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itk::SparseKernelTransform

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#include <itkSparseKernelTransform.h>

Inherits from Transform< TScalarType, NDimensions, NDimensions >

Public Types

Name
typedef SparseKernelTransform Self
typedef Transform< TScalarType, NDimensions, NDimensions > Superclass
typedef SmartPointer< Self > Pointer
typedef SmartPointer< const Self > ConstPointer
typedef Superclass::ScalarType ScalarType
typedef Superclass::ParametersType ParametersType
typedef Superclass::JacobianType JacobianType
typedef Superclass::InputPointType InputPointType
typedef Superclass::OutputPointType OutputPointType
typedef Superclass::InputVectorType InputVectorType
typedef Superclass::OutputVectorType OutputVectorType
typedef DefaultStaticMeshTraits< TScalarType, NDimensions, NDimensions, TScalarType, TScalarType > PointSetTraitsType
typedef PointSet< InputPointType, NDimensions, PointSetTraitsType > PointSetType
typedef PointSetType::Pointer PointSetPointer
typedef PointSetType::PointsContainer PointsContainer
typedef PointSetType::PointsContainerIterator PointsIterator
typedef PointSetType::PointsContainerConstIterator PointsConstIterator
typedef itk::VectorContainer< unsigned long, InputVectorType > VectorSetType
typedef VectorSetType::Pointer VectorSetPointer
typedef Eigen::Matrix< TScalarType, NDimensions, NDimensions > IMatrixType
typedef Eigen::Triplet< TScalarType > TripletType
typedef Eigen::Matrix< TScalarType, NDimensions, NDimensions > GMatrixType
typedef Eigen::SparseMatrix< TScalarType > LMatrixType
typedef Eigen::SparseMatrix< TScalarType > KMatrixType
typedef Eigen::SparseMatrix< TScalarType > PMatrixType
typedef Eigen::Matrix< TScalarType, Eigen::Dynamic, Eigen::Dynamic > YMatrixType
typedef Eigen::Matrix< TScalarType, Eigen::Dynamic, Eigen::Dynamic > WMatrixType
typedef Eigen::Matrix< TScalarType, Eigen::Dynamic, Eigen::Dynamic > DMatrixType
typedef Eigen::Matrix< TScalarType, NDimensions, NDimensions > AMatrixType
typedef Eigen::Matrix< TScalarType, NDimensions, 1 > BMatrixType
typedef Eigen::Matrix< TScalarType, 1, NDimensions > RowMatrixType
typedef Eigen::Matrix< TScalarType, NDimensions, 1 > ColumnMatrixType

Public Functions

Name
itkTypeMacro(SparseKernelTransform , Transform )
itkNewMacro(Self )
itkStaticConstMacro(SpaceDimension , unsigned int , NDimensions )
itkGetObjectMacro(SourceLandmarks , PointSetType )
virtual void SetSourceLandmarks(PointSetType * )
itkGetObjectMacro(TargetLandmarks , PointSetType )
virtual void SetTargetLandmarks(PointSetType * )
itkGetObjectMacro(Displacements , VectorSetType )
void ComputeWMatrix(void ) const
virtual OutputPointType TransformPoint(const InputPointType & thisPoint) const
virtual void SetIdentity()
virtual void SetParameters(const ParametersType & )
virtual void SetFixedParameters(const ParametersType & )
virtual void UpdateParameters(void ) const
virtual const ParametersType & GetParameters(void ) const
virtual const ParametersType & GetFixedParameters(void ) const
virtual void ComputeJacobianWithRespectToParameters(const InputPointType & in, JacobianType & jacobian) const
virtual void SetStiffness(double stiffness)
itkGetMacro(Stiffness , double )

Protected Functions

Name
SparseKernelTransform()
virtual ~SparseKernelTransform()
void PrintSelf(std::ostream & os, Indent indent) const
virtual const GMatrixType & ComputeG(const InputVectorType & landmarkVector) const
virtual const GMatrixType & ComputeReflexiveG(PointsIterator ) const
virtual void ComputeDeformationContribution(const InputPointType & inputPoint, OutputPointType & result) const
void ComputeK() const
void ComputeL() const
void ComputeP() const
void ComputeY() const
void ComputeD() const
void ReorganizeW(void ) const

Public Attributes

Name
PointSetPointer m_SourceLandmarks
PointSetPointer m_TargetLandmarks

Protected Attributes

Name
double m_Stiffness
VectorSetPointer m_Displacements
LMatrixType m_LMatrix
LMatrixType m_LMatrixInverse
KMatrixType m_KMatrix
PMatrixType m_PMatrix
YMatrixType m_YMatrix
WMatrixType m_WMatrix
DMatrixType m_DMatrix
AMatrixType m_AMatrix
BMatrixType m_BVector
GMatrixType m_GMatrix
bool m_WMatrixComputed
bool m_LMatrixComputed
bool m_LInverseComputed
IMatrixType m_I

Detailed Description

template <class TScalarType ,
unsigned int NDimensions>
class itk::SparseKernelTransform;

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.

SparseKernelTransform: 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."

Public Types Documentation

typedef Self

typedef SparseKernelTransform itk::SparseKernelTransform< TScalarType, NDimensions >::Self;

Standard class typedefs.

typedef Superclass

typedef Transform<TScalarType, NDimensions, NDimensions > itk::SparseKernelTransform< TScalarType, NDimensions >::Superclass;

typedef Pointer

typedef SmartPointer<Self> itk::SparseKernelTransform< TScalarType, NDimensions >::Pointer;

typedef ConstPointer

typedef SmartPointer<const Self> itk::SparseKernelTransform< TScalarType, NDimensions >::ConstPointer;

typedef ScalarType

typedef Superclass::ScalarType itk::SparseKernelTransform< TScalarType, NDimensions >::ScalarType;

Scalar type.

typedef ParametersType

typedef Superclass::ParametersType itk::SparseKernelTransform< TScalarType, NDimensions >::ParametersType;

Parameters type.

typedef JacobianType

typedef Superclass::JacobianType itk::SparseKernelTransform< TScalarType, NDimensions >::JacobianType;

Jacobian type.

typedef InputPointType

typedef Superclass::InputPointType itk::SparseKernelTransform< TScalarType, NDimensions >::InputPointType;

Standard coordinate point type for this class.

typedef OutputPointType

typedef Superclass::OutputPointType itk::SparseKernelTransform< TScalarType, NDimensions >::OutputPointType;

typedef InputVectorType

typedef Superclass::InputVectorType itk::SparseKernelTransform< TScalarType, NDimensions >::InputVectorType;

Standard vector type for this class.

typedef OutputVectorType

typedef Superclass::OutputVectorType itk::SparseKernelTransform< TScalarType, NDimensions >::OutputVectorType;

typedef PointSetTraitsType

typedef DefaultStaticMeshTraits<TScalarType, NDimensions, NDimensions, TScalarType, TScalarType> itk::SparseKernelTransform< TScalarType, NDimensions >::PointSetTraitsType;

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

typedef PointSetType

typedef PointSet<InputPointType, NDimensions, PointSetTraitsType> itk::SparseKernelTransform< TScalarType, NDimensions >::PointSetType;

typedef PointSetPointer

typedef PointSetType::Pointer itk::SparseKernelTransform< TScalarType, NDimensions >::PointSetPointer;

typedef PointsContainer

typedef PointSetType::PointsContainer itk::SparseKernelTransform< TScalarType, NDimensions >::PointsContainer;

typedef PointsIterator

typedef PointSetType::PointsContainerIterator itk::SparseKernelTransform< TScalarType, NDimensions >::PointsIterator;

typedef PointsConstIterator

typedef PointSetType::PointsContainerConstIterator itk::SparseKernelTransform< TScalarType, NDimensions >::PointsConstIterator;

typedef VectorSetType

typedef itk::VectorContainer<unsigned long,InputVectorType> itk::SparseKernelTransform< TScalarType, NDimensions >::VectorSetType;

VectorSet typedef.

typedef VectorSetPointer

typedef VectorSetType::Pointer itk::SparseKernelTransform< TScalarType, NDimensions >::VectorSetPointer;

typedef IMatrixType

typedef Eigen::Matrix<TScalarType, NDimensions, NDimensions> itk::SparseKernelTransform< TScalarType, NDimensions >::IMatrixType;

'I' (identity) matrix typedef.

typedef TripletType

typedef Eigen::Triplet<TScalarType> itk::SparseKernelTransform< TScalarType, NDimensions >::TripletType;

triplets used to fill sparse matrices.

typedef GMatrixType

typedef Eigen::Matrix<TScalarType, NDimensions, NDimensions> itk::SparseKernelTransform< TScalarType, NDimensions >::GMatrixType;

'G' matrix typedef.

typedef LMatrixType

typedef Eigen::SparseMatrix<TScalarType> itk::SparseKernelTransform< TScalarType, NDimensions >::LMatrixType;

'L' matrix typedef.

typedef KMatrixType

typedef Eigen::SparseMatrix<TScalarType> itk::SparseKernelTransform< TScalarType, NDimensions >::KMatrixType;

'K' matrix typedef.

typedef PMatrixType

typedef Eigen::SparseMatrix<TScalarType> itk::SparseKernelTransform< TScalarType, NDimensions >::PMatrixType;

'P' matrix typedef.

typedef YMatrixType

typedef Eigen::Matrix<TScalarType, Eigen::Dynamic, Eigen::Dynamic> itk::SparseKernelTransform< TScalarType, NDimensions >::YMatrixType;

'Y' matrix typedef.

typedef WMatrixType

typedef Eigen::Matrix<TScalarType, Eigen::Dynamic, Eigen::Dynamic> itk::SparseKernelTransform< TScalarType, NDimensions >::WMatrixType;

'W' matrix typedef.

typedef DMatrixType

typedef Eigen::Matrix<TScalarType, Eigen::Dynamic, Eigen::Dynamic> itk::SparseKernelTransform< TScalarType, NDimensions >::DMatrixType;

'D' matrix typedef. Deformation component

typedef AMatrixType

typedef Eigen::Matrix<TScalarType, NDimensions, NDimensions> itk::SparseKernelTransform< TScalarType, NDimensions >::AMatrixType;

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

typedef BMatrixType

typedef Eigen::Matrix<TScalarType,NDimensions,1> itk::SparseKernelTransform< TScalarType, NDimensions >::BMatrixType;

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

typedef RowMatrixType

typedef Eigen::Matrix<TScalarType,1,NDimensions> itk::SparseKernelTransform< TScalarType, NDimensions >::RowMatrixType;

Row matrix typedef.

typedef ColumnMatrixType

typedef Eigen::Matrix<TScalarType,NDimensions,1> itk::SparseKernelTransform< TScalarType, NDimensions >::ColumnMatrixType;

Column matrix typedef.

Public Functions Documentation

function itkTypeMacro

itkTypeMacro(
    SparseKernelTransform ,
    Transform 
)

Run-time type information (and related methods).

function itkNewMacro

itkNewMacro(
    Self 
)

New macro for creation of through a Smart Pointer

function itkStaticConstMacro

itkStaticConstMacro(
    SpaceDimension ,
    unsigned int ,
    NDimensions 
)

Dimension of the domain space.

function itkGetObjectMacro

itkGetObjectMacro(
    SourceLandmarks ,
    PointSetType 
)

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

function SetSourceLandmarks

virtual void SetSourceLandmarks(
    PointSetType * 
)

Set the source landmarks list.

function itkGetObjectMacro

itkGetObjectMacro(
    TargetLandmarks ,
    PointSetType 
)

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

function SetTargetLandmarks

virtual void SetTargetLandmarks(
    PointSetType * 
)

Set the target landmarks list.

function itkGetObjectMacro

itkGetObjectMacro(
    Displacements ,
    VectorSetType 
)

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

function ComputeWMatrix

void ComputeWMatrix(
    void 
) const

Compute W matrix.

function TransformPoint

virtual OutputPointType TransformPoint(
    const InputPointType & thisPoint
) const

Compute L matrix inverse. Compute the position of point in the new space

function SetIdentity

virtual void SetIdentity()

Compute the Jacobian Matrix of the transformation at one point Set the Transformation Parameters to be an identity transform

function SetParameters

virtual void SetParameters(
    const ParametersType & 
)

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.

function SetFixedParameters

virtual void SetFixedParameters(
    const ParametersType & 
)

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

function UpdateParameters

virtual void UpdateParameters(
    void 
) const

Update the Parameters array from the landmarks corrdinates.

function GetParameters

virtual const ParametersType & GetParameters(
    void 
) const

Get the Transformation Parameters - Gets the Source Landmarks

function GetFixedParameters

virtual const ParametersType & GetFixedParameters(
    void 
) const

Get Transform Fixed Parameters - Gets the Target Landmarks

function ComputeJacobianWithRespectToParameters

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

Reimplemented by: itk::CompactlySupportedRBFSparseKernelTransform::ComputeJacobianWithRespectToParameters

function SetStiffness

inline virtual void SetStiffness(
    double stiffness
)

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.

function itkGetMacro

itkGetMacro(
    Stiffness ,
    double 
)

Protected Functions Documentation

function SparseKernelTransform

SparseKernelTransform()

function ~SparseKernelTransform

virtual ~SparseKernelTransform()

function PrintSelf

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

function ComputeG

virtual const GMatrixType & ComputeG(
    const InputVectorType & landmarkVector
) const

Reimplemented by: itk::CompactlySupportedRBFSparseKernelTransform::ComputeG

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

function ComputeReflexiveG

virtual const GMatrixType & ComputeReflexiveG(
    PointsIterator 
) const

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.

function ComputeDeformationContribution

virtual void ComputeDeformationContribution(
    const InputPointType & inputPoint,
    OutputPointType & result
) const

Reimplemented by: itk::CompactlySupportedRBFSparseKernelTransform::ComputeDeformationContribution

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

function ComputeK

void ComputeK() const

Compute K matrix.

function ComputeL

void ComputeL() const

Compute L matrix.

function ComputeP

void ComputeP() const

Compute P matrix.

function ComputeY

void ComputeY() const

Compute Y matrix.

function ComputeD

void ComputeD() const

Compute displacements \( q_i - p_i \).

function ReorganizeW

void ReorganizeW(
    void 
) const

Warning: This method release the memory of the W Matrix

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

Public Attributes Documentation

variable m_SourceLandmarks

PointSetPointer m_SourceLandmarks;

The list of source landmarks, denoted 'p'.

variable m_TargetLandmarks

PointSetPointer m_TargetLandmarks;

The list of target landmarks, denoted 'q'.

Protected Attributes Documentation

variable m_Stiffness

double m_Stiffness;

Stiffness parameter

variable m_Displacements

VectorSetPointer m_Displacements;

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

variable m_LMatrix

LMatrixType m_LMatrix;

The L matrix.

variable m_LMatrixInverse

LMatrixType m_LMatrixInverse;

The inverse of L, which we also cache.

variable m_KMatrix

KMatrixType m_KMatrix;

The K matrix.

variable m_PMatrix

PMatrixType m_PMatrix;

The P matrix.

variable m_YMatrix

YMatrixType m_YMatrix;

The Y matrix.

variable m_WMatrix

WMatrixType m_WMatrix;

The W matrix.

variable m_DMatrix

DMatrixType m_DMatrix;

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

variable m_AMatrix

AMatrixType m_AMatrix;

Rotatinoal/Shearing part of the Affine component of the Transformation

variable m_BVector

BMatrixType m_BVector;

Translational part of the Affine component of the Transformation

variable m_GMatrix

GMatrixType m_GMatrix;

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

variable m_WMatrixComputed

bool m_WMatrixComputed;

Has the W matrix been computed?

variable m_LMatrixComputed

bool m_LMatrixComputed;

Has the L matrix been computed?

variable m_LInverseComputed

bool m_LInverseComputed;

Has the L inverse matrix been computed?

variable m_I

IMatrixType m_I;

Identity matrix.


Updated on 2024-07-14 at 17:07:23 +0000