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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

using AMatrixType = vnl_matrix_fixed< TScalarType, NDimensions, NDimensions >
 
using BMatrixType = vnl_vector_fixed< TScalarType, NDimensions >
 
using ColumnMatrixType = vnl_matrix_fixed< TScalarType, NDimensions, 1 >
 
using ConstPointer = SmartPointer< const Self >
 
using DMatrixType = vnl_matrix< TScalarType >
 
using GMatrixType = vnl_matrix_fixed< TScalarType, NDimensions, NDimensions >
 
using IMatrixType = vnl_matrix_fixed< TScalarType, NDimensions, NDimensions >
 
using KMatrixType = vnl_matrix< TScalarType >
 
using LMatrixType = vnl_matrix< TScalarType >
 
using PMatrixType = vnl_matrix< TScalarType >
 
using Pointer = SmartPointer< Self >
 
using PointsConstIterator = typename PointSetType::PointsContainerConstIterator
 
using PointsContainer = typename PointSetType::PointsContainer
 
using PointSetPointer = typename PointSetType::Pointer
 
using PointSetTraitsType = DefaultStaticMeshTraits< TScalarType, NDimensions, NDimensions, TScalarType, TScalarType >
 
using PointSetType = PointSet< InputPointType, NDimensions, PointSetTraitsType >
 
using PointsIterator = typename PointSetType::PointsContainerIterator
 
using RowMatrixType = vnl_matrix_fixed< TScalarType, 1, NDimensions >
 
using Self = KernelTransform2
 
using Superclass = AdvancedTransform< TScalarType, NDimensions, NDimensions >
 
using VectorSetPointer = typename VectorSetType::Pointer
 
using VectorSetType = VectorContainer< unsigned long, InputVectorType >
 
using WMatrixType = vnl_matrix< TScalarType >
 
using YMatrixType = vnl_matrix< TScalarType >
 
- Public Types inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
using ConstPointer = SmartPointer< const Self >
 
using InternalMatrixType = typename SpatialJacobianType::InternalMatrixType
 
using InverseTransformBaseType = typename Superclass::InverseTransformBaseType
 
using JacobianOfSpatialHessianType = std::vector< SpatialHessianType >
 
using JacobianOfSpatialJacobianType = std::vector< SpatialJacobianType >
 
using MovingImageGradientType = OutputCovariantVectorType
 
using MovingImageGradientValueType = typename MovingImageGradientType::ValueType
 
using NonZeroJacobianIndicesType = std::vector< unsigned long >
 
using Pointer = SmartPointer< Self >
 
using Self = AdvancedTransform
 
using SpatialHessianType = FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension >
 
using SpatialJacobianType = Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension >
 
using Superclass = Transform< TScalarType, NInputDimensions, NOutputDimensions >
 
using TransformType = Transform< TScalarType, NInputDimensions, NOutputDimensions >
 
using TransformTypeConstPointer = typename TransformType::ConstPointer
 
using TransformTypePointer = typename TransformType::Pointer
 

Public Member Functions

void ComputeLInverse ()
 
void ComputeWMatrix ()
 
virtual const char * GetClassName () const
 
const ParametersType & GetFixedParameters () const override
 
void GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const override
 
void GetJacobianOfSpatialHessian (const InputPointType &inputPoint, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const override
 
void GetJacobianOfSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const override
 
void GetJacobianOfSpatialJacobian (const InputPointType &inputPoint, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const override
 
void GetJacobianOfSpatialJacobian (const InputPointType &inputPoint, SpatialJacobianType &sj, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const override
 
virtual const std::string & GetMatrixInversionMethod ()
 
NumberOfParametersType GetNumberOfParameters () const override
 
const ParametersType & GetParameters () const override
 
virtual const TScalarType GetPoissonRatio () const
 
void GetSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh) const override
 
void GetSpatialJacobian (const InputPointType &inputPoint, SpatialJacobianType &sj) const override
 
virtual double GetStiffness () const
 
 ITK_DISALLOW_COPY_AND_MOVE (KernelTransform2)
 
 itkGetModifiableObjectMacro (Displacements, VectorSetType)
 
 itkGetModifiableObjectMacro (SourceLandmarks, PointSetType)
 
 itkGetModifiableObjectMacro (TargetLandmarks, PointSetType)
 
 itkStaticConstMacro (SpaceDimension, unsigned int, NDimensions)
 
virtual void SetAlpha (TScalarType)
 
void SetFixedParameters (const ParametersType &) override
 
virtual void SetIdentity ()
 
virtual void SetMatrixInversionMethod (std::string _arg)
 
void SetParameters (const ParametersType &) override
 
virtual void SetPoissonRatio (TScalarType _arg)
 
virtual void SetSourceLandmarks (PointSetType *)
 
virtual void SetStiffness (double stiffness)
 
virtual void SetTargetLandmarks (PointSetType *)
 
OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &) const override
 
OutputPointType TransformPoint (const InputPointType &thisPoint) const override
 
OutputVectorType TransformVector (const InputVectorType &) const override
 
OutputVnlVectorType TransformVector (const InputVnlVectorType &) const override
 
virtual void UpdateParameters ()
 
- Public Member Functions inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
void ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const override
 
virtual void EvaluateJacobianWithImageGradientProduct (const InputPointType &inputPoint, const MovingImageGradientType &movingImageGradient, DerivativeType &imageJacobian, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
 
virtual const char * GetClassName () const
 
virtual bool GetHasNonZeroJacobianOfSpatialHessian () const
 
virtual bool GetHasNonZeroSpatialHessian () const
 
virtual void GetJacobian (const InputPointType &inputPoint, JacobianType &j, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const=0
 
virtual void GetJacobianOfSpatialHessian (const InputPointType &inputPoint, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const=0
 
virtual void GetJacobianOfSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const=0
 
virtual void GetJacobianOfSpatialJacobian (const InputPointType &inputPoint, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const=0
 
virtual void GetJacobianOfSpatialJacobian (const InputPointType &inputPoint, SpatialJacobianType &sj, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const=0
 
virtual NumberOfParametersType GetNumberOfNonZeroJacobianIndices () const
 
virtual void GetSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh) const=0
 
virtual void GetSpatialJacobian (const InputPointType &inputPoint, SpatialJacobianType &sj) const=0
 
 ITK_DISALLOW_COPY_AND_MOVE (AdvancedTransform)
 
 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

using QRDecompositionType = vnl_qr< ScalarType >
 
using SVDDecompositionType = vnl_svd< ScalarType >
 

Protected Member Functions

void ComputeD ()
 
virtual void ComputeDeformationContribution (const InputPointType &inputPoint, OutputPointType &result) const
 
virtual void ComputeG (const InputVectorType &landmarkVector, GMatrixType &GMatrix) const
 
void ComputeK ()
 
void ComputeL ()
 
void ComputeP ()
 
virtual void ComputeReflexiveG (PointsIterator, GMatrixType &GMatrix) const
 
void ComputeY ()
 
 KernelTransform2 ()
 
void PrintSelf (std::ostream &os, Indent indent) const override
 
void ReorganizeW ()
 
 ~KernelTransform2 () override
 
- Protected Member Functions inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >
 AdvancedTransform ()=default
 
 ~AdvancedTransform () override=default
 

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
 
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 Attributes

std::string m_MatrixInversionMethod
 
TScalarType m_PoissonRatio
 

Member Typedef Documentation

◆ AMatrixType

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

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

Definition at line 386 of file itkKernelTransform2.h.

◆ BMatrixType

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

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

Definition at line 389 of file itkKernelTransform2.h.

◆ ColumnMatrixType

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

Column matrix typedef.

Definition at line 395 of file itkKernelTransform2.h.

◆ ConstPointer

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

Definition at line 106 of file itkKernelTransform2.h.

◆ DMatrixType

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

'D' matrix typedef. Deformation component

Definition at line 383 of file itkKernelTransform2.h.

◆ GMatrixType

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

'G' matrix typedef.

Definition at line 365 of file itkKernelTransform2.h.

◆ IMatrixType

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

'I' (identity) matrix typedef.

Definition at line 154 of file itkKernelTransform2.h.

◆ KMatrixType

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

'K' matrix typedef.

Definition at line 371 of file itkKernelTransform2.h.

◆ LMatrixType

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

'L' matrix typedef.

Definition at line 368 of file itkKernelTransform2.h.

◆ PMatrixType

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

'P' matrix typedef.

Definition at line 374 of file itkKernelTransform2.h.

◆ Pointer

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

Definition at line 105 of file itkKernelTransform2.h.

◆ PointsConstIterator

template<class TScalarType , unsigned int NDimensions>
using itk::KernelTransform2< TScalarType, NDimensions >::PointsConstIterator = typename PointSetType::PointsContainerConstIterator

Definition at line 147 of file itkKernelTransform2.h.

◆ PointsContainer

template<class TScalarType , unsigned int NDimensions>
using itk::KernelTransform2< TScalarType, NDimensions >::PointsContainer = typename PointSetType::PointsContainer

Definition at line 145 of file itkKernelTransform2.h.

◆ PointSetPointer

template<class TScalarType , unsigned int NDimensions>
using itk::KernelTransform2< TScalarType, NDimensions >::PointSetPointer = typename PointSetType::Pointer

Definition at line 144 of file itkKernelTransform2.h.

◆ PointSetTraitsType

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

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

Definition at line 142 of file itkKernelTransform2.h.

◆ PointSetType

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

Definition at line 143 of file itkKernelTransform2.h.

◆ PointsIterator

template<class TScalarType , unsigned int NDimensions>
using itk::KernelTransform2< TScalarType, NDimensions >::PointsIterator = typename PointSetType::PointsContainerIterator

Definition at line 146 of file itkKernelTransform2.h.

◆ QRDecompositionType

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

Definition at line 519 of file itkKernelTransform2.h.

◆ RowMatrixType

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

Row matrix typedef.

Definition at line 392 of file itkKernelTransform2.h.

◆ Self

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

Standard class typedefs.

Definition at line 103 of file itkKernelTransform2.h.

◆ Superclass

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

Definition at line 104 of file itkKernelTransform2.h.

◆ SVDDecompositionType

template<class TScalarType , unsigned int NDimensions>
using itk::KernelTransform2< TScalarType, NDimensions >::SVDDecompositionType = vnl_svd<ScalarType>
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 518 of file itkKernelTransform2.h.

◆ VectorSetPointer

template<class TScalarType , unsigned int NDimensions>
using itk::KernelTransform2< TScalarType, NDimensions >::VectorSetPointer = typename VectorSetType::Pointer

Definition at line 151 of file itkKernelTransform2.h.

◆ VectorSetType

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

VectorSet typedef.

Definition at line 150 of file itkKernelTransform2.h.

◆ WMatrixType

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

'W' matrix typedef.

Definition at line 380 of file itkKernelTransform2.h.

◆ YMatrixType

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

'Y' matrix typedef.

Definition at line 377 of file itkKernelTransform2.h.

Constructor & Destructor Documentation

◆ KernelTransform2()

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

◆ ~KernelTransform2()

template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::~KernelTransform2 ( )
overrideprotected

Member Function Documentation

◆ ComputeD()

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

Compute displacements $ q_i - p_i $.

◆ ComputeDeformationContribution()

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

◆ ComputeG()

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

◆ ComputeK()

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

Compute K matrix.

◆ ComputeL()

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

Compute L matrix.

◆ ComputeLInverse()

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

Compute L matrix inverse.

◆ ComputeP()

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

Compute P matrix.

◆ ComputeReflexiveG()

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.

◆ ComputeWMatrix()

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

Compute W matrix.

◆ ComputeY()

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

Compute Y matrix.

◆ GetClassName()

template<class TScalarType , unsigned int NDimensions>
virtual const char * itk::KernelTransform2< TScalarType, NDimensions >::GetClassName ( ) const
virtual

◆ GetFixedParameters()

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

Get Transform Fixed Parameters - Gets the target landmarks.

◆ GetJacobian()

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

Compute the Jacobian of the transformation.

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

◆ GetJacobianOfSpatialHessian() [1/2]

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialHessian ( const InputPointType &  inputPoint,
JacobianOfSpatialHessianType jsh,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlineoverridevirtual

◆ GetJacobianOfSpatialHessian() [2/2]

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialHessian ( const InputPointType &  inputPoint,
SpatialHessianType sh,
JacobianOfSpatialHessianType jsh,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlineoverridevirtual

◆ GetJacobianOfSpatialJacobian() [1/2]

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialJacobian ( const InputPointType &  inputPoint,
JacobianOfSpatialJacobianType jsj,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlineoverridevirtual

◆ GetJacobianOfSpatialJacobian() [2/2]

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::GetJacobianOfSpatialJacobian ( const InputPointType &  inputPoint,
SpatialJacobianType sj,
JacobianOfSpatialJacobianType jsj,
NonZeroJacobianIndicesType nonZeroJacobianIndices 
) const
inlineoverridevirtual

◆ GetMatrixInversionMethod()

template<class TScalarType , unsigned int NDimensions>
virtual const std::string & itk::KernelTransform2< TScalarType, NDimensions >::GetMatrixInversionMethod ( )
virtual

◆ GetNumberOfParameters()

template<class TScalarType , unsigned int NDimensions>
NumberOfParametersType itk::KernelTransform2< TScalarType, NDimensions >::GetNumberOfParameters ( ) const
inlineoverride

Return the number of parameters that completely define the Transform.

Definition at line 158 of file itkKernelTransform2.h.

◆ GetParameters()

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

Get the Transformation Parameters - Gets the source landmarks.

◆ GetPoissonRatio()

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

◆ GetSpatialHessian()

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::GetSpatialHessian ( const InputPointType &  inputPoint,
SpatialHessianType sh 
) const
inlineoverridevirtual

◆ GetSpatialJacobian()

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::GetSpatialJacobian ( const InputPointType &  inputPoint,
SpatialJacobianType sj 
) const
inlineoverridevirtual

Must be provided.

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

Definition at line 306 of file itkKernelTransform2.h.

◆ GetStiffness()

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

◆ ITK_DISALLOW_COPY_AND_MOVE()

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

◆ itkGetModifiableObjectMacro() [1/3]

template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::itkGetModifiableObjectMacro ( Displacements  ,
VectorSetType   
)

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

◆ itkGetModifiableObjectMacro() [2/3]

template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::itkGetModifiableObjectMacro ( SourceLandmarks  ,
PointSetType   
)

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

◆ itkGetModifiableObjectMacro() [3/3]

template<class TScalarType , unsigned int NDimensions>
itk::KernelTransform2< TScalarType, NDimensions >::itkGetModifiableObjectMacro ( TargetLandmarks  ,
PointSetType   
)

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

◆ itkStaticConstMacro()

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

Dimension of the domain space.

◆ New()

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

New macro for creation of through a Smart Pointer.

◆ PrintSelf()

template<class TScalarType , unsigned int NDimensions>
void itk::KernelTransform2< TScalarType, NDimensions >::PrintSelf ( std::ostream &  os,
Indent  indent 
) const
overrideprotected

◆ ReorganizeW()

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

◆ SetAlpha()

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 283 of file itkKernelTransform2.h.

◆ SetFixedParameters()

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

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

◆ SetIdentity()

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

Set the Transformation Parameters to be an identity transform.

◆ SetMatrixInversionMethod()

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

Matrix inversion by SVD or QR decomposition.

◆ SetParameters()

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

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>.

◆ SetPoissonRatio()

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 >.

◆ SetSourceLandmarks()

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

Set the source landmarks list.

◆ SetStiffness()

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 265 of file itkKernelTransform2.h.

◆ SetTargetLandmarks()

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

Set the target landmarks list.

◆ TransformCovariantVector()

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

Definition at line 211 of file itkKernelTransform2.h.

◆ TransformPoint()

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

Compute the position of point in the new space

◆ TransformVector() [1/2]

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

These vector transforms are not implemented for this transform.

Definition at line 197 of file itkKernelTransform2.h.

◆ TransformVector() [2/2]

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

Definition at line 204 of file itkKernelTransform2.h.

◆ UpdateParameters()

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

Update the Parameters array from the landmarks coordinates.

Field Documentation

◆ m_AMatrix

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 491 of file itkKernelTransform2.h.

◆ m_BVector

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 494 of file itkKernelTransform2.h.

◆ m_Displacements

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 463 of file itkKernelTransform2.h.

◆ m_DMatrix

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 488 of file itkKernelTransform2.h.

◆ m_FastComputationPossible

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 533 of file itkKernelTransform2.h.

◆ m_I

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

Identity matrix.

Definition at line 525 of file itkKernelTransform2.h.

◆ m_KMatrix

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

The K matrix.

Definition at line 472 of file itkKernelTransform2.h.

◆ m_LInverseComputed

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

Has the L inverse matrix been computed?

Definition at line 508 of file itkKernelTransform2.h.

◆ m_LMatrix

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

The L matrix.

Definition at line 466 of file itkKernelTransform2.h.

◆ m_LMatrixComputed

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

Has the L matrix been computed?

Definition at line 506 of file itkKernelTransform2.h.

◆ m_LMatrixDecompositionComputed

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

Has the L matrix decomposition been computed?

Definition at line 510 of file itkKernelTransform2.h.

◆ m_LMatrixDecompositionQR

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

Definition at line 522 of file itkKernelTransform2.h.

◆ m_LMatrixDecompositionSVD

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

Definition at line 521 of file itkKernelTransform2.h.

◆ m_LMatrixInverse

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 469 of file itkKernelTransform2.h.

◆ m_MatrixInversionMethod

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

Using SVD or QR decomposition.

Definition at line 539 of file itkKernelTransform2.h.

◆ m_NonZeroJacobianIndices

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

Precomputed nonzero Jacobian indices (simply all params)

Definition at line 528 of file itkKernelTransform2.h.

◆ m_PMatrix

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

The P matrix.

Definition at line 475 of file itkKernelTransform2.h.

◆ m_PoissonRatio

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

Definition at line 536 of file itkKernelTransform2.h.

◆ m_SourceLandmarks

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

The list of source landmarks, denoted 'p'.

Definition at line 398 of file itkKernelTransform2.h.

◆ m_Stiffness

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

Stiffness parameter.

Definition at line 458 of file itkKernelTransform2.h.

◆ m_TargetLandmarks

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

The list of target landmarks, denoted 'q'.

Definition at line 401 of file itkKernelTransform2.h.

◆ m_WMatrix

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

The W matrix.

Definition at line 481 of file itkKernelTransform2.h.

◆ m_WMatrixComputed

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 504 of file itkKernelTransform2.h.

◆ m_YMatrix

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

The Y matrix.

Definition at line 478 of file itkKernelTransform2.h.



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