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itk::KernelTransform2< TScalarType, NDimensions > Class Template Reference

#include <itkKernelTransform2.h>

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 to include it in elastix:

Definition at line 97 of file itkKernelTransform2.h.

Inheritance diagram for itk::KernelTransform2< TScalarType, NDimensions >:
Inheritance graph
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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 SelfConstPointer
 
typedef vnl_matrix< TScalarType > DMatrixType
 
typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > GMatrixType
 
typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > IMatrixType
 
typedef Superclass::InputCovariantVectorType InputCovariantVectorType
 
typedef Superclass::InputPointType InputPointType
 
typedef Superclass::InputVectorType InputVectorType
 
typedef Superclass::InputVnlVectorType InputVnlVectorType
 
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::NumberOfParametersType NumberOfParametersType
 
typedef Superclass::OutputCovariantVectorType OutputCovariantVectorType
 
typedef Superclass::OutputPointType OutputPointType
 
typedef Superclass::OutputVectorType OutputVectorType
 
typedef Superclass::OutputVnlVectorType OutputVnlVectorType
 
typedef Superclass::ParametersType ParametersType
 
typedef vnl_matrix< TScalarType > PMatrixType
 
typedef SmartPointer< SelfPointer
 
typedef PointSetType::PointsContainerConstIterator PointsConstIterator
 
typedef PointSetType::PointsContainer PointsContainer
 
typedef PointSetType::Pointer PointSetPointer
 
typedef DefaultStaticMeshTraits< TScalarType, NDimensions, NDimensions, TScalarType, TScalarType > PointSetTraitsType
 
typedef PointSet< InputPointType, NDimensions, PointSetTraitsTypePointSetType
 
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, InputVectorTypeVectorSetType
 
typedef vnl_matrix< TScalarType > WMatrixType
 
typedef vnl_matrix< TScalarType > YMatrixType
 
- Public Types inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
typedef SmartPointer< const SelfConstPointer
 
typedef Superclass::DerivativeType DerivativeType
 
typedef Superclass::InputCovariantVectorType InputCovariantVectorType
 
typedef Superclass::InputPointType InputPointType
 
typedef Superclass::InputVectorType InputVectorType
 
typedef Superclass::InputVnlVectorType InputVnlVectorType
 
typedef SpatialJacobianType::InternalMatrixType InternalMatrixType
 
typedef Superclass::InverseTransformBasePointer InverseTransformBasePointer
 
typedef Superclass::InverseTransformBaseType InverseTransformBaseType
 
typedef std::vector< SpatialHessianTypeJacobianOfSpatialHessianType
 
typedef std::vector< SpatialJacobianTypeJacobianOfSpatialJacobianType
 
typedef Superclass::JacobianType JacobianType
 
typedef OutputCovariantVectorType MovingImageGradientType
 
typedef MovingImageGradientType::ValueType MovingImageGradientValueType
 
typedef std::vector< unsigned long > NonZeroJacobianIndicesType
 
typedef Superclass::NumberOfParametersType NumberOfParametersType
 
typedef Superclass::OutputCovariantVectorType OutputCovariantVectorType
 
typedef Superclass::OutputPointType OutputPointType
 
typedef Superclass::OutputVectorType OutputVectorType
 
typedef Superclass::OutputVnlVectorType OutputVnlVectorType
 
typedef Superclass::ParametersType ParametersType
 
typedef Superclass::ParametersValueType ParametersValueType
 
typedef SmartPointer< SelfPointer
 
typedef Superclass::ScalarType ScalarType
 
typedef AdvancedTransform Self
 
typedef FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension > SpatialHessianType
 
typedef Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension > SpatialJacobianType
 
typedef Transform< TScalarType, NInputDimensions, NOutputDimensions > Superclass
 
typedef Transform< TScalarType, NInputDimensions, NOutputDimensions > TransformType
 
typedef TransformType::ConstPointer TransformTypeConstPointer
 
typedef TransformType::Pointer TransformTypePointer
 

Public Member Functions

void ComputeLInverse (void)
 
void ComputeWMatrix (void)
 
virtual TScalarType GetAlpha (void) const
 
virtual const char * GetClassName () const
 
virtual VectorSetTypeGetDisplacements ()
 
virtual const ParametersTypeGetFixedParameters (void) const
 
virtual void GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const
 
virtual void GetJacobianOfSpatialHessian (const InputPointType &ipp, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
 
virtual void GetJacobianOfSpatialHessian (const InputPointType &ipp, SpatialHessianType &sh, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
 
virtual void GetJacobianOfSpatialJacobian (const InputPointType &ipp, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
 
virtual void GetJacobianOfSpatialJacobian (const InputPointType &ipp, SpatialJacobianType &sj, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
 
virtual const std::string & GetMatrixInversionMethod ()
 
virtual NumberOfParametersType GetNumberOfParameters (void) const
 
virtual const ParametersTypeGetParameters (void) const
 
virtual const TScalarType GetPoissonRatio (void) const
 
virtual PointSetTypeGetSourceLandmarks ()
 
virtual void GetSpatialHessian (const InputPointType &ipp, SpatialHessianType &sh) const
 
virtual void GetSpatialJacobian (const InputPointType &ipp, SpatialJacobianType &sj) const
 
virtual double GetStiffness ()
 
virtual PointSetTypeGetTargetLandmarks ()
 
 itkStaticConstMacro (SpaceDimension, unsigned int, NDimensions)
 
virtual void SetAlpha (TScalarType)
 
virtual void SetFixedParameters (const ParametersType &)
 
virtual void SetIdentity (void)
 
virtual void SetMatrixInversionMethod (std::string _arg)
 
virtual void SetParameters (const ParametersType &)
 
virtual void SetPoissonRatio (TScalarType _arg)
 
virtual void SetSourceLandmarks (PointSetType *)
 
virtual void SetStiffness (double stiffness)
 
virtual void SetTargetLandmarks (PointSetType *)
 
virtual OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &) const
 
virtual OutputPointType TransformPoint (const InputPointType &thisPoint) const
 
virtual OutputVectorType TransformVector (const InputVectorType &) const
 
virtual OutputVnlVectorType TransformVector (const InputVnlVectorType &) const
 
virtual void UpdateParameters (void)
 
- Public Member Functions inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
virtual void ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const
 
virtual void ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianType &) const
 
virtual void EvaluateJacobianWithImageGradientProduct (const InputPointType &ipp, const MovingImageGradientType &movingImageGradient, DerivativeType &imageJacobian, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
 
virtual bool GetHasNonZeroJacobianOfSpatialHessian () const
 
virtual bool GetHasNonZeroSpatialHessian () const
 
virtual NumberOfParametersType GetNumberOfNonZeroJacobianIndices (void) const
 
 itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)
 
 itkStaticConstMacro (OutputSpaceDimension, unsigned int, NOutputDimensions)
 

Static Public Member Functions

static Pointer New ()
 

Data Fields

PointSetPointer m_SourceLandmarks
 
PointSetPointer m_TargetLandmarks
 

Protected Types

typedef vnl_qr< ScalarTypeQRDecompositionType
 
typedef vnl_svd< ScalarTypeSVDDecompositionType
 

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 Member Functions inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
 AdvancedTransform ()
 
 AdvancedTransform (NumberOfParametersType numberOfParameters)
 
virtual ~AdvancedTransform ()
 

Protected Attributes

AMatrixType m_AMatrix
 
BMatrixType m_BVector
 
VectorSetPointer m_Displacements
 
DMatrixType m_DMatrix
 
bool m_FastComputationPossible
 
IMatrixType m_I
 
KMatrixType m_KMatrix
 
bool m_LInverseComputed
 
LMatrixType m_LMatrix
 
bool m_LMatrixComputed
 
bool m_LMatrixDecompositionComputed
 
QRDecompositionTypem_LMatrixDecompositionQR
 
SVDDecompositionTypem_LMatrixDecompositionSVD
 
LMatrixType m_LMatrixInverse
 
NonZeroJacobianIndicesType m_NonZeroJacobianIndices
 
NonZeroJacobianIndicesType m_NonZeroJacobianIndicesTemp
 
PMatrixType m_PMatrix
 
double m_Stiffness
 
WMatrixType m_WMatrix
 
bool m_WMatrixComputed
 
YMatrixType m_YMatrix
 
- Protected Attributes inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
bool m_HasNonZeroJacobianOfSpatialHessian
 
bool m_HasNonZeroSpatialHessian
 

Private Member Functions

 KernelTransform2 (const Self &)
 
void operator= (const Self &)
 

Private Attributes

std::string m_MatrixInversionMethod
 
TScalarType m_PoissonRatio
 

Member Typedef Documentation

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

'A' matrix typedef. Rotational part of the Affine component

Definition at line 378 of file itkKernelTransform2.h.

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

'B' matrix typedef. Translational part of the Affine component

Definition at line 381 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef vnl_matrix_fixed< TScalarType, NDimensions, 1 > itk::KernelTransform2< TScalarType, NDimensions >::ColumnMatrixType

Column matrix typedef.

Definition at line 387 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef SmartPointer< const Self > itk::KernelTransform2< TScalarType, NDimensions >::ConstPointer

Definition at line 107 of file itkKernelTransform2.h.

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

'D' matrix typedef. Deformation component

Definition at line 375 of file itkKernelTransform2.h.

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

'G' matrix typedef.

Definition at line 357 of file itkKernelTransform2.h.

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

'I' (identity) matrix typedef.

Definition at line 160 of file itkKernelTransform2.h.

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

Definition at line 127 of file itkKernelTransform2.h.

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

Definition at line 123 of file itkKernelTransform2.h.

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

Definition at line 125 of file itkKernelTransform2.h.

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

Definition at line 129 of file itkKernelTransform2.h.

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

Definition at line 141 of file itkKernelTransform2.h.

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

Definition at line 140 of file itkKernelTransform2.h.

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

Definition at line 137 of file itkKernelTransform2.h.

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

Definition at line 122 of file itkKernelTransform2.h.

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

'K' matrix typedef.

Definition at line 363 of file itkKernelTransform2.h.

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

'L' matrix typedef.

Definition at line 360 of file itkKernelTransform2.h.

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

AdvancedTransform typedefs.

Definition at line 134 of file itkKernelTransform2.h.

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

Definition at line 121 of file itkKernelTransform2.h.

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

Definition at line 128 of file itkKernelTransform2.h.

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

Definition at line 124 of file itkKernelTransform2.h.

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

Definition at line 126 of file itkKernelTransform2.h.

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

Definition at line 130 of file itkKernelTransform2.h.

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

Definition at line 120 of file itkKernelTransform2.h.

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

'P' matrix typedef.

Definition at line 366 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef SmartPointer< Self > itk::KernelTransform2< TScalarType, NDimensions >::Pointer

Definition at line 106 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef PointSetType::PointsContainerConstIterator itk::KernelTransform2< TScalarType, NDimensions >::PointsConstIterator

Definition at line 153 of file itkKernelTransform2.h.

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

Definition at line 151 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef PointSetType::Pointer itk::KernelTransform2< TScalarType, NDimensions >::PointSetPointer

Definition at line 150 of file itkKernelTransform2.h.

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

PointList typedef. This type is used for maintaining lists of points, specifically, the source and target landmark lists.

Definition at line 147 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef PointSet< InputPointType, NDimensions, PointSetTraitsType > itk::KernelTransform2< TScalarType, NDimensions >::PointSetType

Definition at line 149 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef PointSetType::PointsContainerIterator itk::KernelTransform2< TScalarType, NDimensions >::PointsIterator

Definition at line 152 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef vnl_qr< ScalarType > itk::KernelTransform2< TScalarType, NDimensions >::QRDecompositionType
protected

Definition at line 506 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef vnl_matrix_fixed< TScalarType, 1, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::RowMatrixType

Row matrix typedef.

Definition at line 384 of file itkKernelTransform2.h.

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

Typedefs.

Definition at line 119 of file itkKernelTransform2.h.

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

Standard class typedefs.

Definition at line 103 of file itkKernelTransform2.h.

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

Definition at line 138 of file itkKernelTransform2.h.

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

Definition at line 135 of file itkKernelTransform2.h.

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

Definition at line 105 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef vnl_svd< ScalarType > itk::KernelTransform2< TScalarType, NDimensions >::SVDDecompositionType
protected

Decompositions, needed for the L matrix. These decompositions are cached for performance reasons during registration. During registration, in every iteration SetParameters() is called, which in turn calls ComputeWMatrix(). The L matrix is not changed however, and therefore it is not needed to redo the decomposition.

Definition at line 505 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef VectorSetType::Pointer itk::KernelTransform2< TScalarType, NDimensions >::VectorSetPointer

Definition at line 157 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
typedef VectorContainer< unsigned long, InputVectorType > itk::KernelTransform2< TScalarType, NDimensions >::VectorSetType

VectorSet typedef.

Definition at line 156 of file itkKernelTransform2.h.

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

'W' matrix typedef.

Definition at line 372 of file itkKernelTransform2.h.

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

'Y' matrix typedef.

Definition at line 369 of file itkKernelTransform2.h.

Constructor & Destructor Documentation

template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::KernelTransform2 ( )
protected
template<class TScalarType , unsigned int NDimensions>
virtual itk::KernelTransform2< TScalarType, NDimensions >::~KernelTransform2 ( )
protectedvirtual
template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::KernelTransform2 ( const Self )
private

Member Function Documentation

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeD ( void  )
protected

Compute displacements $ q_i - p_i $.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::ComputeDeformationContribution ( const InputPointType inputPoint,
OutputPointType result 
) const
protectedvirtual

Compute the contribution of the landmarks weighted by the kernel function to the global deformation of the space.

Reimplemented in itk::ThinPlateSplineKernelTransform2< TScalarType, NDimensions >, itk::ThinPlateR2LogRSplineKernelTransform2< TScalarType, NDimensions >, and itk::VolumeSplineKernelTransform2< TScalarType, NDimensions >.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::ComputeG ( const InputVectorType landmarkVector,
GMatrixType GMatrix 
) const
protectedvirtual
template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeK ( void  )
protected

Compute K matrix.

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeL ( void  )
protected

Compute L matrix.

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeLInverse ( void  )

Compute L matrix inverse.

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeP ( void  )
protected

Compute P matrix.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::ComputeReflexiveG ( PointsIterator  ,
GMatrixType GMatrix 
) const
protectedvirtual

Compute a G(x) for a point to itself (i.e. for the block diagonal elements of the matrix K. Parameter indicates for which landmark the reflexive G is to be computed. The default implementation for the reflexive contribution is a diagonal matrix where the diagonal elements are the stiffness of the spline.

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeWMatrix ( void  )

Compute W matrix.

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ComputeY ( void  )
protected

Compute Y matrix.

template<class TScalarType , unsigned int NDimensions>
virtual TScalarType itk::KernelTransform2< TScalarType, NDimensions >::GetAlpha ( void  ) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual const char* itk::KernelTransform2< TScalarType, NDimensions >::GetClassName ( ) const
virtual
template<class TScalarType , unsigned int NDimensions>
virtual VectorSetType* itk::KernelTransform2< TScalarType, NDimensions >::GetDisplacements ( )
virtual

Get the displacements list, which we will denote $ d $, where $ d_i = q_i - p_i $.

template<class TScalarType , unsigned int NDimensions>
virtual const ParametersType& itk::KernelTransform2< TScalarType, NDimensions >::GetFixedParameters ( void  ) const
virtual

Get Transform Fixed Parameters - Gets the target landmarks.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobian ( const InputPointType ,
JacobianType ,
NonZeroJacobianIndicesType  
) const
virtual

Compute the Jacobian of the transformation.

Implements itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialHessian ( const InputPointType ipp,
JacobianOfSpatialHessianType jsh,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialHessian ( const InputPointType ipp,
SpatialHessianType sh,
JacobianOfSpatialHessianType jsh,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialJacobian ( const InputPointType ipp,
JacobianOfSpatialJacobianType jsj,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialJacobian ( const InputPointType ipp,
SpatialJacobianType sj,
JacobianOfSpatialJacobianType jsj,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual const std::string& itk::KernelTransform2< TScalarType, NDimensions >::GetMatrixInversionMethod ( )
virtual
template<class TScalarType , unsigned int NDimensions>
virtual NumberOfParametersType itk::KernelTransform2< TScalarType, NDimensions >::GetNumberOfParameters ( void  ) const
inlinevirtual

Return the number of parameters that completely define the Transform.

Definition at line 163 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual const ParametersType& itk::KernelTransform2< TScalarType, NDimensions >::GetParameters ( void  ) const
virtual

Get the Transformation Parameters - Gets the source landmarks.

template<class TScalarType , unsigned int NDimensions>
virtual const TScalarType itk::KernelTransform2< TScalarType, NDimensions >::GetPoissonRatio ( void  ) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual PointSetType* itk::KernelTransform2< TScalarType, NDimensions >::GetSourceLandmarks ( )
virtual

Get the source landmarks list, which we will denote $ p $.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetSpatialHessian ( const InputPointType ipp,
SpatialHessianType sh 
) const
inlinevirtual
template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::GetSpatialJacobian ( const InputPointType ipp,
SpatialJacobianType sj 
) const
inlinevirtual

Must be provided.

Implements itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >.

Definition at line 300 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual double itk::KernelTransform2< TScalarType, NDimensions >::GetStiffness ( )
virtual
template<class TScalarType , unsigned int NDimensions>
virtual PointSetType* itk::KernelTransform2< TScalarType, NDimensions >::GetTargetLandmarks ( )
virtual

Get the target landmarks list, which we will denote $ q $.

template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::itkStaticConstMacro ( SpaceDimension  ,
unsigned  int,
NDimensions   
)

Dimension of the domain space.

template<class TScalarType , unsigned int NDimensions>
static Pointer itk::KernelTransform2< TScalarType, NDimensions >::New ( )
static

New macro for creation of through a Smart Pointer.

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::operator= ( const Self )
private
template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::PrintSelf ( std::ostream &  os,
Indent  indent 
) const
protected
template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::ReorganizeW ( void  )
protected

Reorganize the components of W into D (deformable), A (rotation part of affine) and B (translational part of affine ) components.

Warning
This method release the memory of the W Matrix.
template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetAlpha ( TScalarType  )
inlinevirtual

This method makes only sense for the ElasticBody splines. Declare here, so that you can always call it if you don't know the type of kernel beforehand. It will be overridden in the ElasticBodySplineKernelTransform and in the ElasticBodyReciprocalSplineKernelTransform.

Reimplemented in itk::ElasticBodyReciprocalSplineKernelTransform2< TScalarType, NDimensions >, and itk::ElasticBodySplineKernelTransform2< TScalarType, NDimensions >.

Definition at line 279 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetFixedParameters ( const ParametersType )
virtual

Set Transform Fixed Parameters: To support the transform file writer this function was added to set the target landmarks similar to the SetParameters function setting the source landmarks

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetIdentity ( void  )
virtual

Set the Transformation Parameters to be an identity transform.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetMatrixInversionMethod ( std::string  _arg)
virtual

Matrix inversion by SVD or QR decomposition.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetParameters ( const ParametersType )
virtual

Set the Transformation Parameters and update the internal transformation. The parameters represent the source landmarks. Each landmark point is represented by NDimensions doubles. All the landmarks are concatenated to form one flat Array<double>.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetPoissonRatio ( TScalarType  _arg)
virtual

This method makes only sense for the ElasticBody splines. Declare here, so that you can always call it if you don't know the type of kernel beforehand. It will be overridden in the ElasticBodySplineKernelTransform and in the ElasticBodyReciprocalSplineKernelTransform.

Reimplemented in itk::ElasticBodyReciprocalSplineKernelTransform2< TScalarType, NDimensions >, and itk::ElasticBodySplineKernelTransform2< TScalarType, NDimensions >.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetSourceLandmarks ( PointSetType )
virtual

Set the source landmarks list.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetStiffness ( double  stiffness)
inlinevirtual

Stiffness of the spline. A stiffness of zero results in the standard interpolating spline. A non-zero stiffness allows the spline to approximate rather than interpolate the landmarks. Stiffness values are usually rather small, typically in the range of 0.001 to 0.1. The approximating spline 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.

Definition at line 262 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::SetTargetLandmarks ( PointSetType )
virtual

Set the target landmarks list.

template<class TScalarType , unsigned int NDimensions>
virtual OutputCovariantVectorType itk::KernelTransform2< TScalarType, NDimensions >::TransformCovariantVector ( const InputCovariantVectorType ) const
inlinevirtual

Definition at line 212 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual OutputPointType itk::KernelTransform2< TScalarType, NDimensions >::TransformPoint ( const InputPointType thisPoint) const
virtual

Compute the position of point in the new space

template<class TScalarType , unsigned int NDimensions>
virtual OutputVectorType itk::KernelTransform2< TScalarType, NDimensions >::TransformVector ( const InputVectorType ) const
inlinevirtual

These vector transforms are not implemented for this transform.

Definition at line 196 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual OutputVnlVectorType itk::KernelTransform2< TScalarType, NDimensions >::TransformVector ( const InputVnlVectorType ) const
inlinevirtual

Definition at line 204 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
virtual void itk::KernelTransform2< TScalarType, NDimensions >::UpdateParameters ( void  )
virtual

Update the Parameters array from the landmarks coordinates.

Field Documentation

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

Rotational/Shearing part of the Affine component of the Transformation.

Definition at line 478 of file itkKernelTransform2.h.

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

Translational part of the Affine component of the Transformation.

Definition at line 481 of file itkKernelTransform2.h.

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

The list of displacements. d[i] = q[i] - p[i];

Definition at line 450 of file itkKernelTransform2.h.

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

The Deformation matrix. This is an auxiliary matrix that will hold the Deformation (non-affine) part of the transform. Those are the coefficients that will multiply the Kernel function.

Definition at line 475 of file itkKernelTransform2.h.

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

The Jacobian can be computed much faster for some of the derived kerbel transforms, most notably the TPS.

Definition at line 523 of file itkKernelTransform2.h.

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

Identity matrix.

Definition at line 512 of file itkKernelTransform2.h.

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

The K matrix.

Definition at line 459 of file itkKernelTransform2.h.

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

Has the L inverse matrix been computed?

Definition at line 495 of file itkKernelTransform2.h.

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

The L matrix.

Definition at line 453 of file itkKernelTransform2.h.

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

Has the L matrix been computed?

Definition at line 493 of file itkKernelTransform2.h.

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

Has the L matrix decomposition been computed?

Definition at line 497 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
QRDecompositionType* itk::KernelTransform2< TScalarType, NDimensions >::m_LMatrixDecompositionQR
protected

Definition at line 509 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
SVDDecompositionType* itk::KernelTransform2< TScalarType, NDimensions >::m_LMatrixDecompositionSVD
protected

Definition at line 508 of file itkKernelTransform2.h.

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

The inverse of L, which we also cache.

Definition at line 456 of file itkKernelTransform2.h.

template<class TScalarType , unsigned int NDimensions>
std::string itk::KernelTransform2< TScalarType, NDimensions >::m_MatrixInversionMethod
private

Using SVD or QR decomposition.

Definition at line 533 of file itkKernelTransform2.h.

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

Precomputed nonzero Jacobian indices (simply all params)

Definition at line 515 of file itkKernelTransform2.h.

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

for old GetJacobian() method:

Definition at line 518 of file itkKernelTransform2.h.

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

The P matrix.

Definition at line 462 of file itkKernelTransform2.h.

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

Definition at line 530 of file itkKernelTransform2.h.

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

The list of source landmarks, denoted 'p'.

Definition at line 390 of file itkKernelTransform2.h.

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

Stiffness parameter.

Definition at line 445 of file itkKernelTransform2.h.

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

The list of target landmarks, denoted 'q'.

Definition at line 393 of file itkKernelTransform2.h.

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

The W matrix.

Definition at line 468 of file itkKernelTransform2.h.

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

The G matrix. It used to be mutable because m_GMatrix was made an ivar only to avoid copying the matrix at return time but this is not necessary. SK: we don't need this matrix anymore as a member.Has the W matrix been computed?

Definition at line 491 of file itkKernelTransform2.h.

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

The Y matrix.

Definition at line 465 of file itkKernelTransform2.h.



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