itk::AdvancedTransform

Transform maps points, vectors and covariant vectors from an input space to an output space. More...

#include <itkAdvancedTransform.h>

Inherits from Transform< TScalarType, 3, 3 >

Public Types

	Name
typedef AdvancedTransform	Self
typedef Transform< TScalarType, NInputDimensions, NOutputDimensions >	Superclass
typedef SmartPointer< Self >	Pointer
typedef SmartPointer< const Self >	ConstPointer
typedef Superclass::ScalarType	ScalarType
typedef Superclass::ParametersType	ParametersType
typedef Superclass::ParametersValueType	ParametersValueType
typedef Superclass::NumberOfParametersType	NumberOfParametersType
typedef Superclass::DerivativeType	DerivativeType
typedef Superclass::JacobianType	JacobianType
typedef Superclass::InputVectorType	InputVectorType
typedef Superclass::OutputVectorType	OutputVectorType
typedef Superclass ::InputCovariantVectorType	InputCovariantVectorType
typedef Superclass ::OutputCovariantVectorType	OutputCovariantVectorType
typedef Superclass::InputVnlVectorType	InputVnlVectorType
typedef Superclass::OutputVnlVectorType	OutputVnlVectorType
typedef Superclass::InputPointType	InputPointType
typedef Superclass::OutputPointType	OutputPointType
typedef Superclass::InverseTransformBaseType	InverseTransformBaseType
typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer
typedef Transform< TScalarType, NInputDimensions, NOutputDimensions >	TransformType
typedef TransformType::Pointer	TransformTypePointer
typedef TransformType::ConstPointer	TransformTypeConstPointer
typedef std::vector< unsigned long >	NonZeroJacobianIndicesType
typedef Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension >	SpatialJacobianType
typedef std::vector< SpatialJacobianType >	JacobianOfSpatialJacobianType
typedef FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension >	SpatialHessianType
typedef std::vector< SpatialHessianType >	JacobianOfSpatialHessianType
typedef SpatialJacobianType::InternalMatrixType	InternalMatrixType
typedef OutputCovariantVectorType	MovingImageGradientType
typedef MovingImageGradientType::ValueType	MovingImageGradientValueType

Public Functions

	Name
	itkTypeMacro(AdvancedTransform , Transform )
	itkStaticConstMacro(InputSpaceDimension , unsigned int , NInputDimensions )
	itkStaticConstMacro(OutputSpaceDimension , unsigned int , NOutputDimensions )
virtual NumberOfParametersType	GetNumberOfNonZeroJacobianIndices(void ) const
	itkGetConstMacro(HasNonZeroSpatialHessian , bool )
	itkGetConstMacro(HasNonZeroJacobianOfSpatialHessian , bool )
virtual void	GetJacobian(const InputPointType & ipp, JacobianType & j, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const =0
virtual void	EvaluateJacobianWithImageGradientProduct(const InputPointType & ipp, const MovingImageGradientType & movingImageGradient, DerivativeType & imageJacobian, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const
virtual void	GetSpatialJacobian(const InputPointType & ipp, SpatialJacobianType & sj) const =0
virtual void	ComputeJacobianWithRespectToParameters(const InputPointType & itkNotUsedp, JacobianType & itkNotUsedj) const
virtual void	ComputeJacobianWithRespectToPosition(const InputPointType & itkNotUsedp, JacobianType & itkNotUsedj) const
virtual void	GetSpatialHessian(const InputPointType & ipp, SpatialHessianType & sh) const =0
virtual void	GetJacobianOfSpatialJacobian(const InputPointType & ipp, JacobianOfSpatialJacobianType & jsj, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const =0
virtual void	GetJacobianOfSpatialJacobian(const InputPointType & ipp, SpatialJacobianType & sj, JacobianOfSpatialJacobianType & jsj, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const =0
virtual void	GetJacobianOfSpatialHessian(const InputPointType & ipp, JacobianOfSpatialHessianType & jsh, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const =0
virtual void	GetJacobianOfSpatialHessian(const InputPointType & ipp, SpatialHessianType & sh, JacobianOfSpatialHessianType & jsh, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const =0

Protected Functions

	Name
	AdvancedTransform()
	AdvancedTransform(NumberOfParametersType numberOfParameters)
virtual	~AdvancedTransform()

Protected Attributes

	Name
bool	m_HasNonZeroSpatialHessian
bool	m_HasNonZeroJacobianOfSpatialHessian

Detailed Description

template <class TScalarType ,
unsigned int NInputDimensions =3,
unsigned int NOutputDimensions =3>
class itk::AdvancedTransform;

Transform maps points, vectors and covariant vectors from an input space to an output space.

Par: Registration Framework Support

Typically a Transform class has several methods for setting its parameters. For use in the registration framework, the parameters must also be represented by an array of doubles to allow communication with generic optimizers. The Array of transformation parameters is set using the SetParameters() method.

This abstract class define the generic interface for a geometrical transformation from one space to another. The class provides methods for mapping points, vectors and covariant vectors from the input space to the output space.

Given that transformation are not necessarily invertible, this basic class does not provide the methods for back transformation. Back transform methods are implemented in derived classes where appropriate.

Another requirement of the registration framework is the computation of the Jacobian of the transform T. In general, an ImageToImageMetric requires the knowledge of this Jacobian in order to compute the metric derivatives. The Jacobian is a matrix whose element are the partial derivatives of the transformation with respect to the array of parameters mu that defines the transform, evaluated at a point p: dT/dmu(p).

If penalty terms are included in the registration, the transforms also need to implement other derivatives of T. Often, penalty terms are functions of the spatial derivatives of T. Therefore, e.g. the SpatialJacobian dT/dx and the SpatialHessian d^2T/dx_idx_j require implementation. The GetValueAndDerivative() requires the d/dmu of those terms. Therefore, we additionally define GetJacobianOfSpatialJacobian() and GetJacobianOfSpatialHessian().

Public Types Documentation

typedef Self

typedef AdvancedTransform itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::Self;

Standard class typedefs.

typedef Superclass

typedef Transform< TScalarType, NInputDimensions, NOutputDimensions > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::Superclass;

typedef Pointer

typedef SmartPointer< Self > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::Pointer;

typedef ConstPointer

typedef SmartPointer< const Self > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::ConstPointer;

typedef ScalarType

typedef Superclass::ScalarType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::ScalarType;

Typedefs from the Superclass.

typedef ParametersType

typedef Superclass::ParametersType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::ParametersType;

typedef ParametersValueType

typedef Superclass::ParametersValueType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::ParametersValueType;

typedef NumberOfParametersType

typedef Superclass::NumberOfParametersType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::NumberOfParametersType;

typedef DerivativeType

typedef Superclass::DerivativeType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::DerivativeType;

typedef JacobianType

typedef Superclass::JacobianType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::JacobianType;

typedef InputVectorType

typedef Superclass::InputVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InputVectorType;

typedef OutputVectorType

typedef Superclass::OutputVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::OutputVectorType;

typedef InputCovariantVectorType

typedef Superclass ::InputCovariantVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InputCovariantVectorType;

typedef OutputCovariantVectorType

typedef Superclass ::OutputCovariantVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::OutputCovariantVectorType;

typedef InputVnlVectorType

typedef Superclass::InputVnlVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InputVnlVectorType;

typedef OutputVnlVectorType

typedef Superclass::OutputVnlVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::OutputVnlVectorType;

typedef InputPointType

typedef Superclass::InputPointType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InputPointType;

typedef OutputPointType

typedef Superclass::OutputPointType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::OutputPointType;

typedef InverseTransformBaseType

typedef Superclass::InverseTransformBaseType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InverseTransformBaseType;

typedef InverseTransformBasePointer

typedef Superclass::InverseTransformBasePointer itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InverseTransformBasePointer;

typedef TransformType

typedef Transform< TScalarType, NInputDimensions, NOutputDimensions > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::TransformType;

Transform typedefs for the from Superclass.

typedef TransformTypePointer

typedef TransformType::Pointer itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::TransformTypePointer;

typedef TransformTypeConstPointer

typedef TransformType::ConstPointer itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::TransformTypeConstPointer;

typedef NonZeroJacobianIndicesType

typedef std::vector< unsigned long > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::NonZeroJacobianIndicesType;

Types for the (Spatial)Jacobian/Hessian. Using an itk::FixedArray instead of an std::vector gives a performance gain for the SpatialHessianType.

typedef SpatialJacobianType

typedef Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::SpatialJacobianType;

typedef JacobianOfSpatialJacobianType

typedef std::vector< SpatialJacobianType > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::JacobianOfSpatialJacobianType;

typedef SpatialHessianType

typedef FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::SpatialHessianType;

typedef JacobianOfSpatialHessianType

typedef std::vector< SpatialHessianType > itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::JacobianOfSpatialHessianType;

typedef InternalMatrixType

typedef SpatialJacobianType::InternalMatrixType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::InternalMatrixType;

typedef MovingImageGradientType

typedef OutputCovariantVectorType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::MovingImageGradientType;

Typedef for the moving image gradient type. This type is defined by the B-spline interpolator as typedef CovariantVector< RealType, ImageDimension > As we cannot access this type we simply re-construct it to be identical.

typedef MovingImageGradientValueType

typedef MovingImageGradientType::ValueType itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >::MovingImageGradientValueType;

Public Functions Documentation

function itkTypeMacro

itkTypeMacro(
    AdvancedTransform ,
    Transform 
)

New method for creating an object using a factory. Run-time type information (and related methods).

function itkStaticConstMacro

itkStaticConstMacro(
    InputSpaceDimension ,
    unsigned int ,
    NInputDimensions 
)

Dimension of the domain space.

function itkStaticConstMacro

itkStaticConstMacro(
    OutputSpaceDimension ,
    unsigned int ,
    NOutputDimensions 
)

function GetNumberOfNonZeroJacobianIndices

virtual NumberOfParametersType GetNumberOfNonZeroJacobianIndices(
    void 
) const

Get the number of nonzero Jacobian indices. By default all.

function itkGetConstMacro

itkGetConstMacro(
    HasNonZeroSpatialHessian ,
    bool 
)

Whether the advanced transform has nonzero matrices.

function itkGetConstMacro

itkGetConstMacro(
    HasNonZeroJacobianOfSpatialHessian ,
    bool 
)

function GetJacobian

virtual void GetJacobian(
    const InputPointType & ipp,
    JacobianType & j,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const =0

Reimplemented by: itk::KernelTransform2::GetJacobian

This returns a sparse version of the Jacobian of the transformation.

The Jacobian is expressed as a vector of partial derivatives of the transformation components with respect to the parameters $\mu$ that define the transformation $T$, evaluated at a point $p$.

$J=\left[ \begin{array}{cccc} \frac{\partial T_{1}}{\partial \mu_{1}}(p) & \frac{\partial T_{1}}{\partial \mu_{2}}(p) & \cdots & \frac{\partial T_{1}}{\partial \mu_{m}}(p) \\ \frac{\partial T_{2}}{\partial \mu_{1}}(p) & \frac{\partial T_{2}}{\partial \mu_{2}}(p) & \cdots & \frac{\partial T_{2}}{\partial \mu_{m}}(p) \\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial T_{d}}{\partial \mu_{1}}(p) & \frac{\partial T_{d}}{\partial \mu_{2}}(p) & \cdots & \frac{\partial T_{d}}{\partial \mu_{m}}(p) \end{array}\right],$ with $m$ the number of parameters, i.e. the size of $\mu$, and $d$ the dimension of the image.

function EvaluateJacobianWithImageGradientProduct

virtual void EvaluateJacobianWithImageGradientProduct(
    const InputPointType & ipp,
    const MovingImageGradientType & movingImageGradient,
    DerivativeType & imageJacobian,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const

Compute the inner product of the Jacobian with the moving image gradient. The Jacobian is (partially) constructed inside this function, but not returned.

function GetSpatialJacobian

virtual void GetSpatialJacobian(
    const InputPointType & ipp,
    SpatialJacobianType & sj
) const =0

Reimplemented by: itk::KernelTransform2::GetSpatialJacobian, itk::KernelTransform2::GetSpatialJacobian

Compute the spatial Jacobian of the transformation.

The spatial Jacobian is expressed as a vector of partial derivatives of the transformation components with respect to the spatial position $x$, evaluated at a point $p$.

$sJ=\left[ \begin{array}{cccc} \frac{\partial T_{1}}{\partial x_{1}}(p) & \frac{\partial T_{1}}{\partial x_{2}}(p) & \cdots & \frac{\partial T_{1}}{\partial x_{m}}(p) \\ \frac{\partial T_{2}}{\partial x_{1}}(p) & \frac{\partial T_{2}}{\partial x_{2}}(p) & \cdots & \frac{\partial T_{2}}{\partial x_{m}}(p) \\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial T_{d}}{\partial x_{1}}(p) & \frac{\partial T_{d}}{\partial x_{2}}(p) & \cdots & \frac{\partial T_{d}}{\partial x_{m}}(p) \end{array}\right],$ with $m$ the number of parameters, i.e. the size of $\mu$, and $d$ the dimension of the image.

function ComputeJacobianWithRespectToParameters

inline virtual void ComputeJacobianWithRespectToParameters(
    const InputPointType & itkNotUsedp,
    JacobianType & itkNotUsedj
) const

Override some pure virtual ITK4 functions.

function ComputeJacobianWithRespectToPosition

inline virtual void ComputeJacobianWithRespectToPosition(
    const InputPointType & itkNotUsedp,
    JacobianType & itkNotUsedj
) const

function GetSpatialHessian

virtual void GetSpatialHessian(
    const InputPointType & ipp,
    SpatialHessianType & sh
) const =0

Reimplemented by: itk::KernelTransform2::GetSpatialHessian, itk::KernelTransform2::GetSpatialHessian

Compute the spatial Hessian of the transformation.

The spatial Hessian is the vector of matrices of partial second order derivatives of the transformation components with respect to the spatial position $x$, evaluated at a point $p$.

$sH=\left[ \begin{array}{cc} \frac{\partial^2 T_{i}}{\partial x_{1} \partial x_{1}}(p) & \frac{\partial^2 T_{i}}{\partial x_{1} \partial x_{2}}(p) \\ \frac{\partial^2 T_{i}}{\partial x_{1} \partial x_{2}}(p) & \frac{\partial^2 T_{i}}{\partial x_{2} \partial x_{2}}(p) \\ \end{array}\right],$ with i the i-th component of the transformation.

function GetJacobianOfSpatialJacobian

virtual void GetJacobianOfSpatialJacobian(
    const InputPointType & ipp,
    JacobianOfSpatialJacobianType & jsj,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const =0

Reimplemented by: itk::KernelTransform2::GetJacobianOfSpatialJacobian

Compute the Jacobian of the spatial Jacobian of the transformation.

The Jacobian of the spatial Jacobian is the derivative of the spatial Jacobian to the transformation parameters $\mu$, evaluated at a point $p$.

function GetJacobianOfSpatialJacobian

virtual void GetJacobianOfSpatialJacobian(
    const InputPointType & ipp,
    SpatialJacobianType & sj,
    JacobianOfSpatialJacobianType & jsj,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const =0

Reimplemented by: itk::KernelTransform2::GetJacobianOfSpatialJacobian

Compute both the spatial Jacobian and the Jacobian of the spatial Jacobian of the transformation.

function GetJacobianOfSpatialHessian

virtual void GetJacobianOfSpatialHessian(
    const InputPointType & ipp,
    JacobianOfSpatialHessianType & jsh,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const =0

Reimplemented by: itk::KernelTransform2::GetJacobianOfSpatialHessian

Compute the Jacobian of the spatial Hessian of the transformation.

The Jacobian of the spatial Hessian is the derivative of the spatial Hessian to the transformation parameters $\mu$, evaluated at a point $p$.

function GetJacobianOfSpatialHessian

virtual void GetJacobianOfSpatialHessian(
    const InputPointType & ipp,
    SpatialHessianType & sh,
    JacobianOfSpatialHessianType & jsh,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const =0

Reimplemented by: itk::KernelTransform2::GetJacobianOfSpatialHessian

Compute both the spatial Hessian and the Jacobian of the spatial Hessian of the transformation.

Protected Functions Documentation

function AdvancedTransform

AdvancedTransform()

function AdvancedTransform

AdvancedTransform(
    NumberOfParametersType numberOfParameters
)

function ~AdvancedTransform

inline virtual ~AdvancedTransform()

Protected Attributes Documentation

variable m_HasNonZeroSpatialHessian

bool m_HasNonZeroSpatialHessian;

variable m_HasNonZeroJacobianOfSpatialHessian

bool m_HasNonZeroJacobianOfSpatialHessian;

Updated on 2022-07-23 at 16:40:05 -0600