#include <itkTimeVaryingVelocityFieldTransform.h>

Detailed Description

template<typename TParametersValueType, unsigned int VDimension>
class itk::TimeVaryingVelocityFieldTransform< TParametersValueType, VDimension >

Transform objects based on integration of a time-varying velocity field.

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 first-order differential equation:

\[ v(\phi(x,t), t) = \frac{d\phi(x, t)}{dt}, \phi(x, 0) = x \]

In this class, the input is the time-varying velocity field. The output diffeomorphism is produced using fourth order Runge-Kutta.

Warning: The output deformation field needs to have dimensionality of 1 less than the input time-varying velocity field. It is assumed that the last dimension of the time-varying velocity field corresponds to Time, and the other dimensions represent Space.

Author: Nick Tustison; Brian Avants

Definition at line 54 of file itkTimeVaryingVelocityFieldTransform.h.

Inheritance diagram for itk::TimeVaryingVelocityFieldTransform< TParametersValueType, VDimension >:

Collaboration diagram for itk::TimeVaryingVelocityFieldTransform< TParametersValueType, VDimension >:

Public Types
using	ConstPointer = SmartPointer< const Self >

using	FixedParametersValueType = typename FixedParametersType::ValueType

using	ParametersValueType = typename ParametersType::ValueType

using	Pointer = SmartPointer< Self >

using	Self = TimeVaryingVelocityFieldTransform

using	Superclass = VelocityFieldTransform< TParametersValueType, VDimension >

using	TimeVaryingVelocityFieldPointer = typename VelocityFieldType::Pointer

using	TimeVaryingVelocityFieldType = VelocityFieldType

using	TransformPointer = typename Transform< TParametersValueType, VDimension, VDimension >::Pointer

using	VelocityFieldIntegratorType = typename Superclass::VelocityFieldInterpolatorType

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

using	DirectionType = typename VelocityFieldType::DirectionType

using	DisplacementFieldPointer = typename DisplacementFieldType::Pointer

using	IndexType = typename VelocityFieldType::IndexType

using	OptimizerParametersHelperType = ImageVectorOptimizerParametersHelper< ScalarType, Dimension, VelocityFieldDimension >

using	PixelType = typename VelocityFieldType::PixelType

using	Pointer = SmartPointer< Self >

using	PointType = typename VelocityFieldType::PointType

using	RegionType = typename VelocityFieldType::RegionType

using	Self = VelocityFieldTransform

using	SizeType = typename VelocityFieldType::SizeType

using	SpacingType = typename VelocityFieldType::SpacingType

using	Superclass = DisplacementFieldTransform< TParametersValueType, VDimension >

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, VDimension >
using	ConstPointer = SmartPointer< const Self >

using	DirectionType = typename DisplacementFieldType::DirectionType

using	DisplacementFieldConstPointer = typename DisplacementFieldType::ConstPointer

using	DisplacementFieldPointer = typename DisplacementFieldType::Pointer

using	DisplacementFieldType = Image< OutputVectorType, Dimension >

using	IndexType = typename DisplacementFieldType::IndexType

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

using	InterpolatorType = VectorInterpolateImageFunction< DisplacementFieldType, ScalarType >

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

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

using	PixelType = typename DisplacementFieldType::PixelType

using	Pointer = SmartPointer< Self >

using	PointType = typename DisplacementFieldType::PointType

using	RegionType = typename DisplacementFieldType::RegionType

using	Self = DisplacementFieldTransform

using	SizeType = typename DisplacementFieldType::SizeType

using	SpacingType = typename DisplacementFieldType::SpacingType

using	Superclass = Transform< TParametersValueType, VDimension, VDimension >

using	VectorImageDisplacementFieldType = VectorImage< TParametersValueType, Dimension >

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

using	DerivativeType = Array< ParametersValueType >

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

using	InputCovariantVectorType = CovariantVector< TParametersValueType, VInputDimension >

using	InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

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

using	InputPointType = Point< TParametersValueType, VInputDimension >

using	InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension >

using	InputVectorPixelType = VariableLengthVector< TParametersValueType >

using	InputVectorType = Vector< TParametersValueType, VInputDimension >

using	InputVnlVectorType = vnl_vector_fixed< TParametersValueType, VInputDimension >

using	InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension >

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = Transform< TParametersValueType, VOutputDimension, VInputDimension >

using	JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension >

using	JacobianType = Array2D< ParametersValueType >

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

using	OutputCovariantVectorType = CovariantVector< TParametersValueType, VOutputDimension >

using	OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

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

using	OutputPointType = Point< TParametersValueType, VOutputDimension >

using	OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension >

using	OutputVectorPixelType = VariableLengthVector< TParametersValueType >

using	OutputVectorType = Vector< TParametersValueType, VOutputDimension >

using	OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, VOutputDimension >

using	Pointer = SmartPointer< Self >

using	ScalarType = ParametersValueType

using	Self = Transform

using	Superclass = TransformBaseTemplate< TParametersValueType >

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

using	TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory

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
const char *	GetNameOfClass () const override

void	IntegrateVelocityField () override

virtual void	SetTimeVaryingVelocityField (VelocityFieldType *field)


VelocityFieldType *	GetModifiableTimeVaryingVelocityField ()

const VelocityFieldType *	GetTimeVaryingVelocityField () const

Public Member Functions inherited from itk::VelocityFieldTransform< TParametersValueType, VDimension >
bool	GetInverse (Self *inverse) const

InverseTransformBasePointer	GetInverseTransform () const override

virtual ScalarType	GetLowerTimeBound () const

const char *	GetNameOfClass () const override

virtual unsigned int	GetNumberOfIntegrationSteps () const

virtual ScalarType	GetUpperTimeBound () const

virtual const unsigned long &	GetVelocityFieldSetTime () const

virtual void	IntegrateVelocityField ()

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 void	SetVelocityFieldInterpolator (VelocityFieldInterpolatorType *)

virtual VelocityFieldInterpolatorType *	GetModifiableVelocityFieldInterpolator ()

void	SetDisplacementField (DisplacementFieldType *displacementField) override

Public Member Functions inherited from itk::DisplacementFieldTransform< TParametersValueType, VDimension >
void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &point, InverseJacobianPositionType &jacobian) const override

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

virtual void	ComputeJacobianWithRespectToPosition (const IndexType &index, JacobianPositionType &jacobian) const

void	ComputeJacobianWithRespectToPosition (const InputPointType &point, JacobianPositionType &jacobian) const override

virtual const ModifiedTimeType &	GetDisplacementFieldSetTime () const

bool	GetInverse (Self *inverse) const

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

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

InverseTransformBasePointer	GetInverseTransform () const override

const char *	GetNameOfClass () const override

NumberOfParametersType	GetNumberOfLocalParameters () const override

TransformCategoryEnum	GetTransformCategory () const override

void	SetFixedParameters (const FixedParametersType &) override

virtual void	SetIdentity ()

OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const override

OutputVectorPixelType	TransformDiffusionTensor (const InputVectorPixelType &) const

OutputPointType	TransformPoint (const InputPointType &inputPoint) 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 void	SetDisplacementField (VectorImageDisplacementFieldType *field)

void	SetDisplacementField (std::nullptr_t)=delete

virtual DisplacementFieldType *	GetModifiableDisplacementField ()

virtual void	SetInverseDisplacementField (DisplacementFieldType *inverseField)

virtual DisplacementFieldType *	GetModifiableInverseDisplacementField ()

virtual void	SetInterpolator (InterpolatorType *interpolator)

virtual InterpolatorType *	GetModifiableInterpolator ()

virtual void	SetInverseInterpolator (InterpolatorType *interpolator)

virtual InterpolatorType *	GetModifiableInverseInterpolator ()

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, VDimension, VDimension >
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

virtual const std::string &	GetInputSpaceName () const

bool	GetInverse (Self *) const

virtual InverseTransformBasePointer	GetInverseTransform () const

const char *	GetNameOfClass () const override

virtual NumberOfParametersType	GetNumberOfFixedParameters () const

virtual NumberOfParametersType	GetNumberOfLocalParameters () const

NumberOfParametersType	GetNumberOfParameters () const override

unsigned int	GetOutputSpaceDimension () const override

virtual const std::string &	GetOutputSpaceName () const

const ParametersType &	GetParameters () const override

TransformCategoryEnum	GetTransformCategory () const override

std::string	GetTransformTypeAsString () const override

virtual bool	IsLinear () const

	itkCloneMacro (Self)

void	SetFixedParameters (const FixedParametersType &) override=0

virtual void	SetInputSpaceName (std::string _arg)

virtual void	SetOutputSpaceName (std::string _arg)

void	SetParameters (const ParametersType &) override=0

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 &inputTensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &) const

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

virtual OutputPointType	TransformPoint (const InputPointType &) const=0

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const

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

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const

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

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &vector, 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 void	UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0)

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

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

std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void >	ApplyToImageMetadata (TImage *image) const

std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void >	ApplyToImageMetadata (SmartPointer< TImage > image) const

virtual void	CopyInFixedParameters (const FixedParametersValueType const begin, const FixedParametersValueType const end)=0

virtual void	CopyInParameters (const ParametersValueType const begin, const ParametersValueType const end)=0

virtual const FixedParametersType &	GetFixedParameters () const =0

virtual unsigned int	GetInputSpaceDimension () const =0

const char *	GetNameOfClass () const override

virtual NumberOfParametersType	GetNumberOfParameters () const =0

virtual unsigned int	GetOutputSpaceDimension () const =0

virtual const ParametersType &	GetParameters () const =0

virtual TransformCategoryEnum	GetTransformCategory () const =0

virtual std::string	GetTransformTypeAsString () const =0

virtual void	SetFixedParameters (const FixedParametersType &)=0

virtual void	SetParameters (const ParametersType &)=0

virtual void	SetParametersByValue (const ParametersType &p)=0

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

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

unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const

LightObject::Pointer	CreateAnother () const override

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

const char *	GetNameOfClass () const override

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 noexcept override

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
Pointer	Clone () const

virtual Pointer	CreateAnother () const

virtual void	Delete ()

virtual const char *	GetNameOfClass () const

virtual int	GetReferenceCount () const

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

virtual void	Register () const

virtual void	SetReferenceCount (int)

virtual void	UnRegister () const noexcept

Static Public Member Functions
static Pointer	New ()

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

Static Public Member Functions inherited from itk::DisplacementFieldTransform< TParametersValueType, VDimension >
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 val)

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

static Pointer	New ()

Protected Member Functions
	TimeVaryingVelocityFieldTransform ()=default

	~TimeVaryingVelocityFieldTransform () override=default

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

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

	~DisplacementFieldTransform () override=default

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

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

	Transform ()=default

	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

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

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

	~Object () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

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

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

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

virtual	~LightObject ()

Additional Inherited Members
Static Public Attributes inherited from itk::VelocityFieldTransform< TParametersValueType, VDimension >
static constexpr unsigned int	Dimension = VDimension

static constexpr unsigned int	VelocityFieldDimension = VDimension + 1

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

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

static constexpr unsigned int	OutputSpaceDimension

Static Protected Member Functions inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
static InverseTransformBasePointer	InvertTransform (const TTransform &transform)

Protected Attributes inherited from itk::VelocityFieldTransform< TParametersValueType, VDimension >
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, VDimension >
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, VDimension, VDimension >
FixedParametersType	m_FixedParameters

ParametersType	m_Parameters

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