ITK  5.2.0
Insight Toolkit
Public Types | Public Member Functions | Static Public Attributes | List of all members
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions > Class Template Referenceabstract

#include <itkTransform.h>

+ Inheritance diagram for itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >:
+ Collaboration diagram for itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >:

Public Types

using ConstPointer = SmartPointer< const Self >
 
using DerivativeType = Array< ParametersValueType >
 
using DirectionChangeMatrix = Matrix< double, Self::OutputSpaceDimension, Self::InputSpaceDimension >
 
using FixedParametersType = typename Superclass::FixedParametersType
 
using FixedParametersValueType = typename Superclass::FixedParametersValueType
 
using InputCovariantVectorType = CovariantVector< TParametersValueType, NInputDimensions >
 
using InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >
 
using InputDirectionMatrix = Matrix< double, Self::InputSpaceDimension, Self::InputSpaceDimension >
 
using InputPointType = Point< TParametersValueType, NInputDimensions >
 
using InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, NInputDimensions >
 
using InputVectorPixelType = VariableLengthVector< TParametersValueType >
 
using InputVectorType = Vector< TParametersValueType, NInputDimensions >
 
using InputVnlVectorType = vnl_vector_fixed< TParametersValueType, NInputDimensions >
 
using InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, NInputDimensions, NOutputDimensions >
 
using InverseTransformBasePointer = typename InverseTransformBaseType::Pointer
 
using InverseTransformBaseType = Transform< TParametersValueType, NOutputDimensions, NInputDimensions >
 
using JacobianPositionType = vnl_matrix_fixed< ParametersValueType, NOutputDimensions, NInputDimensions >
 
using JacobianType = Array2D< ParametersValueType >
 
using MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension >
 
using NumberOfParametersType = typename Superclass::NumberOfParametersType
 
using OutputCovariantVectorType = CovariantVector< TParametersValueType, NOutputDimensions >
 
using OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >
 
using OutputDirectionMatrix = Matrix< double, Self::OutputSpaceDimension, Self::OutputSpaceDimension >
 
using OutputPointType = Point< TParametersValueType, NOutputDimensions >
 
using OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, NOutputDimensions >
 
using OutputVectorPixelType = VariableLengthVector< TParametersValueType >
 
using OutputVectorType = Vector< TParametersValueType, NOutputDimensions >
 
using OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, NOutputDimensions >
 
using ParametersType = typename Superclass::ParametersType
 
using ParametersValueType = typename Superclass::ParametersValueType
 
using Pointer = SmartPointer< Self >
 
using ScalarType = ParametersValueType
 
using Self = Transform
 
using Superclass = TransformBaseTemplate< TParametersValueType >
 
using TransformCategoryEnum = typename Superclass::TransformCategoryEnum
 
- Public Types inherited from itk::TransformBaseTemplate< TParametersValueType >
using ConstPointer = SmartPointer< const Self >
 
using FixedParametersType = OptimizerParameters< FixedParametersValueType >
 
using FixedParametersValueType = double
 
using NumberOfParametersType = IdentifierType
 
using ParametersType = OptimizerParameters< ParametersValueType >
 
using ParametersValueType = TParametersValueType
 
using Pointer = SmartPointer< Self >
 
using Self = TransformBaseTemplate
 
using Superclass = Object
 
using TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory
 
- Public Types inherited from itk::Object
using ConstPointer = SmartPointer< const Self >
 
using Pointer = SmartPointer< Self >
 
using Self = Object
 
using Superclass = LightObject
 
- Public Types inherited from itk::LightObject
using ConstPointer = SmartPointer< const Self >
 
using Pointer = SmartPointer< Self >
 
using Self = LightObject
 

Public Member Functions

void CopyInFixedParameters (const FixedParametersValueType *const begin, const FixedParametersValueType *const end) override
 
void CopyInParameters (const ParametersValueType *const begin, const ParametersValueType *const end) override
 
const FixedParametersTypeGetFixedParameters () const override
 
unsigned int GetInputSpaceDimension () const override
 
bool GetInverse (Self *) const
 
virtual InverseTransformBasePointer GetInverseTransform () const
 
virtual const char * GetNameOfClass () const
 
virtual NumberOfParametersType GetNumberOfFixedParameters () const
 
virtual NumberOfParametersType GetNumberOfLocalParameters () const
 
NumberOfParametersType GetNumberOfParameters () const override
 
unsigned int GetOutputSpaceDimension () const override
 
const ParametersTypeGetParameters () const override
 
TransformCategoryEnum GetTransformCategory () const override
 
std::string GetTransformTypeAsString () const override
 
virtual bool IsLinear () const
 
 itkCloneMacro (Self)
 
void SetFixedParameters (const FixedParametersType &) override=0
 
void SetParameters (const ParametersType &) override=0
 
void SetParametersByValue (const ParametersType &p) override
 
virtual OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &) const
 
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 &tensor, const InputPointType &point) const
 
virtual OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &) const
 
virtual OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &tensor, const InputPointType &point) const
 
virtual OutputPointType TransformPoint (const InputPointType &) const =0
 
virtual OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const
 
virtual OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &tensor, const InputPointType &point) const
 
virtual OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const
 
virtual OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &tensor, 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 &) const
 
virtual OutputVectorType TransformVector (const InputVectorType &vector, const InputPointType &point) const
 
virtual OutputVnlVectorType TransformVector (const InputVnlVectorType &) const
 
virtual OutputVnlVectorType TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const
 
virtual void UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0)
 
- Public Member Functions inherited from itk::TransformBaseTemplate< TParametersValueType >
virtual void CopyInFixedParameters (const FixedParametersValueType *const begin, const FixedParametersValueType *const end)=0
 
virtual void CopyInParameters (const ParametersValueType *const begin, const ParametersValueType *const end)=0
 
virtual void SetFixedParameters (const FixedParametersType &)=0
 
virtual void SetParameters (const ParametersType &)=0
 
virtual void SetParametersByValue (const ParametersType &p)=0
 
- Public Member Functions inherited from itk::Object
unsigned long AddObserver (const EventObject &event, Command *)
 
unsigned long AddObserver (const EventObject &event, Command *) const
 
unsigned long AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const
 
LightObject::Pointer CreateAnother () const override
 
virtual void DebugOff () const
 
virtual void DebugOn () const
 
CommandGetCommand (unsigned long tag)
 
bool GetDebug () const
 
MetaDataDictionaryGetMetaDataDictionary ()
 
const MetaDataDictionaryGetMetaDataDictionary () const
 
virtual ModifiedTimeType GetMTime () const
 
virtual const TimeStampGetTimeStamp () const
 
bool HasObserver (const EventObject &event) const
 
void InvokeEvent (const EventObject &)
 
void InvokeEvent (const EventObject &) const
 
virtual void Modified () const
 
void Register () const override
 
void RemoveAllObservers ()
 
void RemoveObserver (unsigned long tag)
 
void SetDebug (bool debugFlag) const
 
void SetReferenceCount (int) override
 
void UnRegister () const noexcept override
 
void SetMetaDataDictionary (const MetaDataDictionary &rhs)
 
void SetMetaDataDictionary (MetaDataDictionary &&rrhs)
 
virtual void SetObjectName (std::string _arg)
 
virtual const std::string & GetObjectName () const
 
- Public Member Functions inherited from itk::LightObject
virtual void Delete ()
 
virtual int GetReferenceCount () const
 
 itkCloneMacro (Self)
 
void Print (std::ostream &os, Indent indent=0) const
 

Static Public Attributes

static constexpr unsigned int InputSpaceDimension = NInputDimensions
 
static constexpr unsigned int OutputSpaceDimension = NOutputDimensions
 
ParametersType m_Parameters
 
FixedParametersType m_FixedParameters
 
DirectionChangeMatrix m_DirectionChange
 
virtual void ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const =0
 
virtual void ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const
 
virtual void ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianPositionType &) const
 
 itkLegacyMacro (virtual void ComputeJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const)
 
virtual void ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, InverseJacobianPositionType &jacobian) const
 
 itkLegacyMacro (virtual void ComputeInverseJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const)
 
LightObject::Pointer InternalClone () const override
 
 Transform ()
 
 Transform (NumberOfParametersType NumberOfParameters)
 
 ~Transform () override=default
 
OutputDiffusionTensor3DType PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType &, const InverseJacobianPositionType &) const
 
template<typename TType >
static std::string GetTransformTypeAsString (TType *)
 
static std::string GetTransformTypeAsString (float *)
 
static std::string GetTransformTypeAsString (double *)
 

Additional Inherited Members

- Static Public Member Functions inherited from itk::Object
static bool GetGlobalWarningDisplay ()
 
static void GlobalWarningDisplayOff ()
 
static void GlobalWarningDisplayOn ()
 
static Pointer New ()
 
static void SetGlobalWarningDisplay (bool flag)
 
- Static Public Member Functions inherited from itk::LightObject
static void BreakOnError ()
 
static Pointer New ()
 
- Protected Member Functions inherited from itk::TransformBaseTemplate< TParametersValueType >
 TransformBaseTemplate ()=default
 
 ~TransformBaseTemplate () override=default
 
- Protected Member Functions inherited from itk::Object
 Object ()
 
 ~Object () override
 
void PrintSelf (std::ostream &os, Indent indent) const override
 
bool PrintObservers (std::ostream &os, Indent indent) const
 
virtual void SetTimeStamp (const TimeStamp &time)
 
- Protected Member Functions inherited from itk::LightObject
 LightObject ()
 
virtual void PrintHeader (std::ostream &os, Indent indent) const
 
virtual void PrintTrailer (std::ostream &os, Indent indent) const
 
virtual ~LightObject ()
 
- Protected Attributes inherited from itk::LightObject
std::atomic< int > m_ReferenceCount
 

Detailed Description

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
class itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >

Transform points and vectors from an input space to an output space.

This abstract class defines the generic interface for a geometric 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 transformations 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.

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.

Another requirement of the registration framework is the computation of the transform Jacobian. In general, an ImageToImageMetric requires the knowledge of the Jacobian in order to compute the metric derivatives. The Jacobian is a matrix whose element are the partial derivatives of the output point with respect to the array of parameters that defines the transform.

Subclasses must provide implementations for:
virtual OutputPointType TransformPoint(const InputPointType &) const
virtual OutputVectorType TransformVector(const InputVectorType &) const
virtual OutputVnlVectorType TransformVector(const InputVnlVectorType &) const
virtual OutputCovariantVectorType TransformCovariantVector(const InputCovariantVectorType &) const
virtual void SetParameters(const ParametersType &)
virtual void SetFixedParameters(const FixedParametersType &)
virtual void ComputeJacobianWithRespectToParameters( const InputPointType &, JacobianType &) const
virtual void ComputeJacobianWithRespectToPosition( const InputPointType & x, JacobianPositionType &jacobian ) const;

Since TranformVector and TransformCovariantVector have multiple overloaded methods from the base class, subclasses must specify:
using Superclass::TransformVector;
using Superclass::TransformCovariantVector;

Definition at line 82 of file itkTransform.h.

Member Typedef Documentation

◆ ConstPointer

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ConstPointer = SmartPointer<const Self>

Definition at line 92 of file itkTransform.h.

◆ DerivativeType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::DerivativeType = Array<ParametersValueType>

Definition at line 123 of file itkTransform.h.

◆ DirectionChangeMatrix

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::DirectionChangeMatrix = Matrix<double, Self::OutputSpaceDimension, Self::InputSpaceDimension>

Definition at line 172 of file itkTransform.h.

◆ FixedParametersType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::FixedParametersType = typename Superclass::FixedParametersType

Type of the input parameters.

Definition at line 119 of file itkTransform.h.

◆ FixedParametersValueType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::FixedParametersValueType = typename Superclass::FixedParametersValueType

Definition at line 120 of file itkTransform.h.

◆ InputCovariantVectorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputCovariantVectorType = CovariantVector<TParametersValueType, NInputDimensions>

Standard covariant vector type for this class

Definition at line 151 of file itkTransform.h.

◆ InputDiffusionTensor3DType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputDiffusionTensor3DType = DiffusionTensor3D<TParametersValueType>

Definition at line 147 of file itkTransform.h.

◆ InputDirectionMatrix

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputDirectionMatrix = Matrix<double, Self::InputSpaceDimension, Self::InputSpaceDimension>

Definition at line 171 of file itkTransform.h.

◆ InputPointType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputPointType = Point<TParametersValueType, NInputDimensions>

Standard coordinate point type for this class

Definition at line 159 of file itkTransform.h.

◆ InputSymmetricSecondRankTensorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor<TParametersValueType, NInputDimensions>

Definition at line 143 of file itkTransform.h.

◆ InputVectorPixelType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputVectorPixelType = VariableLengthVector<TParametersValueType>

Standard variable length vector type for this class this provides an interface for the VectorImage class

Definition at line 139 of file itkTransform.h.

◆ InputVectorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputVectorType = Vector<TParametersValueType, NInputDimensions>

Standard vector type for this class.

Definition at line 134 of file itkTransform.h.

◆ InputVnlVectorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputVnlVectorType = vnl_vector_fixed<TParametersValueType, NInputDimensions>

Standard vnl_vector type for this class.

Definition at line 155 of file itkTransform.h.

◆ InverseJacobianPositionType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InverseJacobianPositionType = vnl_matrix_fixed<ParametersValueType, NInputDimensions, NOutputDimensions>

Definition at line 131 of file itkTransform.h.

◆ InverseTransformBasePointer

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

Definition at line 166 of file itkTransform.h.

◆ InverseTransformBaseType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InverseTransformBaseType = Transform<TParametersValueType, NOutputDimensions, NInputDimensions>

Base inverse transform type. This type should not be changed to the concrete inverse transform type or inheritance would be lost.

Definition at line 164 of file itkTransform.h.

◆ JacobianPositionType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::JacobianPositionType = vnl_matrix_fixed<ParametersValueType, NOutputDimensions, NInputDimensions>

Definition at line 130 of file itkTransform.h.

◆ JacobianType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::JacobianType = Array2D<ParametersValueType>

Type of the Jacobian matrix.

Definition at line 129 of file itkTransform.h.

◆ MatrixType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::MatrixType = Matrix<TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension>

Definition at line 168 of file itkTransform.h.

◆ NumberOfParametersType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::NumberOfParametersType = typename Superclass::NumberOfParametersType

Definition at line 174 of file itkTransform.h.

◆ OutputCovariantVectorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputCovariantVectorType = CovariantVector<TParametersValueType, NOutputDimensions>

Definition at line 152 of file itkTransform.h.

◆ OutputDiffusionTensor3DType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputDiffusionTensor3DType = DiffusionTensor3D<TParametersValueType>

Definition at line 148 of file itkTransform.h.

◆ OutputDirectionMatrix

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputDirectionMatrix = Matrix<double, Self::OutputSpaceDimension, Self::OutputSpaceDimension>

Definition at line 170 of file itkTransform.h.

◆ OutputPointType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputPointType = Point<TParametersValueType, NOutputDimensions>

Definition at line 160 of file itkTransform.h.

◆ OutputSymmetricSecondRankTensorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor<TParametersValueType, NOutputDimensions>

Definition at line 144 of file itkTransform.h.

◆ OutputVectorPixelType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputVectorPixelType = VariableLengthVector<TParametersValueType>

Definition at line 140 of file itkTransform.h.

◆ OutputVectorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputVectorType = Vector<TParametersValueType, NOutputDimensions>

Definition at line 135 of file itkTransform.h.

◆ OutputVnlVectorType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputVnlVectorType = vnl_vector_fixed<TParametersValueType, NOutputDimensions>

Definition at line 156 of file itkTransform.h.

◆ ParametersType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ParametersType = typename Superclass::ParametersType

Definition at line 121 of file itkTransform.h.

◆ ParametersValueType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ParametersValueType = typename Superclass::ParametersValueType

Definition at line 122 of file itkTransform.h.

◆ Pointer

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::Pointer = SmartPointer<Self>

Definition at line 91 of file itkTransform.h.

◆ ScalarType

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ScalarType = ParametersValueType

Type of the scalar representing coordinate and vector elements.

Definition at line 126 of file itkTransform.h.

◆ Self

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::Self = Transform

Standard class type aliases.

Definition at line 89 of file itkTransform.h.

◆ Superclass

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::Superclass = TransformBaseTemplate<TParametersValueType>

Definition at line 90 of file itkTransform.h.

◆ TransformCategoryEnum

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
using itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformCategoryEnum = typename Superclass::TransformCategoryEnum

Definition at line 455 of file itkTransform.h.

Constructor & Destructor Documentation

◆ Transform() [1/2]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::Transform ( )
protected

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

◆ Transform() [2/2]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::Transform ( NumberOfParametersType  NumberOfParameters)
protected

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

◆ ~Transform()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::~Transform ( )
overrideprotecteddefault

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Member Function Documentation

◆ ComputeInverseJacobianWithRespectToPosition()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ComputeInverseJacobianWithRespectToPosition ( const InputPointType x,
InverseJacobianPositionType jacobian 
) const
virtual

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 in itk::MatrixOffsetTransformBase< TParametersValueType, 2, 2 >, itk::MatrixOffsetTransformBase< TParametersValueType, 3, 3 >, and itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >.

◆ ComputeJacobianWithRespectToParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ComputeJacobianWithRespectToParameters ( const InputPointType ,
JacobianType  
) const
pure virtual

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Implemented in itk::MatrixOffsetTransformBase< TParametersValueType, 2, 2 >, itk::MatrixOffsetTransformBase< TParametersValueType, 3, 3 >, and itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >.

◆ ComputeJacobianWithRespectToParametersCachedTemporaries()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ComputeJacobianWithRespectToParametersCachedTemporaries ( const InputPointType p,
JacobianType jacobian,
JacobianType  
) const
inlinevirtual

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 512 of file itkTransform.h.

◆ ComputeJacobianWithRespectToPosition()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::ComputeJacobianWithRespectToPosition ( const InputPointType ,
JacobianPositionType  
) const
inlinevirtual

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 in itk::MatrixOffsetTransformBase< TParametersValueType, 2, 2 >, itk::MatrixOffsetTransformBase< TParametersValueType, 3, 3 >, and itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >.

Definition at line 527 of file itkTransform.h.

◆ CopyInFixedParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::CopyInFixedParameters ( const FixedParametersValueType *const  begin,
const FixedParametersValueType *const  end 
)
override

This function allow copying a range of values into the FixedParameters The range of values must conform to std::copy(begin, end, m_FixedParameters) requirements.

◆ CopyInParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::CopyInParameters ( const ParametersValueType *const  begin,
const ParametersValueType *const  end 
)
override

This function allow copying a range of values into the Parameters The range of values must conform to std::copy(begin, end, m_Parameters) requirements.

◆ GetFixedParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
const FixedParametersType& itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetFixedParameters ( ) const
inlineoverridevirtual

◆ GetInputSpaceDimension()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
unsigned int itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetInputSpaceDimension ( ) const
inlineoverridevirtual

Get the size of the input space

Implements itk::TransformBaseTemplate< TParametersValueType >.

Definition at line 106 of file itkTransform.h.

◆ GetInverse()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
bool itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetInverse ( Self ) const
inline

Returns a boolean indicating whether it is possible or not to compute the inverse of this current Transform. If it is possible, then the inverse of the transform is returned in the inverseTransform variable passed by the user. The inverse is recomputed if this current transform has been modified. This method is intended to be overriden as needed by derived classes.

Definition at line 434 of file itkTransform.h.

◆ GetInverseTransform()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual InverseTransformBasePointer itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetInverseTransform ( ) const
inlinevirtual

Return an inverse of this transform. If the inverse has not been implemented, return nullptr. The type of the inverse transform does not necessarily need to match the type of the forward transform. This allows one to return a numeric inverse transform instead.

Reimplemented in itk::MatrixOffsetTransformBase< TParametersValueType, NInputDimensions, NOutputDimensions >, itk::MatrixOffsetTransformBase< TParametersValueType, 2, 2 >, itk::MatrixOffsetTransformBase< TParametersValueType, 3, 3 >, itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >, itk::DisplacementFieldTransform< TParametersValueType, NDimensions >, itk::CompositeTransform< TParametersValueType, NDimensions >, itk::AffineTransform< TParametersValueType, NDimensions >, itk::Rigid2DTransform< TParametersValueType >, itk::IdentityTransform< TParametersValueType, NDimensions >, itk::ScaleTransform< TParametersValueType, NDimensions >, itk::TranslationTransform< TParametersValueType, NDimensions >, itk::Similarity2DTransform< TParametersValueType >, itk::CenteredSimilarity2DTransform< TParametersValueType >, itk::VelocityFieldTransform< TParametersValueType, NDimensions >, itk::CenteredRigid2DTransform< TParametersValueType >, itk::ConstantVelocityFieldTransform< TParametersValueType, NDimensions >, itk::ScalableAffineTransform< TParametersValueType, NDimensions >, itk::v3::Rigid3DTransform< TParametersValueType >, itk::CenteredEuler3DTransform< TParametersValueType >, itk::CenteredAffineTransform< TParametersValueType, NDimensions >, and itk::Euler2DTransform< TParametersValueType >.

Definition at line 446 of file itkTransform.h.

◆ GetNameOfClass()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual const char* itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetNameOfClass ( ) const
virtual

Run-time type information (and related methods).

Reimplemented from itk::TransformBaseTemplate< TParametersValueType >.

Reimplemented in itk::BSplineDeformableTransform< TParametersValueType, NDimensions, VSplineOrder >, itk::MatrixOffsetTransformBase< TParametersValueType, NInputDimensions, NOutputDimensions >, itk::MatrixOffsetTransformBase< TParametersValueType, 2, 2 >, itk::MatrixOffsetTransformBase< TParametersValueType, 3, 3 >, itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >, itk::BSplineTransform< TParametersValueType, NDimensions, VSplineOrder >, itk::AffineTransform< TParametersValueType, NDimensions >, itk::AzimuthElevationToCartesianTransform< TParametersValueType, NDimensions >, itk::CompositeTransform< TParametersValueType, NDimensions >, itk::DisplacementFieldTransform< TParametersValueType, NDimensions >, itk::TimeVaryingBSplineVelocityFieldTransform< TParametersValueType, NDimensions >, itk::MultiTransform< TParametersValueType, NDimensions, NSubDimensions >, itk::Similarity2DTransform< TParametersValueType >, itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >, itk::v3::Rigid3DTransform< TParametersValueType >, itk::KernelTransform< TParametersValueType, NDimensions >, itk::Rigid3DTransform< TParametersValueType >, itk::CenteredSimilarity2DTransform< TParametersValueType >, itk::ScaleSkewVersor3DTransform< TParametersValueType >, itk::BSplineExponentialDiffeomorphicTransform< TParametersValueType, NDimensions >, itk::GaussianExponentialDiffeomorphicTransform< TParametersValueType, NDimensions >, itk::ComposeScaleSkewVersor3DTransform< TParametersValueType >, itk::Rigid2DTransform< TParametersValueType >, itk::CenteredRigid2DTransform< TParametersValueType >, itk::TimeVaryingVelocityFieldTransform< TParametersValueType, NDimensions >, itk::IdentityTransform< TParametersValueType, NDimensions >, itk::BSplineSmoothingOnUpdateDisplacementFieldTransform< TParametersValueType, NDimensions >, itk::ScaleVersor3DTransform< TParametersValueType >, itk::QuaternionRigidTransform< TParametersValueType >, itk::Euler3DTransform< TParametersValueType >, itk::Similarity3DTransform< TParametersValueType >, itk::VersorRigid3DTransform< TParametersValueType >, itk::Rigid3DPerspectiveTransform< TParametersValueType >, itk::VersorTransform< TParametersValueType >, itk::GaussianSmoothingOnUpdateDisplacementFieldTransform< TParametersValueType, NDimensions >, itk::TranslationTransform< TParametersValueType, NDimensions >, itk::ScaleTransform< TParametersValueType, NDimensions >, itk::Euler2DTransform< TParametersValueType >, itk::ElasticBodySplineKernelTransform< TParametersValueType, NDimensions >, itk::ThinPlateR2LogRSplineKernelTransform< TParametersValueType, NDimensions >, itk::CenteredEuler3DTransform< TParametersValueType >, itk::ElasticBodyReciprocalSplineKernelTransform< TParametersValueType, NDimensions >, itk::GaussianSmoothingOnUpdateTimeVaryingVelocityFieldTransform< TParametersValueType, NDimensions >, itk::ScaleLogarithmicTransform< TParametersValueType, NDimensions >, itk::ThinPlateSplineKernelTransform< TParametersValueType, NDimensions >, itk::VolumeSplineKernelTransform< TParametersValueType, NDimensions >, itk::ConstantVelocityFieldTransform< TParametersValueType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TParametersValueType, NDimensions >, itk::VelocityFieldTransform< TParametersValueType, NDimensions >, itk::BSplineBaseTransform< TParametersValueType, NDimensions, VSplineOrder >, itk::CenteredAffineTransform< TParametersValueType, NDimensions >, and itk::ScalableAffineTransform< TParametersValueType, NDimensions >.

◆ GetNumberOfFixedParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual NumberOfParametersType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetNumberOfFixedParameters ( ) const
inlinevirtual

◆ GetNumberOfLocalParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual NumberOfParametersType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetNumberOfLocalParameters ( ) const
inlinevirtual

Return the number of local parameters that completely defines the Transform at an individual voxel. For transforms with local support, this will enable downstream computation of the jacobian wrt only the local support region. For instance, in the case of a deformation field, this will be equal to the number of image dimensions. If it is an affine transform, this will be the same as the GetNumberOfParameters().

Reimplemented in itk::DisplacementFieldTransform< TParametersValueType, NDimensions >, itk::CompositeTransform< TParametersValueType, NDimensions >, itk::BSplineBaseTransform< TParametersValueType, NDimensions, VSplineOrder >, itk::MultiTransform< TParametersValueType, NDimensions, NSubDimensions >, and itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >.

Definition at line 406 of file itkTransform.h.

◆ GetNumberOfParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
NumberOfParametersType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetNumberOfParameters ( ) const
inlineoverridevirtual

Return the number of parameters that completely define the Transfom

Implements itk::TransformBaseTemplate< TParametersValueType >.

Definition at line 413 of file itkTransform.h.

◆ GetOutputSpaceDimension()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
unsigned int itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetOutputSpaceDimension ( ) const
inlineoverridevirtual

Get the size of the output space

Implements itk::TransformBaseTemplate< TParametersValueType >.

Definition at line 113 of file itkTransform.h.

◆ GetParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
const ParametersType& itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetParameters ( ) const
inlineoverridevirtual

◆ GetTransformCategory()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
TransformCategoryEnum itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetTransformCategory ( ) const
inlineoverridevirtual

◆ GetTransformTypeAsString() [1/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
std::string itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetTransformTypeAsString ( ) const
overridevirtual

Generate a platform independent name

Implements itk::TransformBaseTemplate< TParametersValueType >.

◆ GetTransformTypeAsString() [2/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
static std::string itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetTransformTypeAsString ( double *  )
inlinestaticprivate

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 599 of file itkTransform.h.

◆ GetTransformTypeAsString() [3/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
static std::string itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetTransformTypeAsString ( float *  )
inlinestaticprivate

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 591 of file itkTransform.h.

◆ GetTransformTypeAsString() [4/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
template<typename TType >
static std::string itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::GetTransformTypeAsString ( TType *  )
inlinestaticprivate

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 583 of file itkTransform.h.

◆ InternalClone()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
LightObject::Pointer itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InternalClone ( ) const
overrideprotectedvirtual

Clone the current transform. This does a complete copy of the transform state to the new transform

Reimplemented from itk::LightObject.

◆ IsLinear()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual bool itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::IsLinear ( ) const
inlinevirtual

◆ itkCloneMacro()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::itkCloneMacro ( Self  )

define the Clone method

◆ itkLegacyMacro() [1/2]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::itkLegacyMacro ( virtual void ComputeInverseJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const  )

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

◆ itkLegacyMacro() [2/2]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::itkLegacyMacro ( virtual void ComputeJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const  )

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

◆ PreservationOfPrincipalDirectionDiffusionTensor3DReorientation()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
OutputDiffusionTensor3DType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::PreservationOfPrincipalDirectionDiffusionTensor3DReorientation ( const InputDiffusionTensor3DType ,
const InverseJacobianPositionType  
) const
protected

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

◆ SetFixedParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::SetFixedParameters ( const FixedParametersType )
overridepure virtual

◆ SetParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::SetParameters ( const ParametersType )
overridepure virtual

Set the transformation parameters and update internal transformation. SetParameters gives the transform the option to set it's parameters by keeping a reference to the parameters, or by copying. To force the transform to copy it's parameters call SetParametersByValue.

See also
SetParametersByValue

Implemented in itk::DisplacementFieldTransform< TParametersValueType, NDimensions >, itk::MatrixOffsetTransformBase< TParametersValueType, NInputDimensions, NOutputDimensions >, itk::MatrixOffsetTransformBase< TParametersValueType, 2, 2 >, itk::MatrixOffsetTransformBase< TParametersValueType, 3, 3 >, itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >, itk::Rigid2DTransform< TParametersValueType >, itk::Similarity2DTransform< TParametersValueType >, itk::ScaleSkewVersor3DTransform< TParametersValueType >, itk::ComposeScaleSkewVersor3DTransform< TParametersValueType >, itk::CenteredSimilarity2DTransform< TParametersValueType >, itk::QuaternionRigidTransform< TParametersValueType >, itk::Similarity3DTransform< TParametersValueType >, itk::CenteredRigid2DTransform< TParametersValueType >, itk::Rigid3DTransform< TParametersValueType >, itk::ScaleVersor3DTransform< TParametersValueType >, itk::TranslationTransform< TParametersValueType, NDimensions >, itk::VersorTransform< TParametersValueType >, itk::VersorRigid3DTransform< TParametersValueType >, itk::ScaleTransform< TParametersValueType, NDimensions >, itk::Euler3DTransform< TParametersValueType >, itk::CenteredEuler3DTransform< TParametersValueType >, itk::ScaleLogarithmicTransform< TParametersValueType, NDimensions >, itk::CenteredAffineTransform< TParametersValueType, NDimensions >, and itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >.

◆ SetParametersByValue()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::SetParametersByValue ( const ParametersType p)
inlineoverride

Set the transformation parameters and update internal transformation. This method forces the transform to copy the parameters. The default implementation is to call SetParameters. This call must be overridden if the transform normally implements SetParameters by keeping a reference to the parameters.

See also
SetParameters

Definition at line 349 of file itkTransform.h.

◆ TransformCovariantVector() [1/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputCovariantVectorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformCovariantVector ( const InputCovariantVectorType ) const
inlinevirtual

◆ TransformCovariantVector() [2/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputCovariantVectorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformCovariantVector ( const InputCovariantVectorType vector,
const InputPointType point 
) const
virtual

Method to transform a CovariantVector, using a point. Global transforms can ignore the point parameter. Local transforms (e.g. deformation field transform) must override and provide required behavior. By default, point is ignored and TransformCovariantVector(vector) is called

◆ TransformCovariantVector() [3/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformCovariantVector ( const InputVectorPixelType ) const
inlinevirtual

◆ TransformCovariantVector() [4/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformCovariantVector ( const InputVectorPixelType vector,
const InputPointType point 
) const
virtual

Method to transform a CovariantVector, using a point. Global transforms can ignore the point parameter. Local transforms (e.g. deformation field transform) must override and provide required behavior. By default, point is ignored and TransformCovariantVector(vector) is called

◆ TransformDiffusionTensor3D() [1/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputDiffusionTensor3DType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformDiffusionTensor3D ( const InputDiffusionTensor3DType ) const
inlinevirtual

◆ TransformDiffusionTensor3D() [2/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputDiffusionTensor3DType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformDiffusionTensor3D ( const InputDiffusionTensor3DType tensor,
const InputPointType point 
) const
virtual

Method to transform a diffusion tensor at a point. Global transforms can ignore the point parameter. Local transforms (e.g. deformation field transform) must override and provide required behavior. By default, point is ignored and TransformDiffusionTensor(tensor) is called

◆ TransformDiffusionTensor3D() [3/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformDiffusionTensor3D ( const InputVectorPixelType ) const
inlinevirtual

◆ TransformDiffusionTensor3D() [4/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformDiffusionTensor3D ( const InputVectorPixelType tensor,
const InputPointType point 
) const
virtual

◆ TransformPoint()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputPointType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformPoint ( const InputPointType ) const
pure virtual

◆ TransformSymmetricSecondRankTensor() [1/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputSymmetricSecondRankTensorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformSymmetricSecondRankTensor ( const InputSymmetricSecondRankTensorType ) const
inlinevirtual

◆ TransformSymmetricSecondRankTensor() [2/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputSymmetricSecondRankTensorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformSymmetricSecondRankTensor ( const InputSymmetricSecondRankTensorType tensor,
const InputPointType point 
) const
virtual

Method to transform a diffusion tensor at a point. Global transforms can ignore the point parameter. Local transforms (e.g. deformation field transform) must override and provide required behavior. By default, point is ignored and TransformSymmetricSecondRankTensor(tensor) is called

◆ TransformSymmetricSecondRankTensor() [3/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformSymmetricSecondRankTensor ( const InputVectorPixelType ) const
inlinevirtual

◆ TransformSymmetricSecondRankTensor() [4/4]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformSymmetricSecondRankTensor ( const InputVectorPixelType tensor,
const InputPointType point 
) const
virtual

Method to transform a diffusion tensor stored in a VectorImage, at a point. Global transforms can ignore the point parameter. Local transforms (e.g. deformation field transform) must override and provide required behavior. By default, point is ignored and TransformDiffusionTensor(tensor) is called

◆ TransformVector() [1/6]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformVector ( const InputVectorPixelType ) const
inlinevirtual

◆ TransformVector() [2/6]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorPixelType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformVector ( const InputVectorPixelType vector,
const InputPointType point 
) const
virtual

Method to transform a vector stored in a VectorImage, at a point. For global transforms, point is ignored and TransformVector( vector ) is called. Local transforms (e.g. deformation field transform) must override and provide required behavior.

◆ TransformVector() [3/6]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformVector ( const InputVectorType ) const
inlinevirtual

◆ TransformVector() [4/6]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVectorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformVector ( const InputVectorType vector,
const InputPointType point 
) const
virtual

Method to transform a vector at a given location. For global transforms, point is ignored and TransformVector( vector ) is called. Local transforms (e.g. deformation field transform) must override and provide required behavior.

◆ TransformVector() [5/6]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVnlVectorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformVector ( const InputVnlVectorType ) const
inlinevirtual

◆ TransformVector() [6/6]

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual OutputVnlVectorType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::TransformVector ( const InputVnlVectorType vector,
const InputPointType point 
) const
virtual

Method to transform a vnl_vector, at a point. For global transforms, point is ignored and TransformVector( vector ) is called. Local transforms (e.g. deformation field transform) must override and provide required behavior.

◆ UpdateTransformParameters()

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
virtual void itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::UpdateTransformParameters ( const DerivativeType update,
ParametersValueType  factor = 1.0 
)
virtual

Update the transform's parameters by the values in update.

Parameters
updatemust be of the same length as returned by GetNumberOfParameters(). Throw an exception otherwise.
factoris a scalar multiplier for each value in update. SetParameters is called at the end of this method, to allow the transform to perform any required operations on the updated parameters - typically a conversion to member variables for use in TransformPoint.

Member Data Documentation

◆ InputSpaceDimension

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
constexpr unsigned int itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::InputSpaceDimension = NInputDimensions
staticconstexpr

Dimension of the domain space.

Definition at line 98 of file itkTransform.h.

◆ m_DirectionChange

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
DirectionChangeMatrix itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::m_DirectionChange
mutableprotected

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 578 of file itkTransform.h.

◆ m_FixedParameters

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
FixedParametersType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::m_FixedParameters
mutableprotected

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 572 of file itkTransform.h.

◆ m_Parameters

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
ParametersType itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::m_Parameters
mutableprotected

Compute the Jacobian of the transformation

This method computes the Jacobian matrix of the transformation at a given input point. The rank of the Jacobian will also indicate if the transform is invertible at this point.

The Jacobian is be expressed as a matrix of partial derivatives of the output point components with respect to the parameters that defined the transform:

\[ J=\left[ \begin{array}{cccc} \frac{\partial x_{1}}{\partial p_{1}} & \frac{\partial x_{1}}{\partial p_{2}} & \cdots & \frac{\partial x_{1}}{\partial p_{m}}\\ \frac{\partial x_{2}}{\partial p_{1}} & \frac{\partial x_{2}}{\partial p_{2}} & \cdots & \frac{\partial x_{2}}{\partial p_{m}}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial x_{n}}{\partial p_{1}} & \frac{\partial x_{n}}{\partial p_{2}} & \cdots & \frac{\partial x_{n}}{\partial p_{m}} \end{array}\right] \]

This is also used for efficient computation of a point-local jacobian for dense transforms. jacobian is assumed to be thread-local variable, otherwise memory corruption will most likely occur during multi-threading. To avoid repetitive memory allocation, pass in 'jacobian' with its size already set.

Definition at line 571 of file itkTransform.h.

◆ OutputSpaceDimension

template<typename TParametersValueType, unsigned int NInputDimensions = 3, unsigned int NOutputDimensions = 3>
constexpr unsigned int itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >::OutputSpaceDimension = NOutputDimensions
staticconstexpr

Definition at line 99 of file itkTransform.h.


The documentation for this class was generated from the following file: