ITK  6.0.0
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itk::KernelTransform< TParametersValueType, VDimension > Class Template Reference
Group Core » Module ITKTransform

#include <itkKernelTransform.h>

Detailed Description

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

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.

KernelTransform: 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.

Definition at line 61 of file itkKernelTransform.h.

+ Inheritance diagram for itk::KernelTransform< TParametersValueType, VDimension >:
+ Collaboration diagram for itk::KernelTransform< TParametersValueType, VDimension >:

Public Types

using AMatrixType = vnl_matrix_fixed< TParametersValueType, VDimension, VDimension >
 
using BMatrixType = vnl_vector_fixed< TParametersValueType, VDimension >
 
using ColumnMatrixType = vnl_matrix_fixed< TParametersValueType, VDimension, 1 >
 
using ConstPointer = SmartPointer< const Self >
 
using DMatrixType = vnl_matrix< TParametersValueType >
 
using GMatrixType = vnl_matrix_fixed< TParametersValueType, VDimension, VDimension >
 
using IMatrixType = vnl_matrix_fixed< TParametersValueType, VDimension, VDimension >
 
using KMatrixType = vnl_matrix< TParametersValueType >
 
using LMatrixType = vnl_matrix< TParametersValueType >
 
using PMatrixType = vnl_matrix< TParametersValueType >
 
using Pointer = SmartPointer< Self >
 
using PointIdentifier = typename PointSetType::PointIdentifier
 
using PointsConstIterator = typename PointSetType::PointsContainerConstIterator
 
using PointsContainer = typename PointSetType::PointsContainer
 
using PointSetPointer = typename PointSetType::Pointer
 
using PointSetTraitsType = DefaultStaticMeshTraits< TParametersValueType, VDimension, VDimension, TParametersValueType, TParametersValueType >
 
using PointSetType = PointSet< InputPointType, VDimension, PointSetTraitsType >
 
using PointsIterator = typename PointSetType::PointsContainerIterator
 
using RowMatrixType = vnl_matrix_fixed< TParametersValueType, 1, VDimension >
 
using Self = KernelTransform
 
using Superclass = Transform< TParametersValueType, VDimension, VDimension >
 
using VectorSetPointer = typename VectorSetType::Pointer
 
using VectorSetType = itk::VectorContainer< InputVectorType >
 
using WMatrixType = vnl_matrix< TParametersValueType >
 
using YMatrixType = vnl_matrix< TParametersValueType >
 
- Public Types inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
using ConstPointer = SmartPointer< const Self >
 
using DerivativeType = Array< ParametersValueType >
 
using DirectionChangeMatrix = Matrix< double, Self::OutputSpaceDimension, Self::InputSpaceDimension >
 
using InputCovariantVectorType = CovariantVector< TParametersValueType, VInputDimension >
 
using InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >
 
using InputDirectionMatrix = Matrix< double, Self::InputSpaceDimension, Self::InputSpaceDimension >
 
using InputPointType = Point< TParametersValueType, VInputDimension >
 
using InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension >
 
using InputVectorPixelType = VariableLengthVector< TParametersValueType >
 
using InputVectorType = Vector< TParametersValueType, VInputDimension >
 
using InputVnlVectorType = vnl_vector_fixed< TParametersValueType, VInputDimension >
 
using InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension >
 
using InverseTransformBasePointer = typename InverseTransformBaseType::Pointer
 
using InverseTransformBaseType = Transform< TParametersValueType, VOutputDimension, VInputDimension >
 
using JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension >
 
using JacobianType = Array2D< ParametersValueType >
 
using MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension >
 
using OutputCovariantVectorType = CovariantVector< TParametersValueType, VOutputDimension >
 
using OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >
 
using OutputDirectionMatrix = Matrix< double, Self::OutputSpaceDimension, Self::OutputSpaceDimension >
 
using OutputPointType = Point< TParametersValueType, VOutputDimension >
 
using OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension >
 
using OutputVectorPixelType = VariableLengthVector< TParametersValueType >
 
using OutputVectorType = Vector< TParametersValueType, VOutputDimension >
 
using OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, VOutputDimension >
 
using Pointer = SmartPointer< Self >
 
using ScalarType = ParametersValueType
 
using Self = Transform
 
using Superclass = TransformBaseTemplate< TParametersValueType >
 

Public Member Functions

void ComputeJacobianWithRespectToParameters (const InputPointType &p, JacobianType &jacobian) const override
 
void ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianPositionType &) const override
 
void ComputeWMatrix ()
 
const FixedParametersType & GetFixedParameters () const override
 
virtual VectorSetType * GetModifiableDisplacements ()
 
const char * GetNameOfClass () const override
 
const ParametersType & GetParameters () const override
 
TransformCategoryEnum GetTransformCategory () const override
 
void SetFixedParameters (const FixedParametersType &) override
 
void SetParameters (const ParametersType &) override
 
OutputPointType TransformPoint (const InputPointType &thisPoint) const override
 
OutputVnlVectorType TransformVector (const InputVnlVectorType &) const override
 
virtual void UpdateParameters () const
 
virtual PointSetType * GetModifiableSourceLandmarks ()
 
virtual void SetSourceLandmarks (PointSetType *)
 
virtual PointSetType * GetModifiableTargetLandmarks ()
 
virtual void SetTargetLandmarks (PointSetType *)
 
OutputVectorType TransformVector (const InputVectorType &) const override
 
OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &) const override
 
virtual void SetStiffness (double _arg)
 
virtual double GetStiffness () const
 
- Public Member Functions inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
virtual void ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const
 
void CopyInFixedParameters (const FixedParametersValueType *const begin, const FixedParametersValueType *const end) override
 
void CopyInParameters (const ParametersValueType *const begin, const ParametersValueType *const end) override
 
const FixedParametersType & GetFixedParameters () const override
 
unsigned int GetInputSpaceDimension () const override
 
bool GetInverse (Self *) const
 
virtual InverseTransformBasePointer GetInverseTransform () const
 
const char * GetNameOfClass () const override
 
virtual NumberOfParametersType GetNumberOfFixedParameters () const
 
virtual NumberOfParametersType GetNumberOfLocalParameters () const
 
NumberOfParametersType GetNumberOfParameters () const override
 
unsigned int GetOutputSpaceDimension () const override
 
const ParametersType & GetParameters () const override
 
TransformCategoryEnum GetTransformCategory () const override
 
std::string GetTransformTypeAsString () const override
 
virtual bool IsLinear () const
 
 itkCloneMacro (Self)
 
void SetParametersByValue (const ParametersType &p) override
 
virtual OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const
 
virtual OutputVectorPixelType TransformCovariantVector (const InputVectorPixelType &) const
 
virtual OutputVectorPixelType TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const
 
virtual OutputDiffusionTensor3DType TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const
 
virtual OutputDiffusionTensor3DType TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor, const InputPointType &point) const
 
virtual OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &) const
 
virtual OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor, const InputPointType &point) const
 
virtual OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const
 
virtual OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor, const InputPointType &point) const
 
virtual OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const
 
virtual OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor, const InputPointType &point) const
 
virtual OutputVectorPixelType TransformVector (const InputVectorPixelType &) const
 
virtual OutputVectorPixelType TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const
 
virtual OutputVectorType TransformVector (const InputVectorType &vector, const InputPointType &point) const
 
virtual OutputVnlVectorType TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const
 
virtual void UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0)
 
template< typename TImage > std std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > ApplyToImageMetadata (SmartPointer< TImage > image) const
 

Static Public Member Functions

static Pointer New ()
 

Static Public Attributes

static constexpr unsigned int SpaceDimension = VDimension
 
- Static Public Attributes inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
static constexpr unsigned int InputSpaceDimension
 
static constexpr unsigned int OutputSpaceDimension
 

Protected Member Functions

void ComputeD ()
 
virtual void ComputeDeformationContribution (const InputPointType &thisPoint, OutputPointType &result) const
 
virtual void ComputeG (const InputVectorType &landmarkVector, GMatrixType &gmatrix) const
 
void ComputeK ()
 
void ComputeL ()
 
void ComputeP ()
 
virtual const GMatrixType & ComputeReflexiveG (PointsIterator) const
 
void ComputeY ()
 
 KernelTransform ()
 
void PrintSelf (std::ostream &os, Indent indent) const override
 
void ReorganizeW ()
 
 ~KernelTransform () override=default
 
- Protected Member Functions inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
LightObject::Pointer InternalClone () const override
 
OutputDiffusionTensor3DType PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType &, const InverseJacobianPositionType &) const
 
 Transform ()=default
 
 Transform (NumberOfParametersType numberOfParameters)
 
 ~Transform () override=default
 

Protected Attributes

AMatrixType m_AMatrix {}
 
BMatrixType m_BVector {}
 
VectorSetPointer m_Displacements {}
 
DMatrixType m_DMatrix {}
 
GMatrixType m_GMatrix {}
 
IMatrixType m_I {}
 
KMatrixType m_KMatrix {}
 
LMatrixType m_LMatrix {}
 
PMatrixType m_PMatrix {}
 
PointSetPointer m_SourceLandmarks {}
 
double m_Stiffness {}
 
PointSetPointer m_TargetLandmarks {}
 
WMatrixType m_WMatrix {}
 
bool m_WMatrixComputed {}
 
YMatrixType m_YMatrix {}
 
- Protected Attributes inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
FixedParametersType m_FixedParameters
 
ParametersType m_Parameters
 

Additional Inherited Members

- Public Attributes inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
InverseJacobianPositionType &jacobian const
 
- Static Protected Member Functions inherited from itk::Transform< TParametersValueType, VDimension, VDimension >
static InverseTransformBasePointer InvertTransform (const TTransform &transform)
 

Member Typedef Documentation

◆ AMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::AMatrixType = vnl_matrix_fixed<TParametersValueType, VDimension, VDimension>

'A' matrix type alias. Rotational part of the Affine component

Definition at line 275 of file itkKernelTransform.h.

◆ BMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::BMatrixType = vnl_vector_fixed<TParametersValueType, VDimension>

'B' matrix type alias. Translational part of the Affine component

Definition at line 278 of file itkKernelTransform.h.

◆ ColumnMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::ColumnMatrixType = vnl_matrix_fixed<TParametersValueType, VDimension, 1>

Column matrix type alias.

Definition at line 284 of file itkKernelTransform.h.

◆ ConstPointer

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::ConstPointer = SmartPointer<const Self>

Definition at line 70 of file itkKernelTransform.h.

◆ DMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::DMatrixType = vnl_matrix<TParametersValueType>

'D' matrix type alias. Deformation component

Definition at line 272 of file itkKernelTransform.h.

◆ GMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::GMatrixType = vnl_matrix_fixed<TParametersValueType, VDimension, VDimension>

'G' matrix type alias.

Definition at line 254 of file itkKernelTransform.h.

◆ IMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::IMatrixType = vnl_matrix_fixed<TParametersValueType, VDimension, VDimension>

'I' (identity) matrix type alias.

Definition at line 181 of file itkKernelTransform.h.

◆ KMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::KMatrixType = vnl_matrix<TParametersValueType>

'K' matrix type alias.

Definition at line 260 of file itkKernelTransform.h.

◆ LMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::LMatrixType = vnl_matrix<TParametersValueType>

'L' matrix type alias.

Definition at line 257 of file itkKernelTransform.h.

◆ PMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PMatrixType = vnl_matrix<TParametersValueType>

'P' matrix type alias.

Definition at line 263 of file itkKernelTransform.h.

◆ Pointer

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::Pointer = SmartPointer<Self>

Definition at line 69 of file itkKernelTransform.h.

◆ PointIdentifier

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointIdentifier = typename PointSetType::PointIdentifier

Definition at line 125 of file itkKernelTransform.h.

◆ PointsConstIterator

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointsConstIterator = typename PointSetType::PointsContainerConstIterator

Definition at line 124 of file itkKernelTransform.h.

◆ PointsContainer

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointsContainer = typename PointSetType::PointsContainer

Definition at line 122 of file itkKernelTransform.h.

◆ PointSetPointer

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointSetPointer = typename PointSetType::Pointer

Definition at line 121 of file itkKernelTransform.h.

◆ PointSetTraitsType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointSetTraitsType = DefaultStaticMeshTraits<TParametersValueType, VDimension, VDimension, TParametersValueType, TParametersValueType>

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

Definition at line 118 of file itkKernelTransform.h.

◆ PointSetType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointSetType = PointSet<InputPointType, VDimension, PointSetTraitsType>

Definition at line 119 of file itkKernelTransform.h.

◆ PointsIterator

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::PointsIterator = typename PointSetType::PointsContainerIterator

Definition at line 123 of file itkKernelTransform.h.

◆ RowMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::RowMatrixType = vnl_matrix_fixed<TParametersValueType, 1, VDimension>

Row matrix type alias.

Definition at line 281 of file itkKernelTransform.h.

◆ Self

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::Self = KernelTransform

Standard class type aliases.

Definition at line 67 of file itkKernelTransform.h.

◆ Superclass

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::Superclass = Transform<TParametersValueType, VDimension, VDimension>

Definition at line 68 of file itkKernelTransform.h.

◆ VectorSetPointer

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::VectorSetPointer = typename VectorSetType::Pointer

Definition at line 129 of file itkKernelTransform.h.

◆ VectorSetType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::VectorSetType = itk::VectorContainer<InputVectorType>

VectorSet type alias.

Definition at line 128 of file itkKernelTransform.h.

◆ WMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::WMatrixType = vnl_matrix<TParametersValueType>

'W' matrix type alias.

Definition at line 269 of file itkKernelTransform.h.

◆ YMatrixType

template<typename TParametersValueType , unsigned int VDimension>
using itk::KernelTransform< TParametersValueType, VDimension >::YMatrixType = vnl_matrix<TParametersValueType>

'Y' matrix type alias.

Definition at line 266 of file itkKernelTransform.h.

Constructor & Destructor Documentation

◆ KernelTransform()

template<typename TParametersValueType , unsigned int VDimension>
itk::KernelTransform< TParametersValueType, VDimension >::KernelTransform ( )
protected

◆ ~KernelTransform()

template<typename TParametersValueType , unsigned int VDimension>
itk::KernelTransform< TParametersValueType, VDimension >::~KernelTransform ( )
overrideprotecteddefault

Member Function Documentation

◆ ComputeD()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeD ( )
protected

Compute displacements \( q_i - p_i \).

◆ ComputeDeformationContribution()

template<typename TParametersValueType , unsigned int VDimension>
virtual void itk::KernelTransform< TParametersValueType, VDimension >::ComputeDeformationContribution ( const InputPointType &  thisPoint,
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::ThinPlateR2LogRSplineKernelTransform< TParametersValueType, VDimension >, itk::ThinPlateSplineKernelTransform< TParametersValueType, VDimension >, and itk::VolumeSplineKernelTransform< TParametersValueType, VDimension >.

◆ ComputeG()

template<typename TParametersValueType , unsigned int VDimension>
virtual void itk::KernelTransform< TParametersValueType, VDimension >::ComputeG ( const InputVectorType &  landmarkVector,
GMatrixType &  gmatrix 
) const
protectedvirtual

Compute G(x) This is essentially the kernel of the transform. By overriding this method, we can obtain (among others): Elastic body spline Thin plate spline Volume spline

Reimplemented in itk::ElasticBodySplineKernelTransform< TParametersValueType, VDimension >, itk::ElasticBodyReciprocalSplineKernelTransform< TParametersValueType, VDimension >, itk::ThinPlateR2LogRSplineKernelTransform< TParametersValueType, VDimension >, itk::ThinPlateSplineKernelTransform< TParametersValueType, VDimension >, and itk::VolumeSplineKernelTransform< TParametersValueType, VDimension >.

◆ ComputeJacobianWithRespectToParameters()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeJacobianWithRespectToParameters ( const InputPointType &  p,
JacobianType &  jacobian 
) const
overridevirtual

Compute the Jacobian Matrix of the transformation at one point

Implements itk::Transform< TParametersValueType, VDimension, VDimension >.

◆ ComputeJacobianWithRespectToPosition()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeJacobianWithRespectToPosition ( const InputPointType &  ,
JacobianPositionType &   
) const
inlineoverridevirtual

This provides the ability to get a local jacobian value in a dense/local transform, e.g. DisplacementFieldTransform. For such transforms it would be unclear what parameters would refer to. Generally, global transforms should return an identity jacobian since there is no change with respect to position.

Reimplemented from itk::Transform< TParametersValueType, VDimension, VDimension >.

Definition at line 188 of file itkKernelTransform.h.

References GetNameOfClass().

◆ ComputeK()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeK ( )
protected

Compute K matrix.

◆ ComputeL()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeL ( )
protected

Compute L matrix.

◆ ComputeP()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeP ( )
protected

Compute P matrix.

◆ ComputeReflexiveG()

template<typename TParametersValueType , unsigned int VDimension>
virtual const GMatrixType& itk::KernelTransform< TParametersValueType, VDimension >::ComputeReflexiveG ( PointsIterator  ) 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.

Warning
this method is not thread-safe. However this method is called only through ComputeWMatrix() that is itself normally called from a single thread during the initialization of the Transform.

◆ ComputeWMatrix()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeWMatrix ( )

Compute W matrix.

◆ ComputeY()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::ComputeY ( )
protected

Compute Y matrix.

◆ GetFixedParameters()

template<typename TParametersValueType , unsigned int VDimension>
const FixedParametersType& itk::KernelTransform< TParametersValueType, VDimension >::GetFixedParameters ( ) const
override

Get Transform Fixed Parameters - Gets the Target Landmarks

◆ GetModifiableDisplacements()

template<typename TParametersValueType , unsigned int VDimension>
virtual VectorSetType* itk::KernelTransform< TParametersValueType, VDimension >::GetModifiableDisplacements ( )
virtual

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

◆ GetModifiableSourceLandmarks()

template<typename TParametersValueType , unsigned int VDimension>
virtual PointSetType* itk::KernelTransform< TParametersValueType, VDimension >::GetModifiableSourceLandmarks ( )
virtual

Get/Set the source landmarks list, which we will denote \( p \).

◆ GetModifiableTargetLandmarks()

template<typename TParametersValueType , unsigned int VDimension>
virtual PointSetType* itk::KernelTransform< TParametersValueType, VDimension >::GetModifiableTargetLandmarks ( )
virtual

Get the target landmarks list, which we will denote \( q \).

◆ GetNameOfClass()

template<typename TParametersValueType , unsigned int VDimension>
const char* itk::KernelTransform< TParametersValueType, VDimension >::GetNameOfClass ( ) const
override
See also
LightObject::GetNameOfClass()

◆ GetParameters()

template<typename TParametersValueType , unsigned int VDimension>
const ParametersType& itk::KernelTransform< TParametersValueType, VDimension >::GetParameters ( ) const
override

Get the Transformation Parameters - Gets the Source Landmarks

◆ GetStiffness()

template<typename TParametersValueType , unsigned int VDimension>
virtual double itk::KernelTransform< TParametersValueType, VDimension >::GetStiffness ( ) const
virtual

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.

◆ GetTransformCategory()

template<typename TParametersValueType , unsigned int VDimension>
TransformCategoryEnum itk::KernelTransform< TParametersValueType, VDimension >::GetTransformCategory ( ) const
inlineoverride

This transform is not linear, because the transformation of a linear combination of points is not equal to the linear combination of the transformations of individual points

Definition at line 227 of file itkKernelTransform.h.

◆ New()

template<typename TParametersValueType , unsigned int VDimension>
static Pointer itk::KernelTransform< TParametersValueType, VDimension >::New ( )
static

New macro for creation of through a Smart Pointer

◆ PrintSelf()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::PrintSelf ( std::ostream &  os,
Indent  indent 
) const
overrideprotected

◆ ReorganizeW()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::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

◆ SetFixedParameters()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::SetFixedParameters ( const FixedParametersType &  )
overridevirtual

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

Implements itk::Transform< TParametersValueType, VDimension, VDimension >.

◆ SetParameters()

template<typename TParametersValueType , unsigned int VDimension>
void itk::KernelTransform< TParametersValueType, VDimension >::SetParameters ( const ParametersType &  )
overridevirtual

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

Implements itk::Transform< TParametersValueType, VDimension, VDimension >.

◆ SetSourceLandmarks()

template<typename TParametersValueType , unsigned int VDimension>
virtual void itk::KernelTransform< TParametersValueType, VDimension >::SetSourceLandmarks ( PointSetType *  )
virtual

Get/Set the source landmarks list, which we will denote \( p \).

◆ SetStiffness()

template<typename TParametersValueType , unsigned int VDimension>
virtual void itk::KernelTransform< TParametersValueType, VDimension >::SetStiffness ( double  _arg)
virtual

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.

◆ SetTargetLandmarks()

template<typename TParametersValueType , unsigned int VDimension>
virtual void itk::KernelTransform< TParametersValueType, VDimension >::SetTargetLandmarks ( PointSetType *  )
virtual

Get the target landmarks list, which we will denote \( q \).

◆ TransformCovariantVector()

template<typename TParametersValueType , unsigned int VDimension>
OutputCovariantVectorType itk::KernelTransform< TParametersValueType, VDimension >::TransformCovariantVector ( const InputCovariantVectorType &  ) const
inlineoverridevirtual

Method to transform a CovariantVector.

Reimplemented from itk::Transform< TParametersValueType, VDimension, VDimension >.

Definition at line 173 of file itkKernelTransform.h.

◆ TransformPoint()

template<typename TParametersValueType , unsigned int VDimension>
OutputPointType itk::KernelTransform< TParametersValueType, VDimension >::TransformPoint ( const InputPointType &  thisPoint) const
overridevirtual

Compute the position of point in the new space

Implements itk::Transform< TParametersValueType, VDimension, VDimension >.

◆ TransformVector() [1/2]

template<typename TParametersValueType , unsigned int VDimension>
OutputVectorType itk::KernelTransform< TParametersValueType, VDimension >::TransformVector ( const InputVectorType &  ) const
inlineoverridevirtual

Method to transform a vector.

Reimplemented from itk::Transform< TParametersValueType, VDimension, VDimension >.

Definition at line 158 of file itkKernelTransform.h.

◆ TransformVector() [2/2]

template<typename TParametersValueType , unsigned int VDimension>
OutputVnlVectorType itk::KernelTransform< TParametersValueType, VDimension >::TransformVector ( const InputVnlVectorType &  ) const
inlineoverridevirtual

Method to transform a vnl_vector.

Reimplemented from itk::Transform< TParametersValueType, VDimension, VDimension >.

Definition at line 165 of file itkKernelTransform.h.

◆ UpdateParameters()

template<typename TParametersValueType , unsigned int VDimension>
virtual void itk::KernelTransform< TParametersValueType, VDimension >::UpdateParameters ( ) const
virtual

Update the Parameters array from the landmarks coordinates.

Member Data Documentation

◆ m_AMatrix

template<typename TParametersValueType , unsigned int VDimension>
AMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_AMatrix {}
protected

Rotational/Shearing part of the Affine component of the Transformation

Definition at line 369 of file itkKernelTransform.h.

◆ m_BVector

template<typename TParametersValueType , unsigned int VDimension>
BMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_BVector {}
protected

Translational part of the Affine component of the Transformation

Definition at line 372 of file itkKernelTransform.h.

◆ m_Displacements

template<typename TParametersValueType , unsigned int VDimension>
VectorSetPointer itk::KernelTransform< TParametersValueType, VDimension >::m_Displacements {}
protected

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

Definition at line 344 of file itkKernelTransform.h.

◆ m_DMatrix

template<typename TParametersValueType , unsigned int VDimension>
DMatrixType itk::KernelTransform< TParametersValueType, VDimension >::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 366 of file itkKernelTransform.h.

◆ m_GMatrix

template<typename TParametersValueType , unsigned int VDimension>
GMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_GMatrix {}
mutableprotected

The G matrix. It is made mutable because m_GMatrix was made an ivar only to avoid copying the matrix at return time

Definition at line 377 of file itkKernelTransform.h.

◆ m_I

template<typename TParametersValueType , unsigned int VDimension>
IMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_I {}
protected

Identity matrix.

Definition at line 383 of file itkKernelTransform.h.

◆ m_KMatrix

template<typename TParametersValueType , unsigned int VDimension>
KMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_KMatrix {}
protected

The K matrix.

Definition at line 350 of file itkKernelTransform.h.

◆ m_LMatrix

template<typename TParametersValueType , unsigned int VDimension>
LMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_LMatrix {}
protected

The L matrix.

Definition at line 347 of file itkKernelTransform.h.

◆ m_PMatrix

template<typename TParametersValueType , unsigned int VDimension>
PMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_PMatrix {}
protected

The P matrix.

Definition at line 353 of file itkKernelTransform.h.

◆ m_SourceLandmarks

template<typename TParametersValueType , unsigned int VDimension>
PointSetPointer itk::KernelTransform< TParametersValueType, VDimension >::m_SourceLandmarks {}
protected

The list of source landmarks, denoted 'p'.

Definition at line 386 of file itkKernelTransform.h.

◆ m_Stiffness

template<typename TParametersValueType , unsigned int VDimension>
double itk::KernelTransform< TParametersValueType, VDimension >::m_Stiffness {}
protected

Stiffness parameter

Definition at line 340 of file itkKernelTransform.h.

◆ m_TargetLandmarks

template<typename TParametersValueType , unsigned int VDimension>
PointSetPointer itk::KernelTransform< TParametersValueType, VDimension >::m_TargetLandmarks {}
protected

The list of target landmarks, denoted 'q'.

Definition at line 389 of file itkKernelTransform.h.

◆ m_WMatrix

template<typename TParametersValueType , unsigned int VDimension>
WMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_WMatrix {}
protected

The W matrix.

Definition at line 359 of file itkKernelTransform.h.

◆ m_WMatrixComputed

template<typename TParametersValueType , unsigned int VDimension>
bool itk::KernelTransform< TParametersValueType, VDimension >::m_WMatrixComputed {}
protected

Has the W matrix been computed?

Definition at line 380 of file itkKernelTransform.h.

◆ m_YMatrix

template<typename TParametersValueType , unsigned int VDimension>
YMatrixType itk::KernelTransform< TParametersValueType, VDimension >::m_YMatrix {}
protected

The Y matrix.

Definition at line 356 of file itkKernelTransform.h.

◆ SpaceDimension

template<typename TParametersValueType , unsigned int VDimension>
constexpr unsigned int itk::KernelTransform< TParametersValueType, VDimension >::SpaceDimension = VDimension
staticconstexpr

Dimension of the domain space.

Definition at line 79 of file itkKernelTransform.h.

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