#include <itkTimeVaryingBSplineVelocityFieldTransform.h>

Detailed Description

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

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.

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

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

Public Types
using	ConstPointer = SmartPointer< const Self >

using	DisplacementFieldDirectionType = typename DisplacementFieldType::DirectionType

using	DisplacementFieldPointType = typename DisplacementFieldType::PointType

using	DisplacementFieldSizeType = typename DisplacementFieldType::SizeType

using	DisplacementFieldSpacingType = typename DisplacementFieldType::SpacingType

using	DisplacementVectorType = typename DisplacementFieldType::PixelType

using	FixedParametersValueType = typename FixedParametersType::ValueType

using	ParametersValueType = typename ParametersType::ValueType

using	Pointer = SmartPointer< Self >

using	Self = TimeVaryingBSplineVelocityFieldTransform

using	Superclass = VelocityFieldTransform< TParametersValueType, VDimension >

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

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 Member Functions
const char *	GetNameOfClass () const override

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, 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

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

const char *	GetNameOfClass () const override

NumberOfParametersType	GetNumberOfLocalParameters () const override

TransformCategoryEnum	GetTransformCategory () const 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

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

bool	GetInverse (Self *) const

const char *	GetNameOfClass () const override

virtual NumberOfParametersType	GetNumberOfFixedParameters () const

NumberOfParametersType	GetNumberOfParameters () const override

unsigned int	GetOutputSpaceDimension () const override

const ParametersType &	GetParameters () const override

TransformCategoryEnum	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 &vector, const InputPointType &point) 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 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 &vector, const InputPointType &point) const

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

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

	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

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 Attributes
static constexpr unsigned int	Dimension = VDimension

static constexpr unsigned int	VelocityFieldDimension = VDimension + 1

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

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

	TimeVaryingBSplineVelocityFieldTransform ()

	~TimeVaryingBSplineVelocityFieldTransform () 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

Private Attributes
unsigned int	m_SplineOrder {}

bool	m_TemporalPeriodicity {}

VelocityFieldDirectionType	m_VelocityFieldDirection {}

VelocityFieldPointType	m_VelocityFieldOrigin {}

VelocityFieldSizeType	m_VelocityFieldSize {}

VelocityFieldSpacingType	m_VelocityFieldSpacing {}

Additional Inherited Members
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