDomain (const VirtualIndexType &index) const
Public Member Functions inherited from itk::ObjectToObjectMetricBase
MeasureType	GetCurrentValue () const
virtual GradientSourceType	GetGradientSource () const
bool	GetGradientSourceIncludesFixed () const
bool	GetGradientSourceIncludesMoving () const
virtual void	GetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const =0
virtual void	SetGradientSource (GradientSourceType _arg)
Public Member Functions inherited from itk::SingleValuedCostFunctionv4
virtual void	GetValueAndDerivative (MeasureType &value, DerivativeType &derivative) const =0

Static Public Member Functions
static Pointer	New ()

Static Public Attributes
static const ImageDimensionType	FixedImageDimension = ::itk::GetImageDimension<TFixedImage>::ImageDimension
static const ImageDimensionType	MovingImageDimension = ::itk::GetImageDimension<TMovingImage>::ImageDimension
static const ImageDimensionType	VirtualImageDimension = ::itk::GetImageDimension<TVirtualImage>::ImageDimension
Static Public Attributes inherited from itk::ImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >
Static Public Attributes inherited from itk::ObjectToObjectMetric< TFixedImage::ImageDimension, TMovingImage::ImageDimension, TVirtualImage >
static const DimensionType	FixedDimension
static const DimensionType	MovingDimension
static const DimensionType	VirtualDimension

Protected Types
typedef CorrelationImageToImageMetricv4GetValueAndDerivativeThreader < ThreadedImageRegionPartitioner < Superclass::VirtualImageDimension > , Superclass, Self >	CorrelationDenseGetValueAndDerivativeThreaderType
typedef CorrelationImageToImageMetricv4HelperThreader < ThreadedImageRegionPartitioner < Superclass::VirtualImageDimension > , Superclass, Self >	CorrelationHelperDenseThreaderType
typedef CorrelationImageToImageMetricv4HelperThreader < ThreadedIndexedContainerPartitioner, Superclass, Self >	CorrelationHelperSparseThreaderType
typedef CorrelationImageToImageMetricv4GetValueAndDerivativeThreader < ThreadedIndexedContainerPartitioner, Superclass, Self >	CorrelationSparseGetValueAndDerivativeThreaderType
Protected Types inherited from itk::ImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >
typedef LinearInterpolateImageFunction < FixedImageGradientImageType, CoordinateRepresentationType >	FixedImageGradientInterpolatorType
typedef LinearInterpolateImageFunction < MovingImageGradientImageType, CoordinateRepresentationType >	MovingImageGradientInterpolatorType

Protected Member Functions
	CorrelationImageToImageMetricv4 ()
virtual void	InitializeForIteration () const
void	PrintSelf (std::ostream &os, Indent indent) const
virtual	~CorrelationImageToImageMetricv4 ()
Protected Member Functions inherited from itk::ImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >
virtual void	ComputeFixedImageGradientAtIndex (const VirtualIndexType &index, FixedImageGradientType &gradient) const
virtual void	ComputeFixedImageGradientAtPoint (const FixedImagePointType &mappedPoint, FixedImageGradientType &gradient) const
virtual void	ComputeFixedImageGradientFilterImage ()
virtual void	ComputeMovingImageGradientAtIndex (const VirtualIndexType &index, MovingImageGradientType &gradient) const
virtual void	ComputeMovingImageGradientAtPoint (const MovingImagePointType &mappedPoint, MovingImageGradientType &gradient) const
virtual void	ComputeMovingImageGradientFilterImage () const
virtual void	GetValueAndDerivativeExecute () const
	ImageToImageMetricv4 ()
bool	TransformAndEvaluateFixedPoint (const VirtualIndexType &index, const VirtualPointType &point, const bool computeImageGradient, FixedImagePointType &mappedFixedPoint, FixedImagePixelType &mappedFixedPixelValue, FixedImageGradientType &mappedFixedImageGradient) const
bool	TransformAndEvaluateMovingPoint (const VirtualIndexType &index, const VirtualPointType &point, const bool computeImageGradient, MovingImagePointType &mappedMovingPoint, MovingImagePixelType &mappedMovingPixelValue, MovingImageGradientType &mappedMovingImageGradient) const
virtual	~ImageToImageMetricv4 ()
virtual void	InitializeDefaultFixedImageGradientFilter (void)
virtual void	InitializeDefaultMovingImageGradientFilter (void)
Protected Member Functions inherited from itk::ObjectToObjectMetric< TFixedImage::ImageDimension, TMovingImage::ImageDimension, TVirtualImage >
MovingDisplacementFieldTransformType *	GetMovingDisplacementFieldTransform () const
	ObjectToObjectMetric ()
bool	TransformPhysicalPointToVirtualIndex (const VirtualPointType &, VirtualIndexType &) const
void	TransformVirtualIndexToPhysicalPoint (const VirtualIndexType &, VirtualPointType &) const
virtual void	VerifyDisplacementFieldSizeAndPhysicalSpace ()
bool	VerifyNumberOfValidPoints (MeasureType &value, DerivativeType &derivative) const
virtual	~ObjectToObjectMetric ()
Protected Member Functions inherited from itk::ObjectToObjectMetricBase
	ObjectToObjectMetricBase ()
virtual	~ObjectToObjectMetricBase ()
Protected Member Functions inherited from itk::SingleValuedCostFunctionv4
	SingleValuedCostFunctionv4 ()
virtual	~SingleValuedCostFunctionv4 ()
Protected Member Functions inherited from itk::CostFunction
	CostFunction ()
virtual	~CostFunction ()
Protected Member Functions inherited from itk::Object
	Object ()
bool	PrintObservers (std::ostream &os, Indent indent) const
virtual void	SetTimeStamp (const TimeStamp &time)
virtual	~Object ()
Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const
	LightObject ()
virtual void	PrintHeader (std::ostream &os, Indent indent) const
virtual void	PrintTrailer (std::ostream &os, Indent indent) const
virtual	~LightObject ()

Protected Attributes
MeasureType	m_AverageFix
MeasureType	m_AverageMov
CorrelationHelperDenseThreaderType::Pointer	m_HelperDenseThreader
CorrelationHelperSparseThreaderType::Pointer	m_HelperSparseThreader
Protected Attributes inherited from itk::ImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >
DefaultFixedImageGradientFilter::Pointer	m_DefaultFixedImageGradientFilter
DefaultMovingImageGradientFilter::Pointer	m_DefaultMovingImageGradientFilter
ImageToImageMetricv4GetValueAndDerivativeThreader < ThreadedImageRegionPartitioner < VirtualImageDimension > , Self >::Pointer	m_DenseGetValueAndDerivativeThreader
DerivativeType *	m_DerivativeResult
FixedImageConstPointer	m_FixedImage
FixedImageGradientCalculatorPointer	m_FixedImageGradientCalculator
FixedImageGradientFilterPointer	m_FixedImageGradientFilter
FixedImageGradientImagePointer	m_FixedImageGradientImage
FixedImageGradientInterpolatorType::Pointer	m_FixedImageGradientInterpolator
FixedImageMaskConstPointer	m_FixedImageMask
FixedInterpolatorPointer	m_FixedInterpolator
FixedSampledPointSetConstPointer	m_FixedSampledPointSet
MovingImageConstPointer	m_MovingImage
MovingImageGradientCalculatorPointer	m_MovingImageGradientCalculator
MovingImageGradientFilterPointer	m_MovingImageGradientFilter
MovingImageGradientImagePointer	m_MovingImageGradientImage
MovingImageGradientInterpolatorType::Pointer	m_MovingImageGradientInterpolator
MovingImageMaskConstPointer	m_MovingImageMask
MovingInterpolatorPointer	m_MovingInterpolator
ImageToImageMetricv4GetValueAndDerivativeThreader < ThreadedIndexedContainerPartitioner, Self >::Pointer	m_SparseGetValueAndDerivativeThreader
bool	m_UseFixedImageGradientFilter
bool	m_UseFixedSampledPointSet
bool	m_UseMovingImageGradientFilter
VirtualPointSetPointer	m_VirtualSampledPointSet
Protected Attributes inherited from itk::ObjectToObjectMetric< TFixedImage::ImageDimension, TMovingImage::ImageDimension, TVirtualImage >
FixedTransformPointer	m_FixedTransform
MovingTransformPointer	m_MovingTransform
SizeValueType	m_NumberOfValidPoints
bool	m_UserHasSetVirtualDomain
VirtualImagePointer	m_VirtualImage
Protected Attributes inherited from itk::ObjectToObjectMetricBase
GradientSourceType	m_GradientSource
MeasureType	m_Value

Private Member Functions
	CorrelationImageToImageMetricv4 (const Self &)
void	operator= (const Self &)

Friends
class	CorrelationImageToImageMetricv4GetValueAndDerivativeThreader< ThreadedImageRegionPartitioner< Superclass::VirtualImageDimension >, Superclass, Self >
class	CorrelationImageToImageMetricv4GetValueAndDerivativeThreader< ThreadedIndexedContainerPartitioner, Superclass, Self >
class	CorrelationImageToImageMetricv4HelperThreader< ThreadedImageRegionPartitioner< Superclass::VirtualImageDimension >, Superclass, Self >
class	CorrelationImageToImageMetricv4HelperThreader< ThreadedIndexedContainerPartitioner, Superclass, Self >
class	ImageToImageMetricv4GetValueAndDerivativeThreader< ThreadedImageRegionPartitioner< Superclass::VirtualImageDimension >, Self >
class	ImageToImageMetricv4GetValueAndDerivativeThreader< ThreadedIndexedContainerPartitioner, Self >
class	ImageToImageMetricv4GetValueAndDerivativeThreaderBase< ThreadedImageRegionPartitioner< Superclass::VirtualImageDimension >, Self >
class	ImageToImageMetricv4GetValueAndDerivativeThreaderBase< ThreadedIndexedContainerPartitioner, Self >

Detailed Description

template<class TFixedImage, class TMovingImage, class TVirtualImage = TFixedImage>
class itk::CorrelationImageToImageMetricv4< TFixedImage, TMovingImage, TVirtualImage >

Class implementing normalized cross correlation image metric.

Definition of the normalized cross correlation metric used here:

negative square of normalized cross correlation

$C(f, m) = -\frac{<f-\bar{f}, m-\bar{m} >^2}{|f-\bar{f}}|^2 |m-\bar{m}|^2}$

in which, f, m are the vectors of image pixel intensities, $\bar{f}$ and $\bar{m}$ are the mean values of f and m. <,> denotes inner product, $|\cdot|$ denotes the 2-norm of the vector. The minus sign makes the metric to optimize towards its minimal value. Note that this uses the square of the mathematical notion of normalized cross correlation to avoid the square root computation in practice.

Moving image (m) is a function of the parameters (p) of the moving transforms. So $ C(f, m) = C(f, m(p)) $ GetValueAndDerivative will return the value as $ C(f,m) $ and the derivative as

$\frac{d}{dp} C = 2 \frac{<f1, m1>}{|f1|^2 |m1|^2} * ( <f1, \frac{dm}{dp}> - \frac{<f1, m1>}{|m1|^2} < m1, \frac{dm}{dp} > )$

in which, $f1 = f - \bar{f}$ , $m1 = m - \bar{m}$ (Note: there should be a minus sign of $\frac{d}{dp}$ mathematically, which is not in the implementation to match the requirement of the metricv4 optimization framework.

See CorrelationImageToImageMetricv4GetValueAndDerivativeThreader::ProcessPoint for algorithm implementation.

This metric only works with the global transform. It throws an exception if the transform has local support.

Definition at line 73 of file itkCorrelationImageToImageMetricv4.h.