#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::VirtualPointType	VirtualPointType
typedef Superclass::VirtualSampledPointSetType	VirtualSampledPointSetType
Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual const char *	GetNameOfClass () const
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
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 Member Functions
	CorrelationImageToImageMetricv4 ()
virtual void	InitializeForIteration () const
void	PrintSelf (std::ostream &os, Indent indent) const
virtual	~CorrelationImageToImageMetricv4 ()
Protected Attributes
MeasureType	m_AverageFix
MeasureType	m_AverageMov
CorrelationHelperDenseThreaderType::Pointer	m_HelperDenseThreader
CorrelationHelperSparseThreaderType::Pointer	m_HelperSparseThreader
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.