#include <itkTimeVaryingBSplineVelocityFieldTransform.h>

Inheritance diagram for itk::TimeVaryingBSplineVelocityFieldTransform< TParametersValueType, NDimensions >:

Collaboration diagram for itk::TimeVaryingBSplineVelocityFieldTransform< TParametersValueType, NDimensions >:

Detailed Description

template<typename TParametersValueType, unsigned int NDimensions>
class itk::TimeVaryingBSplineVelocityFieldTransform< TParametersValueType, NDimensions >

Integrate a time-varying velocity field represented by a B-spline control point lattice.

Diffeomorphisms are topology-preserving mappings that are useful for describing biologically plausible deformations. Mathematically, a diffeomorphism, $\phi$ , is generated from a time-varying velocity field, v, as described by the integral equation:

$\phi(t_b) = \phi(t_a) + \int_{t_a}^{t_b} v(\phi(t),t) dt$

In typical registration applications it is computationally more efficient to sample the B-spline transform to its corresponding displacement field. Therefore, the user needs to specify the domain parameters of that displacement field using the following functions:

SetDisplacementFieldSpacing()
SetDisplacementFieldOrigin()
SetDisplacementFieldSize()
SetDisplacementFieldDirection()

It's important that these parameters match up with the fixed parameters of this transform which are defined as the parameters of the (N+1)-D B-spline grid representing the continuous velocity field. This control point lattice is set using SetTimeVaryingVelocityFieldControlPointLattice() or it can be created by setting the fixed parameters.

Note: For readability of the code, it is important to note that we store the control point lattice in the m_VelocityField variable since they are of the same type. It's only when we call IntegrateVelocityField() that a sampled velocity field is created from the control point lattice.

Author: Nick Tustison; Brian Avants

Definition at line 68 of file itkTimeVaryingBSplineVelocityFieldTransform.h.

Public Types
using	ConstPointer = SmartPointer< const Self >

using	DerivativeType = typename Superclass::DerivativeType

using	DisplacementFieldDirectionType = typename DisplacementFieldType::DirectionType

using	DisplacementFieldPointType = typename DisplacementFieldType::PointType

using	DisplacementFieldSizeType = typename DisplacementFieldType::SizeType

using	DisplacementFieldSpacingType = typename DisplacementFieldType::SpacingType

using	DisplacementFieldType = typename Superclass::DisplacementFieldType

using	DisplacementVectorType = typename DisplacementFieldType::PixelType

using	FixedParametersType = typename Superclass::FixedParametersType

using	FixedParametersValueType = typename FixedParametersType::ValueType

using	InterpolatorType = typename Superclass::InterpolatorType

using	InverseTransformBasePointer = typename Superclass::InverseTransformBasePointer

using	NumberOfParametersType = typename Superclass::NumberOfParametersType

using	ParametersType = typename Superclass::ParametersType

using	ParametersValueType = typename ParametersType::ValueType

using	Pointer = SmartPointer< Self >

using	ScalarType = typename Superclass::ScalarType

using	Self = TimeVaryingBSplineVelocityFieldTransform

using	Superclass = VelocityFieldTransform< TParametersValueType, NDimensions >

using	TimeVaryingVelocityFieldControlPointLatticePointer = typename VelocityFieldType::Pointer

using	TimeVaryingVelocityFieldControlPointLatticeType = VelocityFieldType

using	VelocityFieldDirectionType = typename VelocityFieldType::DirectionType

using	VelocityFieldIntegratorType = typename Superclass::VelocityFieldInterpolatorType

using	VelocityFieldPointType = typename VelocityFieldType::PointType

using	VelocityFieldSizeType = typename VelocityFieldType::SizeType

using	VelocityFieldSpacingType = typename VelocityFieldType::SpacingType

using	VelocityFieldType = typename Superclass::VelocityFieldType

Public Types inherited from itk::VelocityFieldTransform< TParametersValueType, NDimensions >
using	ConstPointer = SmartPointer< const Self >

using	DerivativeType = typename Superclass::DerivativeType

using	DirectionType = typename VelocityFieldType::DirectionType

using	DisplacementFieldPointer = typename DisplacementFieldType::Pointer

using	DisplacementFieldType = typename Superclass::DisplacementFieldType

using	FixedParametersType = typename Superclass::FixedParametersType

using	FixedParametersValueType = typename Superclass::FixedParametersValueType

using	IndexType = typename VelocityFieldType::IndexType

using	InputPointType = typename Superclass::InputPointType

using	InputVectorPixelType = typename Superclass::InputVectorPixelType

using	InputVectorType = typename Superclass::InputVectorType

using	InverseTransformBasePointer = typename Superclass::InverseTransformBasePointer

using	NumberOfParametersType = typename Superclass::NumberOfParametersType

using	OptimizerParametersHelperType = ImageVectorOptimizerParametersHelper< ScalarType, Dimension, VelocityFieldDimension >

using	OutputPointType = typename Superclass::OutputPointType

using	OutputVectorPixelType = typename Superclass::OutputVectorPixelType

using	OutputVectorType = typename Superclass::OutputVectorType

using	ParametersType = typename Superclass::ParametersType

using	ParametersValueType = typename Superclass::ParametersValueType

using	PixelType = typename VelocityFieldType::PixelType

using	Pointer = SmartPointer< Self >

using	PointType = typename VelocityFieldType::PointType

using	RegionType = typename VelocityFieldType::RegionType

using	ScalarType = typename Superclass::ScalarType

using	Self = VelocityFieldTransform

using	SizeType = typename VelocityFieldType::SizeType

using	SpacingType = typename VelocityFieldType::SpacingType

using	Superclass = DisplacementFieldTransform< TParametersValueType, NDimensions >

using	TransformCategoryType = typename Superclass::TransformCategoryType

using	VelocityFieldInterpolatorPointer = typename VelocityFieldInterpolatorType::Pointer

using	VelocityFieldInterpolatorType = VectorInterpolateImageFunction< VelocityFieldType, ScalarType >

using	VelocityFieldPointer = typename VelocityFieldType::Pointer

using	VelocityFieldType = Image< OutputVectorType, VelocityFieldDimension >

Public Types inherited from itk::DisplacementFieldTransform< TParametersValueType, NDimensions >
using	ConstPointer = SmartPointer< const Self >

using	DerivativeType = typename Superclass::DerivativeType

using	DirectionType = typename DisplacementFieldType::DirectionType

using	DisplacementFieldConstPointer = typename DisplacementFieldType::ConstPointer

using	DisplacementFieldPointer = typename DisplacementFieldType::Pointer

using	DisplacementFieldType = Image< OutputVectorType, Dimension >

using	FixedParametersType = typename Superclass::FixedParametersType

using	FixedParametersValueType = typename Superclass::FixedParametersValueType

using	IndexType = typename DisplacementFieldType::IndexType

using	InputCovariantVectorType = typename Superclass::InputCovariantVectorType

using	InputDiffusionTensor3DType = typename Superclass::InputDiffusionTensor3DType

using	InputPointType = typename Superclass::InputPointType

using	InputTensorEigenVectorType = CovariantVector< ScalarType, InputDiffusionTensor3DType::Dimension >

using	InputVectorPixelType = typename Superclass::InputVectorPixelType

using	InputVectorType = typename Superclass::InputVectorType

using	InputVnlVectorType = typename Superclass::InputVnlVectorType

using	InterpolatorType = VectorInterpolateImageFunction< DisplacementFieldType, ScalarType >

using	InverseJacobianPositionType = typename Superclass::InverseJacobianPositionType

using	InverseTransformBasePointer = typename Superclass::InverseTransformBasePointer

using	JacobianPositionType = typename Superclass::JacobianPositionType

using	JacobianType = typename Superclass::JacobianType

using	NumberOfParametersType = typename Superclass::NumberOfParametersType

using	OptimizerParametersHelperType = ImageVectorOptimizerParametersHelper< ScalarType, OutputVectorType::Dimension, Dimension >

using	OutputCovariantVectorType = typename Superclass::OutputCovariantVectorType

using	OutputDiffusionTensor3DType = typename Superclass::OutputDiffusionTensor3DType

using	OutputPointType = typename Superclass::OutputPointType

using	OutputTensorEigenVectorType = CovariantVector< ScalarType, OutputDiffusionTensor3DType::Dimension >

using	OutputVectorPixelType = typename Superclass::OutputVectorPixelType

using	OutputVectorType = typename Superclass::OutputVectorType

using	OutputVnlVectorType = typename Superclass::OutputVnlVectorType

using	ParametersType = typename Superclass::ParametersType

using	ParametersValueType = typename Superclass::ParametersValueType

using	PixelType = typename DisplacementFieldType::PixelType

using	Pointer = SmartPointer< Self >

using	PointType = typename DisplacementFieldType::PointType

using	RegionType = typename DisplacementFieldType::RegionType

using	ScalarType = typename Superclass::ScalarType

using	Self = DisplacementFieldTransform

using	SizeType = typename DisplacementFieldType::SizeType

using	SpacingType = typename DisplacementFieldType::SpacingType

using	Superclass = Transform< TParametersValueType, NDimensions, NDimensions >

using	TransformCategoryType = typename Superclass::TransformCategoryType

Public Types inherited from itk::Transform< TParametersValueType, NDimensions, NDimensions >
using	ConstPointer = SmartPointer< const Self >

using	DerivativeType = Array< ParametersValueType >

using	DirectionChangeMatrix = Matrix< double, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	FixedParametersType = typename Superclass::FixedParametersType

using	FixedParametersValueType = typename Superclass::FixedParametersValueType

using	InputCovariantVectorType = CovariantVector< TParametersValueType, NInputDimensions >

using	InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

using	InputDirectionMatrix = Matrix< double, Self::InputSpaceDimension, Self::InputSpaceDimension >

using	InputPointType = Point< TParametersValueType, NInputDimensions >

using	InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, NInputDimensions >

using	InputVectorPixelType = VariableLengthVector< TParametersValueType >

using	InputVectorType = Vector< TParametersValueType, NInputDimensions >

using	InputVnlVectorType = vnl_vector_fixed< TParametersValueType, NInputDimensions >

using	InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, NInputDimensions, NOutputDimensions >

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = Transform< TParametersValueType, NOutputDimensions, NInputDimensions >

using	JacobianPositionType = vnl_matrix_fixed< ParametersValueType, NOutputDimensions, NInputDimensions >

using	JacobianType = Array2D< ParametersValueType >

using	MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	NumberOfParametersType = typename Superclass::NumberOfParametersType

using	OutputCovariantVectorType = CovariantVector< TParametersValueType, NOutputDimensions >

using	OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

using	OutputDirectionMatrix = Matrix< double, Self::OutputSpaceDimension, Self::OutputSpaceDimension >

using	OutputPointType = Point< TParametersValueType, NOutputDimensions >

using	OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, NOutputDimensions >

using	OutputVectorPixelType = VariableLengthVector< TParametersValueType >

using	OutputVectorType = Vector< TParametersValueType, NOutputDimensions >

using	OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, NOutputDimensions >

using	ParametersType = typename Superclass::ParametersType

using	ParametersValueType = typename Superclass::ParametersValueType

using	Pointer = SmartPointer< Self >

using	ScalarType = ParametersValueType

using	Self = Transform

using	Superclass = TransformBaseTemplate< TParametersValueType >

using	TransformCategoryType = typename Superclass::TransformCategoryType

Public Types inherited from itk::TransformBaseTemplate< TParametersValueType >
using	ConstPointer = SmartPointer< const Self >

using	FixedParametersType = OptimizerParameters< FixedParametersValueType >

using	FixedParametersValueType = double

using	NumberOfParametersType = IdentifierType

using	ParametersType = OptimizerParameters< ParametersValueType >

using	ParametersValueType = TParametersValueType

using	Pointer = SmartPointer< Self >

using	Self = TransformBaseTemplate

using	Superclass = Object

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

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

using	Pointer = SmartPointer< Self >

using	Self = Object

using	Superclass = LightObject

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

using	Pointer = SmartPointer< Self >

using	Self = LightObject

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

virtual const char *	GetNameOfClass () const

VelocityFieldType *	GetTimeVaryingVelocityFieldControlPointLattice ()

void	IntegrateVelocityField () override

virtual void	SetTimeVaryingVelocityFieldControlPointLattice (VelocityFieldType *fieldLattice)

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


virtual void	SetVelocityFieldOrigin (VelocityFieldPointType _arg)

virtual VelocityFieldPointType	GetVelocityFieldOrigin () const


virtual void	SetVelocityFieldSpacing (VelocityFieldSpacingType _arg)

virtual VelocityFieldSpacingType	GetVelocityFieldSpacing () const


virtual void	SetVelocityFieldSize (VelocityFieldSizeType _arg)

virtual VelocityFieldSizeType	GetVelocityFieldSize () const


virtual void	SetVelocityFieldDirection (VelocityFieldDirectionType _arg)

virtual VelocityFieldDirectionType	GetVelocityFieldDirection () const


virtual void	SetSplineOrder (unsigned int _arg)

virtual unsigned int	GetSplineOrder () const

Public Member Functions inherited from itk::VelocityFieldTransform< TParametersValueType, NDimensions >
virtual ::itk::LightObject::Pointer	CreateAnother () const

bool	GetInverse (Self *inverse) const

InverseTransformBasePointer	GetInverseTransform () const override

virtual ScalarType	GetLowerTimeBound () const

virtual unsigned int	GetNumberOfIntegrationSteps () const

virtual ScalarType	GetUpperTimeBound () const

virtual const unsigned long &	GetVelocityFieldSetTime () const

void	SetFixedParameters (const FixedParametersType &) override

virtual void	SetLowerTimeBound (ScalarType _arg)

virtual void	SetNumberOfIntegrationSteps (unsigned int _arg)

virtual void	SetUpperTimeBound (ScalarType _arg)

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

virtual void	SetVelocityField (VelocityFieldType *)

virtual VelocityFieldType *	GetModifiableVelocityField ()

virtual const VelocityFieldType *	GetVelocityField () const

virtual void	SetVelocityFieldInterpolator (VelocityFieldInterpolatorType *)

virtual VelocityFieldInterpolatorType *	GetModifiableVelocityFieldInterpolator ()

virtual const VelocityFieldInterpolatorType *	GetVelocityFieldInterpolator () const

void	SetDisplacementField (DisplacementFieldType *displacementField) override

Public Member Functions inherited from itk::DisplacementFieldTransform< TParametersValueType, NDimensions >
void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, InverseJacobianPositionType &j) const override

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

void	ComputeJacobianWithRespectToPosition (const InputPointType &x, JacobianPositionType &j) const override

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

virtual const ModifiedTimeType &	GetDisplacementFieldSetTime () const

bool	GetInverse (Self *inverse) const

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

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

NumberOfParametersType	GetNumberOfLocalParameters () const override

TransformCategoryType	GetTransformCategory () const override

virtual void	SetIdentity ()

OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const override

OutputVectorPixelType	TransformDiffusionTensor (const InputVectorPixelType &) const

OutputPointType	TransformPoint (const InputPointType &thisPoint) const override

OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const override

OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const override

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

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

OutputVectorType	TransformVector (const InputVectorType &) const override

OutputDiffusionTensor3DType	TransformDiffusionTensor (const InputDiffusionTensor3DType &) const

OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const override

void	SetParameters (const ParametersType &params) override

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

virtual void	SetCoordinateTolerance (double _arg)

virtual double	GetCoordinateTolerance () const

virtual void	SetDirectionTolerance (double _arg)

virtual double	GetDirectionTolerance () const

Public Member Functions inherited from itk::Transform< TParametersValueType, NDimensions, NDimensions >
virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const =0

virtual void	ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const

void	CopyInFixedParameters (const FixedParametersValueType const begin, const FixedParametersValueType const end) override

void	CopyInParameters (const ParametersValueType const begin, const ParametersValueType const end) override

const FixedParametersType &	GetFixedParameters () const override

unsigned int	GetInputSpaceDimension () const override

bool	GetInverse (Self *) const

virtual NumberOfParametersType	GetNumberOfFixedParameters () const

NumberOfParametersType	GetNumberOfParameters () const override

unsigned int	GetOutputSpaceDimension () const override

const ParametersType &	GetParameters () const override

TransformCategoryType	GetTransformCategory () const override

std::string	GetTransformTypeAsString () const override

virtual bool	IsLinear () const

	itkCloneMacro (Self)

void	SetParametersByValue (const ParametersType &p) override

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, ParametersValueType factor=1.0)

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

	itkLegacyMacro (virtual void ComputeJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const)

	itkLegacyMacro (virtual void ComputeInverseJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const)

virtual void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, InverseJacobianPositionType &jacobian) const

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *)

unsigned long	AddObserver (const EventObject &event, Command *) const

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetReferenceCount (int) override

void	UnRegister () const noexceptoverride

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

void	SetMetaDataDictionary (MetaDataDictionary &&rrhs)

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

void	Print (std::ostream &os, Indent indent=0) const

Static Public Member Functions
static Pointer	New ()

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

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

Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool flag)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Static Public Attributes
static constexpr unsigned int	Dimension = NDimensions

static constexpr unsigned int	VelocityFieldDimension = NDimensions + 1

Static Public Attributes inherited from itk::VelocityFieldTransform< TParametersValueType, NDimensions >
static constexpr unsigned int	Dimension = NDimensions

static constexpr unsigned int	VelocityFieldDimension = NDimensions + 1

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

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

static constexpr unsigned int	OutputSpaceDimension

Protected Member Functions
void	PrintSelf (std::ostream &os, Indent indent) const override

	TimeVaryingBSplineVelocityFieldTransform ()

	~TimeVaryingBSplineVelocityFieldTransform () override=default

Protected Member Functions inherited from itk::VelocityFieldTransform< TParametersValueType, NDimensions >
DisplacementFieldType::Pointer	CopyDisplacementField (const DisplacementFieldType *) const

LightObject::Pointer	InternalClone () const override

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

	VelocityFieldTransform ()

	~VelocityFieldTransform () override=default

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

	~DisplacementFieldTransform () override=default

Protected Member Functions inherited from itk::Transform< TParametersValueType, NDimensions, NDimensions >
LightObject::Pointer	InternalClone () const override

OutputDiffusionTensor3DType	PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType &, const InverseJacobianPositionType &) const

	Transform ()

	Transform (NumberOfParametersType NumberOfParameters)

	~Transform () override=default

Protected Member Functions inherited from itk::TransformBaseTemplate< TParametersValueType >
	TransformBaseTemplate ()=default

	~TransformBaseTemplate () override=default

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

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &time)

	~Object () override

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 Attributes
unsigned int	m_SplineOrder

bool	m_TemporalPeriodicity

VelocityFieldDirectionType	m_VelocityFieldDirection

VelocityFieldPointType	m_VelocityFieldOrigin

VelocityFieldSizeType	m_VelocityFieldSize

VelocityFieldSpacingType	m_VelocityFieldSpacing

Additional Inherited Members
Protected Attributes inherited from itk::VelocityFieldTransform< TParametersValueType, NDimensions >
ScalarType	m_LowerTimeBound

unsigned int	m_NumberOfIntegrationSteps

ScalarType	m_UpperTimeBound

VelocityFieldPointer	m_VelocityField

VelocityFieldInterpolatorType::Pointer	m_VelocityFieldInterpolator

unsigned long	m_VelocityFieldSetTime

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

ModifiedTimeType	m_DisplacementFieldSetTime { 0 }

JacobianType	m_IdentityJacobian

InterpolatorType::Pointer	m_Interpolator

DisplacementFieldType::Pointer	m_InverseDisplacementField

InterpolatorType::Pointer	m_InverseInterpolator

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

FixedParametersType	m_FixedParameters

ParametersType	m_Parameters

Protected Attributes inherited from itk::LightObject
std::atomic< int >	m_ReferenceCount