#include <itkBSplineExponentialDiffeomorphicTransform.h>

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

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

Detailed Description

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

Exponential transform using B-splines as the 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 a B-spline smoothing (i.e. fitting) operation, $S_{update}$ defined by SplineOrder and NumberOfControlPointsForTheUpdateField. 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 56 of file itkBSplineExponentialDiffeomorphicTransform.h.

Public Types
typedef BSplineFilterType::ArrayType	ArrayType

typedef ArrayType::ValueType	ArrayValueType

typedef DisplacementFieldToBSplineImageFilter < ConstantVelocityFieldType, ConstantVelocityFieldType >	BSplineFilterType

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 PointSet < ConstantVelocityFieldType, Dimension >	PointSetType

typedef Superclass::ScalarType	ScalarType

typedef BSplineExponentialDiffeomorphicTransform	Self

typedef unsigned int	SplineOrderType

typedef ConstantVelocityFieldTransform < TScalar, NDimensions >	Superclass

typedef BSplineFilterType::WeightsContainerType	WeightsContainerType

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::ConstPointer	DisplacementFieldConstPointer

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 ConstantVelocityFieldPointer	BSplineSmoothConstantVelocityField (const ConstantVelocityFieldType *, const ArrayType &)

virtual ::itk::LightObject::Pointer	CreateAnother (void) const

virtual const char *	GetNameOfClass () const

void	SetMeshSizeForTheConstantVelocityField (const ArrayType &)

void	SetMeshSizeForTheUpdateField (const ArrayType &)

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


virtual void	SetSplineOrder (SplineOrderType _arg)

virtual SplineOrderType	GetSplineOrder () const


virtual void	SetNumberOfControlPointsForTheConstantVelocityField (ArrayType _arg)

virtual ArrayType	GetNumberOfControlPointsForTheConstantVelocityField () const


virtual void	SetNumberOfControlPointsForTheUpdateField (ArrayType _arg)

virtual ArrayType	GetNumberOfControlPointsForTheUpdateField () const

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

virtual void	CalculateNumberOfIntegrationStepsAutomaticallyOn ()

virtual ::itk::LightObject::Pointer	CreateAnother (void) const

virtual bool	GetCalculateNumberOfIntegrationStepsAutomatically () const

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	SetFixedParameters (const ParametersType &)

virtual void	SetLowerTimeBound (ScalarType _arg)

virtual void	SetNumberOfIntegrationSteps (unsigned int _arg)

virtual void	SetUpperTimeBound (ScalarType _arg)

virtual void	SetConstantVelocityField (ConstantVelocityFieldType *)

virtual ConstantVelocityFieldType *	GetModifiableConstantVelocityField ()

virtual const ConstantVelocityFieldType *	GetConstantVelocityField () const

virtual void	SetConstantVelocityFieldInterpolator (ConstantVelocityFieldInterpolatorType *)

virtual ConstantVelocityFieldInterpolatorType *	GetModifiableConstantVelocityFieldInterpolator ()

virtual const ConstantVelocityFieldInterpolatorType *	GetConstantVelocityFieldInterpolator () const

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 ::itk::LightObject::Pointer	CreateAnother (void) const

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 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 void	SetDisplacementField (DisplacementFieldType *field)

virtual DisplacementFieldType *	GetModifiableDisplacementField ()

virtual const DisplacementFieldType *	GetDisplacementField () const

virtual void	SetInverseDisplacementField (DisplacementFieldType *inverseDisplacementField)

virtual DisplacementFieldType *	GetModifiableInverseDisplacementField ()

virtual const DisplacementFieldType *	GetInverseDisplacementField () const

virtual void	SetInterpolator (InterpolatorType *interpolator)

virtual InterpolatorType *	GetModifiableInterpolator ()

virtual const InterpolatorType *	GetInterpolator () const

virtual void	SetInverseInterpolator (InterpolatorType *interpolator)

virtual InterpolatorType *	GetModifiableInverseInterpolator ()

virtual const InterpolatorType *	GetInverseInterpolator () const

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 Member Functions
	BSplineExponentialDiffeomorphicTransform ()

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

virtual	~BSplineExponentialDiffeomorphicTransform ()

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

DisplacementFieldType::Pointer	CopyDisplacementField (const DisplacementFieldType *) const

virtual LightObject::Pointer	InternalClone () const

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

virtual	~ConstantVelocityFieldTransform ()

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

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

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 ()

Private Member Functions
	BSplineExponentialDiffeomorphicTransform (const Self &)

void	operator= (const Self &)

Private Attributes
ArrayType	m_NumberOfControlPointsForTheConstantVelocityField

ArrayType	m_NumberOfControlPointsForTheUpdateField

SplineOrderType	m_SplineOrder

Additional Inherited Members
Protected Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

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