#include <itkKernelTransform2.h>

Inheritance diagram for itk::KernelTransform2< TScalarType, NDimensions >:

Collaboration diagram for itk::KernelTransform2< TScalarType, NDimensions >:

Public Types
typedef vnl_matrix_fixed < TScalarType, NDimensions, NDimensions >	AMatrixType
typedef vnl_vector_fixed < TScalarType, NDimensions >	BMatrixType
typedef vnl_matrix_fixed < TScalarType, NDimensions, 1 >	ColumnMatrixType
typedef SmartPointer< const Self >	ConstPointer
typedef vnl_matrix< TScalarType >	DMatrixType
typedef vnl_matrix_fixed < TScalarType, NDimensions, NDimensions >	GMatrixType
typedef vnl_matrix_fixed < TScalarType, NDimensions, NDimensions >	IMatrixType
typedef Superclass::InputPointType	InputPointType
typedef Superclass::InputVectorType	InputVectorType
typedef Superclass::InternalMatrixType	InternalMatrixType
typedef Superclass::JacobianOfSpatialHessianType	JacobianOfSpatialHessianType
typedef Superclass::JacobianOfSpatialJacobianType	JacobianOfSpatialJacobianType
typedef Superclass::JacobianType	JacobianType
typedef vnl_matrix< TScalarType >	KMatrixType
typedef vnl_matrix< TScalarType >	LMatrixType
typedef Superclass::NonZeroJacobianIndicesType	NonZeroJacobianIndicesType
typedef Superclass::OutputPointType	OutputPointType
typedef Superclass::OutputVectorType	OutputVectorType
typedef Superclass::ParametersType	ParametersType
typedef vnl_matrix< TScalarType >	PMatrixType
typedef SmartPointer< Self >	Pointer
typedef PointSetType::PointsContainerConstIterator	PointsConstIterator
typedef PointSetType::PointsContainer	PointsContainer
typedef PointSetType::Pointer	PointSetPointer
typedef DefaultStaticMeshTraits < TScalarType, NDimensions, NDimensions, TScalarType, TScalarType >	PointSetTraitsType
typedef PointSet < InputPointType, NDimensions, PointSetTraitsType >	PointSetType
typedef PointSetType::PointsContainerIterator	PointsIterator
typedef vnl_matrix_fixed < TScalarType, 1, NDimensions >	RowMatrixType
typedef Superclass::ScalarType	ScalarType
typedef KernelTransform2	Self
typedef Superclass::SpatialHessianType	SpatialHessianType
typedef Superclass::SpatialJacobianType	SpatialJacobianType
typedef AdvancedTransform < TScalarType, NDimensions, NDimensions >	Superclass
typedef VectorSetType::Pointer	VectorSetPointer
typedef VectorContainer < unsigned long, InputVectorType >	VectorSetType
typedef vnl_matrix< TScalarType >	WMatrixType
typedef vnl_matrix< TScalarType >	YMatrixType
Public Member Functions
void	ComputeLInverse (void)
void	ComputeWMatrix (void)
virtual TScalarType	GetAlpha (void) const
virtual const char *	GetClassName () const
virtual VectorSetType *	GetDisplacements ()
virtual const ParametersType &	GetFixedParameters (void) const
virtual bool	GetHasNonZeroSpatialHessian (void) const
virtual const JacobianType &	GetJacobian (const InputPointType &point) const
virtual void	GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const
virtual unsigned int	GetNumberOfParameters (void) const
virtual const ParametersType &	GetParameters (void) const
virtual const TScalarType	GetPoissonRatio (void) const
virtual PointSetType *	GetSourceLandmarks ()
virtual double	GetStiffness ()
virtual PointSetType *	GetTargetLandmarks ()
virtual bool	HasNonZeroJacobianOfSpatialHessian (void) const
	itkStaticConstMacro (SpaceDimension, unsigned int, NDimensions)
virtual void	SetAlpha (TScalarType Alpha)
virtual void	SetFixedParameters (const ParametersType &)
virtual void	SetIdentity (void)
virtual void	SetParameters (const ParametersType &)
virtual void	SetPoissonRatio (TScalarType _arg)
virtual void	SetSourceLandmarks (PointSetType *)
virtual void	SetStiffness (double stiffness)
virtual void	SetTargetLandmarks (PointSetType *)
virtual OutputPointType	TransformPoint (const InputPointType &thisPoint) const
virtual void	UpdateParameters (void)
Static Public Member Functions
static Pointer	New ()
Data Fields
PointSetPointer	m_SourceLandmarks
PointSetPointer	m_TargetLandmarks
Protected Member Functions
void	ComputeD (void)
virtual void	ComputeDeformationContribution (const InputPointType &inputPoint, OutputPointType &result) const
virtual void	ComputeG (const InputVectorType &landmarkVector, GMatrixType &GMatrix) const
void	ComputeK (void)
void	ComputeL (void)
void	ComputeP (void)
virtual void	ComputeReflexiveG (PointsIterator, GMatrixType &GMatrix) const
void	ComputeY (void)
	KernelTransform2 ()
void	PrintSelf (std::ostream &os, Indent indent) const
void	ReorganizeW (void)
virtual	~KernelTransform2 ()
Protected Attributes
AMatrixType	m_AMatrix
BMatrixType	m_BVector
VectorSetPointer	m_Displacements
DMatrixType	m_DMatrix
IMatrixType	m_I
KMatrixType	m_KMatrix
bool	m_LInverseComputed
LMatrixType	m_LMatrix
bool	m_LMatrixComputed
LMatrixType	m_LMatrixInverse
NonZeroJacobianIndicesType	m_NonZeroJacobianIndices
NonZeroJacobianIndicesType	m_NonZeroJacobianIndicesTemp
PMatrixType	m_PMatrix
double	m_Stiffness
WMatrixType	m_WMatrix
bool	m_WMatrixComputed
YMatrixType	m_YMatrix
Private Member Functions
	KernelTransform2 (const Self &)
void	operator= (const Self &)
Private Attributes
TScalarType	m_PoissonRatio

Detailed Description

template<class TScalarType, unsigned int NDimensions>
class itk::KernelTransform2< TScalarType, NDimensions >

Intended to be a base class for elastic body spline and thin plate spline. This is implemented in as straightforward a manner as possible from the IEEE TMI paper by Davis, Khotanzad, Flamig, and Harms, Vol. 16, No. 3 June 1997. Notation closely follows their paper, so if you have it in front of you, this code will make a lot more sense.

KernelTransform2: Provides support for defining source and target landmarks Defines a number of data types used in the computations Defines the mathematical framework used to compute all splines, so that subclasses need only provide a kernel specific to that spline

This formulation allows the stiffness of the spline to be adjusted, allowing the spline to vary from interpolating the landmarks to approximating the landmarks. This part of the formulation is based on the short paper by R. Sprengel, K. Rohr, H. Stiehl. "Thin-Plate Spline Approximation for Image Registration". In 18th International Conference of the IEEE Engineering in Medicine and Biology Society. 1996.

This class was modified to support its use in the ITK registration framework by Rupert Brooks, McGill Centre for Intelligent Machines, Montreal, Canada March 2007. See the Insight Journal Paper by Brooks, R., Arbel, T. "Improvements to the itk::KernelTransform and its subclasses."

Modified a bit to include it in elastix:

style
make it inherit from AdvancedTransform
make it threadsafe, like was done in the itk as well.

Definition at line 75 of file itkKernelTransform2.h.