Detailed Description

template<typename TScalar = double, unsigned int NDimensions = 3>
class itk::AffineTransform< TScalar, NDimensions >

Affine transformation of a vector space (e.g. space coordinates)

This class allows the definition and manipulation of affine transformations of an n-dimensional affine space (and its associated vector space) onto itself. One common use is to define and manipulate Euclidean coordinate transformations in two and three dimensions, but other uses are possible as well.

An affine transformation is defined mathematically as a linear transformation plus a constant offset. If A is a constant n x n matrix and b is a constant n-vector, then y = Ax+b defines an affine transformation from the n-vector x to the n-vector y.

The difference between two points is a vector and transforms linearly, using the matrix only. That is, (y1-y2) = A*(x1-x2).

The AffineTransform class determines whether to transform an object as a point or a vector by examining its type. An object of type Point transforms as a point; an object of type Vector transforms as a vector.

One common use of affine transformations is to define coordinate conversions in two- and three-dimensional space. In this application, x is a two- or three-dimensional vector containing the "source" coordinates of a point, y is a vector containing the "target" coordinates, the matrix A defines the scaling and rotation of the coordinate systems from the source to the target, and b defines the translation of the origin from the source to the target. More generally, A can also define anisotropic scaling and shearing transformations. Any good textbook on computer graphics will discuss coordinate transformations in more detail. Several of the methods in this class are designed for this purpose and use the language appropriate to coordinate conversions.

Any two affine transformations may be composed and the result is another affine transformation. However, the order is important. Given two affine transformations T1 and T2, we will say that "precomposing T1 with T2" yields the transformation which applies T1 to the source, and then applies T2 to that result to obtain the target. Conversely, we will say that "postcomposing T1 with T2" yields the transformation which applies T2 to the source, and then applies T1 to that result to obtain the target. (Whether T1 or T2 comes first lexicographically depends on whether you choose to write mappings from right-to-left or vice versa; we avoid the whole problem by referring to the order of application rather than the textual order.)

There are two template parameters for this class:

ScalarT The type to be used for scalar numeric values. Either float or double.

NDimensions The number of dimensions of the vector space.

This class provides several methods for setting the matrix and vector defining the transform. To support the registration framework, the transform parameters can also be set as an Array<double> of size (NDimension + 1) * NDimension using method SetParameters(). The first (NDimension x NDimension) parameters defines the matrix in row-major order (where the column index varies the fastest). The last NDimension parameters defines the translation in each dimensions.

This class also supports the specification of a center of rotation (center) and a translation that is applied with respect to that centered rotation. By default the center of rotation is set to the origin.

Examples:: Filtering/ResampleImageFilter.cxx, Filtering/ResampleImageFilter2.cxx, Filtering/ResampleImageFilter3.cxx, Filtering/ResampleImageFilter4.cxx, Filtering/ResampleImageFilter7.cxx, Filtering/ResampleImageFilter8.cxx, IO/TransformReadWrite.cxx, RegistrationITKv3/DeformableRegistration15.cxx, RegistrationITKv3/ImageRegistration19.cxx, RegistrationITKv3/ImageRegistration20.cxx, RegistrationITKv3/ImageRegistration9.cxx, RegistrationITKv3/MultiResImageRegistration2.cxx, RegistrationITKv4/DeformableRegistration15.cxx, RegistrationITKv4/ImageRegistration19.cxx, RegistrationITKv4/ImageRegistration20.cxx, RegistrationITKv4/ImageRegistration9.cxx, and RegistrationITKv4/MultiResImageRegistration2.cxx.

Definition at line 104 of file itkAffineTransform.h.

Public Types
typedef Superclass::CenterType	CenterType

typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef Superclass::InverseMatrixType	InverseMatrixType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Superclass::InverseTransformBaseType	InverseTransformBaseType

typedef Superclass::JacobianType	JacobianType

typedef Superclass::MatrixType	MatrixType

typedef Superclass::OffsetType	OffsetType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef AffineTransform	Self

typedef MatrixOffsetTransformBase < TScalar, NDimensions, NDimensions >	Superclass

typedef Superclass::TranslationType	TranslationType

Public Types inherited from itk::MatrixOffsetTransformBase< TScalar, NDimensions, NDimensions >
typedef InputPointType	CenterType

typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::InputDiffusionTensor3DType	InputDiffusionTensor3DType

typedef Superclass::InputSymmetricSecondRankTensorType	InputSymmetricSecondRankTensorType

typedef CovariantVector < TScalar, InputDiffusionTensor3DType::Dimension >	InputTensorEigenVectorType

typedef Superclass::InputVectorPixelType	InputVectorPixelType

typedef Matrix< TScalar, itkGetStaticConstMacro(InputSpaceDimension), itkGetStaticConstMacro(OutputSpaceDimension)>	InverseMatrixType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Superclass::InverseTransformBaseType	InverseTransformBaseType

typedef Superclass::JacobianType	JacobianType

typedef OutputVectorType	OffsetType

typedef OffsetType::ValueType	OffsetValueType

typedef Superclass::OutputDiffusionTensor3DType	OutputDiffusionTensor3DType

typedef Superclass::OutputSymmetricSecondRankTensorType	OutputSymmetricSecondRankTensorType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef MatrixOffsetTransformBase	Self

typedef Transform< TScalar, NInputDimensions, NOutputDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

typedef OutputVectorType	TranslationType

typedef TranslationType::ValueType	TranslationValueType

typedef Vector< TScalar, itkGetStaticConstMacro(InputSpaceDimension)>	InputVectorType

typedef Vector< TScalar, itkGetStaticConstMacro(OutputSpaceDimension)>	OutputVectorType

typedef OutputVectorType::ValueType	OutputVectorValueType

typedef CovariantVector < TScalar, itkGetStaticConstMacro(InputSpaceDimension)>	InputCovariantVectorType

typedef CovariantVector < TScalar, itkGetStaticConstMacro(OutputSpaceDimension)>	OutputCovariantVectorType

typedef vnl_vector_fixed < TScalar, itkGetStaticConstMacro(InputSpaceDimension)>	InputVnlVectorType

typedef vnl_vector_fixed < TScalar, itkGetStaticConstMacro(OutputSpaceDimension)>	OutputVnlVectorType

typedef Point< TScalar, itkGetStaticConstMacro(InputSpaceDimension)>	InputPointType

typedef InputPointType::ValueType	InputPointValueType

typedef Point< TScalar, itkGetStaticConstMacro(OutputSpaceDimension)>	OutputPointType

typedef OutputPointType::ValueType	OutputPointValueType

typedef Matrix< TScalar, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	MatrixType

typedef MatrixType::ValueType	MatrixValueType

Public Types inherited from itk::Transform< TScalar, NInputDimensions, NOutputDimensions >
typedef SmartPointer< const Self >	ConstPointer

typedef Array < ParametersValueType >	DerivativeType

typedef Matrix< double, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	DirectionChangeMatrix

typedef CovariantVector < TScalar, NInputDimensions >	InputCovariantVectorType

typedef DiffusionTensor3D < TScalar >	InputDiffusionTensor3DType

typedef Matrix< double, itkGetStaticConstMacro(InputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	InputDirectionMatrix

typedef Point< TScalar, NInputDimensions >	InputPointType

typedef SymmetricSecondRankTensor < TScalar, NInputDimensions >	InputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalar >	InputVectorPixelType

typedef Vector< TScalar, NInputDimensions >	InputVectorType

typedef vnl_vector_fixed < TScalar, NInputDimensions >	InputVnlVectorType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Transform< TScalar, NOutputDimensions, NInputDimensions >	InverseTransformBaseType

typedef Array2D < ParametersValueType >	JacobianType

typedef Matrix< TScalar, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	MatrixType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef CovariantVector < TScalar, NOutputDimensions >	OutputCovariantVectorType

typedef DiffusionTensor3D < TScalar >	OutputDiffusionTensor3DType

typedef Matrix< double, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(OutputSpaceDimension)>	OutputDirectionMatrix

typedef Point< TScalar, NOutputDimensions >	OutputPointType

typedef SymmetricSecondRankTensor < TScalar, NOutputDimensions >	OutputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalar >	OutputVectorPixelType

typedef Vector< TScalar, NOutputDimensions >	OutputVectorType

typedef vnl_vector_fixed < TScalar, NOutputDimensions >	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TScalar	ScalarType

typedef Transform	Self

typedef TransformBaseTemplate < TScalar >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

Public Types inherited from itk::TransformBaseTemplate< TScalar >
typedef SmartPointer< const Self >	ConstPointer

typedef IdentifierType	NumberOfParametersType

typedef OptimizerParameters < ParametersValueType >	ParametersType

typedef TScalar	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TransformBaseTemplate	Self

typedef Object	Superclass

enum	TransformCategoryType { UnknownTransformCategory =0, Linear =1, BSpline =2, Spline =3, DisplacementField =4, VelocityField =5 }

Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

bool	GetInverse (Self *inverse) const

virtual InverseTransformBasePointer	GetInverseTransform () const

virtual const char *	GetNameOfClass () const

	itkLegacyMacro (InputPointType BackTransformPoint(const OutputPointType &point) const)

ScalarType	Metric (const Self *other) const

ScalarType	Metric (void) const

void	Rotate2D (TScalar angle, bool pre=0)

void	Rotate3D (const OutputVectorType &axis, TScalar angle, bool pre=0)

void	Scale (const OutputVectorType &factor, bool pre=0)

void	Scale (const TScalar &factor, bool pre=0)

void	Shear (int axis1, int axis2, TScalar coef, bool pre=0)

void	Translate (const OutputVectorType &offset, bool pre=0)


void	Rotate (int axis1, int axis2, TScalar angle, bool pre=0)


	itkLegacyMacro (InputPointType BackTransform(const OutputPointType &point) const)

	itkLegacyMacro (InputVectorType BackTransform(const OutputVectorType &vector) const)

	itkLegacyMacro (InputVnlVectorType BackTransform(const OutputVnlVectorType &vector) const)

	itkLegacyMacro (InputCovariantVectorType BackTransform(const OutputCovariantVectorType &vector) const)

Public Member Functions inherited from itk::MatrixOffsetTransformBase< TScalar, NDimensions, NDimensions >
void	Compose (const Self *other, bool pre=0)

virtual void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, JacobianType &jac) const

virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &x, JacobianType &j) const

virtual void	ComputeJacobianWithRespectToPosition (const InputPointType &x, JacobianType &jac) const

virtual ::itk::LightObject::Pointer	CreateAnother (void) const

const InputPointType &	GetCenter () const

virtual const ParametersType &	GetFixedParameters (void) const

virtual const MatrixType &	GetMatrix () const

const OutputVectorType &	GetOffset (void) const

const ParametersType &	GetParameters (void) const

virtual TransformCategoryType	GetTransformCategory () const

const OutputVectorType &	GetTranslation (void) const

virtual bool	IsLinear () const

virtual void	SetFixedParameters (const ParametersType &)

virtual void	SetIdentity (void)

void	SetParameters (const ParametersType &parameters)

OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector) const

OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &vector) const

OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor) const

OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &tensor) const

OutputPointType	TransformPoint (const InputPointType &point) const

OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &tensor) const

OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &tensor) const

OutputVectorType	TransformVector (const InputVectorType &vector) const

OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector) const

OutputVectorPixelType	TransformVector (const InputVectorPixelType &vector) const

virtual void	SetMatrix (const MatrixType &matrix)

void	SetOffset (const OutputVectorType &offset)

void	SetCenter (const InputPointType &center)

void	SetTranslation (const OutputVectorType &translation)

bool	GetInverse (Self *inverse) const

Public Member Functions inherited from itk::Transform< TScalar, NInputDimensions, NOutputDimensions >
virtual void	ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const

unsigned int	GetInputSpaceDimension (void) const

bool	GetInverse (Self *) const

virtual NumberOfParametersType	GetNumberOfLocalParameters (void) const

virtual NumberOfParametersType	GetNumberOfParameters (void) const

unsigned int	GetOutputSpaceDimension (void) const

virtual std::string	GetTransformTypeAsString () const

	itkCloneMacro (Self)

virtual void	SetParametersByValue (const ParametersType &p)

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &tensor, const InputPointType &point) const

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &tensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &tensor, const InputPointType &point) const

virtual OutputVectorType	TransformVector (const InputVectorType &vector, const InputPointType &point) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual void	UpdateTransformParameters (const DerivativeType &update, TScalar factor=1.0)

Public Member Functions inherited from itk::TransformBaseTemplate< TScalar >
virtual void	SetFixedParameters (const ParametersType &)=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

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary (void)

const MetaDataDictionary &	GetMetaDataDictionary (void) const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

virtual void	Register () const ITK_OVERRIDE

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

virtual void	SetReferenceCount (int) ITK_OVERRIDE

virtual void	UnRegister () const ITK_OVERRIDE

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 Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::MatrixOffsetTransformBase< TScalar, NDimensions, NDimensions >
static Pointer	New ()

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 ()

Static Public Attributes

static const unsigned int	InputSpaceDimension = NDimensions

static const unsigned int	OutputSpaceDimension = NDimensions

static const unsigned int	SpaceDimension = NDimensions

static const unsigned int	ParametersDimension = NDimensions *( NDimensions + 1 )

Static Public Attributes inherited from itk::MatrixOffsetTransformBase< TScalar, NDimensions, NDimensions >
static const unsigned int	InputSpaceDimension

static const unsigned int	OutputSpaceDimension

static const unsigned int	ParametersDimension

Static Public Attributes inherited from itk::Transform< TScalar, NInputDimensions, NOutputDimensions >
static const unsigned int	InputSpaceDimension = NInputDimensions

static const unsigned int	OutputSpaceDimension = NOutputDimensions

Protected Member Functions
void	PrintSelf (std::ostream &s, Indent indent) const

virtual	~AffineTransform ()


	AffineTransform (const MatrixType &matrix, const OutputVectorType &offset)

	AffineTransform (unsigned int paramDims)

	AffineTransform ()

Protected Member Functions inherited from itk::MatrixOffsetTransformBase< TScalar, NDimensions, NDimensions >
virtual void	ComputeMatrix (void)

virtual void	ComputeMatrixParameters (void)

virtual void	ComputeOffset (void)

virtual void	ComputeTranslation (void)

const InverseMatrixType &	GetInverseMatrix (void) const

const InverseMatrixType &	GetVarInverseMatrix (void) const

bool	InverseMatrixIsOld (void) const

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

void	SetVarCenter (const InputPointType &center)

void	SetVarInverseMatrix (const InverseMatrixType &matrix) const

void	SetVarMatrix (const MatrixType &matrix)

void	SetVarOffset (const OutputVectorType &offset)

void	SetVarTranslation (const OutputVectorType &translation)

virtual	~MatrixOffsetTransformBase ()

	MatrixOffsetTransformBase (const MatrixType &matrix, const OutputVectorType &offset)

	MatrixOffsetTransformBase (unsigned int paramDims)

	MatrixOffsetTransformBase ()

Protected Member Functions inherited from itk::Transform< TScalar, NInputDimensions, NOutputDimensions >
virtual LightObject::Pointer	InternalClone () const

OutputDiffusionTensor3DType	PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType, const JacobianType) const

	Transform ()

	Transform (NumberOfParametersType NumberOfParameters)

virtual	~Transform ()

Protected Member Functions inherited from itk::TransformBaseTemplate< TScalar >
	TransformBaseTemplate ()

virtual	~TransformBaseTemplate ()

Protected Member Functions inherited from itk::Object
	Object ()

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &time)

virtual	~Object ()

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 ()

Private Member Functions
	AffineTransform (const Self &other)

const Self &	operator= (const Self &)

Additional Inherited Members
Protected Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

Protected Attributes inherited from itk::Transform< TScalar, NInputDimensions, NOutputDimensions >
DirectionChangeMatrix	m_DirectionChange

ParametersType	m_FixedParameters

ParametersType	m_Parameters

Protected Attributes inherited from itk::LightObject
InternalReferenceCountType	m_ReferenceCount

SimpleFastMutexLock	m_ReferenceCountLock