#include <itkTimeVaryingBSplineVelocityFieldTransform.h>

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

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

Detailed Description

template<class TScalar, unsigned int NDimensions>
class itk::TimeVaryingBSplineVelocityFieldTransform< TScalar, 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
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DerivativeType	DerivativeType

typedef DisplacementFieldType::DirectionType	DisplacementFieldDirectionType

typedef DisplacementFieldType::PointType	DisplacementFieldPointType

typedef DisplacementFieldType::SizeType	DisplacementFieldSizeType

typedef DisplacementFieldType::SpacingType	DisplacementFieldSpacingType

typedef Superclass::DisplacementFieldType	DisplacementFieldType

typedef DisplacementFieldType::PixelType	DisplacementVectorType

typedef Superclass::InterpolatorType	InterpolatorType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef Superclass::ParametersType	ParametersType

typedef ParametersType::ValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef TimeVaryingBSplineVelocityFieldTransform	Self

typedef VelocityFieldTransform < TScalar, NDimensions >	Superclass

typedef VelocityFieldType::Pointer	TimeVaryingVelocityFieldControlPointLatticePointer

typedef VelocityFieldType	TimeVaryingVelocityFieldControlPointLatticeType

typedef VelocityFieldType::DirectionType	VelocityFieldDirectionType

typedef Superclass::VelocityFieldInterpolatorType	VelocityFieldIntegratorType

typedef VelocityFieldType::PointType	VelocityFieldPointType

typedef VelocityFieldType::SizeType	VelocityFieldSizeType

typedef VelocityFieldType::SpacingType	VelocityFieldSpacingType

typedef Superclass::VelocityFieldType	VelocityFieldType

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

typedef Superclass::DerivativeType	DerivativeType

typedef VelocityFieldType::DirectionType	DirectionType

typedef DisplacementFieldType::Pointer	DisplacementFieldPointer

typedef Superclass::DisplacementFieldType	DisplacementFieldType

typedef VelocityFieldType::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, VelocityFieldDimension >	OptimizerParametersHelperType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef VelocityFieldType::PixelType	PixelType

typedef SmartPointer< Self >	Pointer

typedef VelocityFieldType::PointType	PointType

typedef VelocityFieldType::RegionType	RegionType

typedef Superclass::ScalarType	ScalarType

typedef VelocityFieldTransform	Self

typedef VelocityFieldType::SizeType	SizeType

typedef VelocityFieldType::SpacingType	SpacingType

typedef DisplacementFieldTransform < TScalar, NDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

typedef VelocityFieldInterpolatorType::Pointer	VelocityFieldInterpolatorPointer

typedef VectorInterpolateImageFunction < VelocityFieldType, ScalarType >	VelocityFieldInterpolatorType

typedef VelocityFieldType::Pointer	VelocityFieldPointer

typedef Image < OutputVectorType, VelocityFieldDimension >	VelocityFieldType

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

typedef Superclass::DerivativeType	DerivativeType

typedef DisplacementFieldType::DirectionType	DirectionType

typedef DisplacementFieldType::Pointer	DisplacementFieldPointer

typedef Image < OutputVectorType, Dimension >	DisplacementFieldType

typedef DisplacementFieldType::IndexType	IndexType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputDiffusionTensor3DType	InputDiffusionTensor3DType

typedef Superclass::InputPointType	InputPointType

typedef CovariantVector < ScalarType, InputDiffusionTensor3DType::Dimension >	InputTensorEigenVectorType

typedef Superclass::InputVectorPixelType	InputVectorPixelType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef VectorInterpolateImageFunction < DisplacementFieldType, ScalarType >	InterpolatorType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::JacobianType	JacobianType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

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

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputDiffusionTensor3DType	OutputDiffusionTensor3DType

typedef Superclass::OutputPointType	OutputPointType

typedef CovariantVector < ScalarType, OutputDiffusionTensor3DType::Dimension >	OutputTensorEigenVectorType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef DisplacementFieldType::PixelType	PixelType

typedef SmartPointer< Self >	Pointer

typedef DisplacementFieldType::PointType	PointType

typedef DisplacementFieldType::RegionType	RegionType

typedef Superclass::ScalarType	ScalarType

typedef DisplacementFieldTransform	Self

typedef DisplacementFieldType::SizeType	SizeType

typedef DisplacementFieldType::SpacingType	SpacingType

typedef Transform< TScalar, NDimensions, NDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

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

typedef Array < ParametersValueType >	DerivativeType

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

typedef CovariantVector < TScalar, NInputDimensions >	InputCovariantVectorType

typedef DiffusionTensor3D < TScalar >	InputDiffusionTensor3DType

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

typedef Point< TScalar, NInputDimensions >	InputPointType

typedef SymmetricSecondRankTensor < TScalar, NInputDimensions >	InputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalar >	InputVectorPixelType

typedef Vector< TScalar, NInputDimensions >	InputVectorType

typedef vnl_vector_fixed < TScalar, NInputDimensions >	InputVnlVectorType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Transform< TScalar, NOutputDimensions, NInputDimensions >	InverseTransformBaseType

typedef Array2D < ParametersValueType >	JacobianType

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

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef CovariantVector < TScalar, NOutputDimensions >	OutputCovariantVectorType

typedef DiffusionTensor3D < TScalar >	OutputDiffusionTensor3DType

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

typedef Point< TScalar, NOutputDimensions >	OutputPointType

typedef SymmetricSecondRankTensor < TScalar, NOutputDimensions >	OutputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalar >	OutputVectorPixelType

typedef Vector< TScalar, NOutputDimensions >	OutputVectorType

typedef vnl_vector_fixed < TScalar, NOutputDimensions >	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TScalar	ScalarType

typedef Transform	Self

typedef TransformBase	Superclass

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

typedef IdentifierType	NumberOfParametersType

typedef OptimizerParameters < ParametersValueType >	ParametersType

typedef double	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TransformBase	Self

typedef Object	Superclass

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

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

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

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

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
virtual const char *	GetNameOfClass () const

VelocityFieldType::Pointer	GetTimeVaryingVelocityFieldControlPointLattice ()

virtual void	IntegrateVelocityField ()

virtual void	SetTimeVaryingVelocityFieldControlPointLattice (VelocityFieldType *fieldLattice)

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


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< TScalar, NDimensions >
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

bool	GetInverse (Self *inverse) const

virtual InverseTransformBasePointer	GetInverseTransform () const

virtual ScalarType	GetLowerTimeBound () const

virtual unsigned int	GetNumberOfIntegrationSteps () const

virtual ScalarType	GetUpperTimeBound () const

virtual VelocityFieldType *	GetVelocityField ()

virtual const unsigned long &	GetVelocityFieldSetTime ()

virtual void	SetDisplacementField (DisplacementFieldType *_arg)

virtual void	SetFixedParameters (const ParametersType &)

virtual void	SetLowerTimeBound (ScalarType _arg)

virtual void	SetNumberOfIntegrationSteps (unsigned int _arg)

virtual void	SetUpperTimeBound (ScalarType _arg)

virtual void	SetVelocityField (VelocityFieldType *)

virtual VelocityFieldInterpolatorType *	GetVelocityFieldInterpolator ()

virtual void	SetVelocityFieldInterpolator (VelocityFieldInterpolatorType *)

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

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

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

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

virtual DisplacementFieldType *	GetDisplacementField ()

virtual const ModifiedTimeType &	GetDisplacementFieldSetTime ()

bool	GetInverse (Self *inverse) const

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

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

virtual NumberOfParametersType	GetNumberOfLocalParameters (void) const

virtual TransformCategoryType	GetTransformCategory () const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const

OutputVectorPixelType	TransformDiffusionTensor (const InputVectorPixelType &) const

virtual OutputPointType	TransformPoint (const InputPointType &thisPoint) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

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

virtual DisplacementFieldType *	GetInverseDisplacementField ()

virtual void	SetInverseDisplacementField (DisplacementFieldType *inverseDisplacementField)

virtual InterpolatorType *	GetInterpolator ()

virtual void	SetInterpolator (InterpolatorType *interpolator)

virtual InterpolatorType *	GetInverseInterpolator ()

virtual void	SetInverseInterpolator (InterpolatorType *interpolator)

virtual OutputVectorType	TransformVector (const InputVectorType &) const

OutputDiffusionTensor3DType	TransformDiffusionTensor (const InputDiffusionTensor3DType &) const

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

virtual void	SetParameters (const ParametersType &params)

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

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

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

virtual const ParametersType &	GetFixedParameters (void) const

unsigned int	GetInputSpaceDimension (void) const

bool	GetInverse (Self *) const

virtual NumberOfParametersType	GetNumberOfParameters (void) const

unsigned int	GetOutputSpaceDimension (void) const

virtual const ParametersType &	GetParameters (void) const

virtual std::string	GetTransformTypeAsString () const

virtual bool	IsLinear () const

	itkCloneMacro (Self)

virtual void	SetParametersByValue (const ParametersType &p)

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

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

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const

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

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const

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

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &) const

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

virtual OutputPointType	TransformPoint (const InputPointType &) const =0

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

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const

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

virtual OutputVectorType	TransformVector (const InputVectorType &) const

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

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

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

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

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

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

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

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::VelocityFieldTransform< 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	Dimension = NDimensions

static const unsigned int	VelocityFieldDimension = NDimensions + 1

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

static const unsigned int	VelocityFieldDimension = NDimensions + 1

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

	TimeVaryingBSplineVelocityFieldTransform ()

virtual	~TimeVaryingBSplineVelocityFieldTransform ()

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

virtual LightObject::Pointer	InternalClone () const

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

	VelocityFieldTransform ()

virtual	~VelocityFieldTransform ()

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

virtual	~DisplacementFieldTransform ()

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

	Transform ()

	Transform (NumberOfParametersType NumberOfParameters)

virtual	~Transform ()

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

virtual	~TransformBase ()

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

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

virtual void	SetTimeStamp (const TimeStamp &time)

virtual	~Object ()

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

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

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

virtual	~LightObject ()

Private Member Functions
void	operator= (const Self &)

	TimeVaryingBSplineVelocityFieldTransform (const Self &)

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 Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

Protected Attributes inherited from itk::VelocityFieldTransform< TScalar, NDimensions >
ScalarType	m_LowerTimeBound

unsigned int	m_NumberOfIntegrationSteps

ScalarType	m_UpperTimeBound

VelocityFieldPointer	m_VelocityField

VelocityFieldInterpolatorType::Pointer	m_VelocityFieldInterpolator

unsigned long	m_VelocityFieldSetTime