#include <itkGaussianExponentialDiffeomorphicTransform.h>

Inheritance diagram for itk::GaussianExponentialDiffeomorphicTransform< TScalar, NDimensions >:

Collaboration diagram for itk::GaussianExponentialDiffeomorphicTransform< TScalar, NDimensions >:

Detailed Description

template<class TScalar, unsigned int NDimensions>
class itk::GaussianExponentialDiffeomorphicTransform< TScalar, NDimensions >

Exponential transform using a Gaussian smoothing kernel.

Exponential transform inspired by the work of J. Ashburner (see reference below). Assuming a constant velocity field, the transform takes as input the update field at time point t = 1, $u$ and smooths it using Gaussian smoothing, $S_{update}$ defined by GaussianSmoothingVarianceForTheUpdateField We add that the current estimate of the velocity field and then perform a second smoothing step such that the new velocity field is

$\begin{eqnarray*} v_{new} = S_{velocity}( v_{old} + S_{update}( u ) ). \end{eqnarray*}$

We then exponentiate $v_{new}$ using the class ExponentialDisplacementImageFilter to yield both the forward and inverse displacement fields.

J. Ashburner. A Fast Diffeomorphic Image Registration Algorithm. NeuroImage, 38(1):95-113, 2007.

Author: Nick Tustison; Brian Avants

Definition at line 57 of file itkGaussianExponentialDiffeomorphicTransform.h.

Public Types
typedef Superclass::ConstantVelocityFieldPointer	ConstantVelocityFieldPointer

typedef Superclass::ConstantVelocityFieldType	ConstantVelocityFieldType

typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DerivativeType	DerivativeType

typedef DerivativeType::ValueType	DerivativeValueType

typedef Superclass::DisplacementFieldPointer	DisplacementFieldPointer

typedef Superclass::DisplacementFieldType	DisplacementFieldType

typedef DisplacementFieldType::PixelType	DisplacementVectorType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef GaussianExponentialDiffeomorphicTransform	Self

typedef ConstantVelocityFieldTransform < TScalar, NDimensions >	Superclass

Public Types inherited from itk::ConstantVelocityFieldTransform< TScalar, NDimensions >
typedef ConstantVelocityFieldInterpolatorType::Pointer	ConstantVelocityFieldInterpolatorPointer

typedef VectorInterpolateImageFunction < ConstantVelocityFieldType, ScalarType >	ConstantVelocityFieldInterpolatorType

typedef ConstantVelocityFieldType::Pointer	ConstantVelocityFieldPointer

typedef Image < OutputVectorType, ConstantVelocityFieldDimension >	ConstantVelocityFieldType

typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DerivativeType	DerivativeType

typedef ConstantVelocityFieldType::DirectionType	DirectionType

typedef DisplacementFieldType::Pointer	DisplacementFieldPointer

typedef Superclass::DisplacementFieldType	DisplacementFieldType

typedef ConstantVelocityFieldType::IndexType	IndexType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputVectorPixelType	InputVectorPixelType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef ImageVectorOptimizerParametersHelper < ScalarType, Dimension, ConstantVelocityFieldDimension >	OptimizerParametersHelperType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef ConstantVelocityFieldType::PixelType	PixelType

typedef SmartPointer< Self >	Pointer

typedef ConstantVelocityFieldType::PointType	PointType

typedef ConstantVelocityFieldType::RegionType	RegionType

typedef Superclass::ScalarType	ScalarType

typedef ConstantVelocityFieldTransform	Self

typedef ConstantVelocityFieldType::SizeType	SizeType

typedef ConstantVelocityFieldType::SpacingType	SpacingType

typedef DisplacementFieldTransform < TScalar, NDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

typedef ConstantVelocityFieldType	VelocityFieldType

Public Types inherited from itk::DisplacementFieldTransform< TScalar, NDimensions >
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DerivativeType	DerivativeType

typedef DisplacementFieldType::DirectionType	DirectionType

typedef DisplacementFieldType::Pointer	DisplacementFieldPointer

typedef Image < OutputVectorType, Dimension >	DisplacementFieldType

typedef DisplacementFieldType::IndexType	IndexType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputDiffusionTensor3DType	InputDiffusionTensor3DType

typedef Superclass::InputPointType	InputPointType

typedef CovariantVector < ScalarType, InputDiffusionTensor3DType::Dimension >	InputTensorEigenVectorType

typedef Superclass::InputVectorPixelType	InputVectorPixelType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef VectorInterpolateImageFunction < DisplacementFieldType, ScalarType >	InterpolatorType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::JacobianType	JacobianType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef ImageVectorOptimizerParametersHelper < ScalarType, OutputVectorType::Dimension, Dimension >	OptimizerParametersHelperType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputDiffusionTensor3DType	OutputDiffusionTensor3DType

typedef Superclass::OutputPointType	OutputPointType

typedef CovariantVector < ScalarType, OutputDiffusionTensor3DType::Dimension >	OutputTensorEigenVectorType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef DisplacementFieldType::PixelType	PixelType

typedef SmartPointer< Self >	Pointer

typedef DisplacementFieldType::PointType	PointType

typedef DisplacementFieldType::RegionType	RegionType

typedef Superclass::ScalarType	ScalarType

typedef DisplacementFieldTransform	Self

typedef DisplacementFieldType::SizeType	SizeType

typedef DisplacementFieldType::SpacingType	SpacingType

typedef Transform< TScalar, NDimensions, NDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

Public Types inherited from itk::Transform< TScalar, NDimensions, NDimensions >
typedef SmartPointer< const Self >	ConstPointer

typedef Array < ParametersValueType >	DerivativeType

typedef Matrix< double, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	DirectionChangeMatrix

typedef CovariantVector < TScalar, NInputDimensions >	InputCovariantVectorType

typedef DiffusionTensor3D < TScalar >	InputDiffusionTensor3DType

typedef Matrix< double, itkGetStaticConstMacro(InputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	InputDirectionMatrix

typedef Point< TScalar, NInputDimensions >	InputPointType

typedef SymmetricSecondRankTensor < TScalar, NInputDimensions >	InputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalar >	InputVectorPixelType

typedef Vector< TScalar, NInputDimensions >	InputVectorType

typedef vnl_vector_fixed < TScalar, NInputDimensions >	InputVnlVectorType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Transform< TScalar, NOutputDimensions, NInputDimensions >	InverseTransformBaseType

typedef Array2D < ParametersValueType >	JacobianType

typedef Matrix< TScalar, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	MatrixType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef CovariantVector < TScalar, NOutputDimensions >	OutputCovariantVectorType

typedef DiffusionTensor3D < TScalar >	OutputDiffusionTensor3DType

typedef Matrix< double, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(OutputSpaceDimension)>	OutputDirectionMatrix

typedef Point< TScalar, NOutputDimensions >	OutputPointType

typedef SymmetricSecondRankTensor < TScalar, NOutputDimensions >	OutputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalar >	OutputVectorPixelType

typedef Vector< TScalar, NOutputDimensions >	OutputVectorType

typedef vnl_vector_fixed < TScalar, NOutputDimensions >	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TScalar	ScalarType

typedef Transform	Self

typedef TransformBase	Superclass

Public Types inherited from itk::TransformBase
typedef SmartPointer< const Self >	ConstPointer

typedef IdentifierType	NumberOfParametersType

typedef OptimizerParameters < ParametersValueType >	ParametersType

typedef double	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TransformBase	Self

typedef Object	Superclass

enum	TransformCategoryType { UnknownTransformCategory =0, Linear =1, BSpline =2, Spline =3, DisplacementField =4, VelocityField =5 }

Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

virtual ConstantVelocityFieldPointer	GaussianSmoothConstantVelocityField (ConstantVelocityFieldType *, ScalarType)

virtual const char *	GetNameOfClass () const

virtual void	UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0)


virtual void	SetGaussianSmoothingVarianceForTheConstantVelocityField (ScalarType _arg)

virtual ScalarType	GetGaussianSmoothingVarianceForTheConstantVelocityField () const


virtual void	SetGaussianSmoothingVarianceForTheUpdateField (ScalarType _arg)

virtual ScalarType	GetGaussianSmoothingVarianceForTheUpdateField () const

Public Member Functions inherited from itk::ConstantVelocityFieldTransform< TScalar, NDimensions >
virtual void	CalculateNumberOfIntegrationStepsAutomaticallyOff ()

virtual void	CalculateNumberOfIntegrationStepsAutomaticallyOn ()

virtual bool	GetCalculateNumberOfIntegrationStepsAutomatically () const

virtual ConstantVelocityFieldType *	GetConstantVelocityField ()

virtual const ModifiedTimeType &	GetConstantVelocityFieldSetTime ()

bool	GetInverse (Self *inverse) const

virtual InverseTransformBasePointer	GetInverseTransform () const

virtual ScalarType	GetLowerTimeBound () const

virtual unsigned int	GetNumberOfIntegrationSteps () const

virtual ScalarType	GetUpperTimeBound () const

virtual void	IntegrateVelocityField ()

virtual void	SetCalculateNumberOfIntegrationStepsAutomatically (bool _arg)

virtual void	SetConstantVelocityField (ConstantVelocityFieldType *)

virtual void	SetFixedParameters (const ParametersType &)

virtual void	SetLowerTimeBound (ScalarType _arg)

virtual void	SetNumberOfIntegrationSteps (unsigned int _arg)

virtual void	SetUpperTimeBound (ScalarType _arg)

virtual ConstantVelocityFieldInterpolatorType *	GetConstantVelocityFieldInterpolator ()

virtual void	SetConstantVelocityFieldInterpolator (ConstantVelocityFieldInterpolatorType *)

Public Member Functions inherited from itk::DisplacementFieldTransform< TScalar, NDimensions >
virtual void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, JacobianType &j) const

virtual void	ComputeJacobianWithRespectToParameters (const IndexType &, JacobianType &j) const

virtual void	ComputeJacobianWithRespectToPosition (const InputPointType &x, JacobianType &j) const

virtual void	ComputeJacobianWithRespectToPosition (const IndexType &x, JacobianType &j) const

virtual DisplacementFieldType *	GetDisplacementField ()

virtual const ModifiedTimeType &	GetDisplacementFieldSetTime ()

bool	GetInverse (Self *inverse) const

virtual void	GetInverseJacobianOfForwardFieldWithRespectToPosition (const InputPointType &point, JacobianType &jacobian, bool useSVD=false) const

virtual void	GetInverseJacobianOfForwardFieldWithRespectToPosition (const IndexType &index, JacobianType &jacobian, bool useSVD=false) const

virtual NumberOfParametersType	GetNumberOfLocalParameters (void) const

virtual TransformCategoryType	GetTransformCategory () const

virtual void	SetDisplacementField (DisplacementFieldType *field)

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const

OutputVectorPixelType	TransformDiffusionTensor (const InputVectorPixelType &) const

virtual OutputPointType	TransformPoint (const InputPointType &thisPoint) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

virtual void	UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0)

virtual DisplacementFieldType *	GetInverseDisplacementField ()

virtual void	SetInverseDisplacementField (DisplacementFieldType *inverseDisplacementField)

virtual InterpolatorType *	GetInterpolator ()

virtual void	SetInterpolator (InterpolatorType *interpolator)

virtual InterpolatorType *	GetInverseInterpolator ()

virtual void	SetInverseInterpolator (InterpolatorType *interpolator)

virtual OutputVectorType	TransformVector (const InputVectorType &) const

OutputDiffusionTensor3DType	TransformDiffusionTensor (const InputDiffusionTensor3DType &) const

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

virtual void	SetParameters (const ParametersType &params)

virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &j) const

Public Member Functions inherited from itk::Transform< TScalar, NDimensions, NDimensions >
virtual void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, JacobianType &jacobian) const

virtual void	ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianType &) const

virtual const ParametersType &	GetFixedParameters (void) const

unsigned int	GetInputSpaceDimension (void) const

bool	GetInverse (Self *) const

virtual NumberOfParametersType	GetNumberOfParameters (void) const

unsigned int	GetOutputSpaceDimension (void) const

virtual const ParametersType &	GetParameters (void) const

virtual std::string	GetTransformTypeAsString () const

virtual bool	IsLinear () const

	itkCloneMacro (Self)

virtual void	SetParametersByValue (const ParametersType &p)

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &tensor, const InputPointType &point) const

virtual OutputPointType	TransformPoint (const InputPointType &) const =0

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &tensor, const InputPointType &point) const

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &tensor, const InputPointType &point) const

virtual OutputVectorType	TransformVector (const InputVectorType &) const

virtual OutputVectorType	TransformVector (const InputVectorType &vector, const InputPointType &point) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual void	UpdateTransformParameters (const DerivativeType &update, TScalarfactor=1.0)

virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::ConstantVelocityFieldTransform< TScalar, NDimensions >
static Pointer	New ()

Static Public Member Functions inherited from itk::DisplacementFieldTransform< TScalar, NDimensions >
static Pointer	New ()

Static Public Attributes
static const unsigned int	ConstantVelocityFieldDimension = NDimensions

static const unsigned int	Dimension = NDimensions

Static Public Attributes inherited from itk::ConstantVelocityFieldTransform< TScalar, NDimensions >
static const unsigned int	ConstantVelocityFieldDimension = NDimensions

static const unsigned int	Dimension = NDimensions

Static Public Attributes inherited from itk::DisplacementFieldTransform< TScalar, NDimensions >
static const unsigned int	Dimension = NDimensions

Static Public Attributes inherited from itk::Transform< TScalar, NDimensions, NDimensions >
static const unsigned int	InputSpaceDimension

static const unsigned int	OutputSpaceDimension

Protected Types
typedef GaussianOperator < ScalarType, NDimensions >	GaussianSmoothingOperatorType

typedef VectorNeighborhoodOperatorImageFilter < ConstantVelocityFieldType, ConstantVelocityFieldType >	GaussianSmoothingSmootherType

Protected Member Functions
	GaussianExponentialDiffeomorphicTransform ()

void	PrintSelf (std::ostream &, Indent) const

virtual	~GaussianExponentialDiffeomorphicTransform ()

Protected Member Functions inherited from itk::ConstantVelocityFieldTransform< TScalar, NDimensions >
	ConstantVelocityFieldTransform ()

DisplacementFieldType::Pointer	CopyDisplacementField (const DisplacementFieldType *) const

virtual LightObject::Pointer	InternalClone () const

virtual	~ConstantVelocityFieldTransform ()

Protected Member Functions inherited from itk::DisplacementFieldTransform< TScalar, NDimensions >
	DisplacementFieldTransform ()

virtual	~DisplacementFieldTransform ()

Protected Member Functions inherited from itk::Transform< TScalar, NDimensions, NDimensions >
OutputDiffusionTensor3DType	PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType, const JacobianType) const

	Transform ()

	Transform (NumberOfParametersType NumberOfParameters)

virtual	~Transform ()

Protected Member Functions inherited from itk::TransformBase
	TransformBase ()

virtual	~TransformBase ()

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
	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Protected Attributes
GaussianSmoothingOperatorType	m_GaussianSmoothingOperator

Protected Attributes inherited from itk::ConstantVelocityFieldTransform< TScalar, NDimensions >
bool	m_CalculateNumberOfIntegrationStepsAutomatically

ConstantVelocityFieldPointer	m_ConstantVelocityField

ConstantVelocityFieldInterpolatorPointer	m_ConstantVelocityFieldInterpolator

ModifiedTimeType	m_ConstantVelocityFieldSetTime

ScalarType	m_LowerTimeBound

unsigned int	m_NumberOfIntegrationSteps

ScalarType	m_UpperTimeBound

Protected Attributes inherited from itk::DisplacementFieldTransform< TScalar, NDimensions >
DisplacementFieldType::Pointer	m_DisplacementField

ModifiedTimeType	m_DisplacementFieldSetTime

JacobianType	m_IdentityJacobian

InterpolatorType::Pointer	m_Interpolator

DisplacementFieldType::Pointer	m_InverseDisplacementField

InterpolatorType::Pointer	m_InverseInterpolator

Protected Attributes inherited from itk::Transform< TScalar, NDimensions, NDimensions >
DirectionChangeMatrix	m_DirectionChange

ParametersType	m_FixedParameters

ParametersType	m_Parameters

Private Member Functions
	GaussianExponentialDiffeomorphicTransform (const Self &)

void	operator= (const Self &)

Private Attributes
ScalarType	m_GaussianSmoothingVarianceForTheConstantVelocityField

ScalarType	m_GaussianSmoothingVarianceForTheUpdateField