#include <itkAffineDTI3DTransform.h>

Detailed Description

template<class TScalarType = double>
class itk::AffineDTI3DTransform< TScalarType >

AffineDTI3DTransform of a vector space (e.g. space coordinates)

This transform applies an affine transformation, but is parameterized by angles, shear factors, scales, and translation, instead of by the affine matrix. It is meant for registration of MR diffusion weighted images, but could be used for other images as well of course.

The affine model is adopted from the following paper: [1] A. Leemans and D.K. Jones. "The B-matrix must be rotated when correcting for subject motion in DTI data". Magnetic Resonance in Medicine, Volume 61, Issue 6, pages 1336 - 1349, 2009.

The model is as follows:
T(x) = R G S (x-c) + t + c
with:

R = Rx Ry Rz (rotation matrices)
G = Gx Gy Gz (shear matrices)
S = diag( [sx sy sz] ) (scaling matrix)
c = center of rotation
t = translation See [1] for exact expressions for Rx, Gx etc.

Using this model, the rotation components can be easily extracted an applied to the B-matrix.

The parameters are ordered as follows: in 2D: [ Angle ShearX ShearY ScaleX ScaleY TranslationX TranslationY ] in 3D: [ AngleX AngleY AngleZ ShearX ShearY ShearZ ScaleX ScaleY ScaleZ TranslationX TranslationY TranslationZ ]

The serialization of the fixed parameters is an array of 2 elements defining the center of rotation.

This transform applies an affine transformation, but is parameterized by angles, shear factors, scales, and translation, instead of by the affine matrix. It is meant for registration of MR diffusion weighted images, but could be used for other images as well of course.

The affine model is adopted from the following paper: [1] A. Leemans and D.K. Jones. "The B-matrix must be rotated when correcting for subject motion in DTI data". Magnetic Resonance in Medicine, Volume 61, Issue 6, pages 1336 - 1349, 2009.

The model is as follows:
T(x) = R G S (x-c) + t + c
with:

R = Rx Ry Rz (rotation matrices)
G = Gx Gy Gz (shear matrices)
S = diag( [sx sy sz] ) (scaling matrix)
c = center of rotation
t = translation See [1] for exact expressions for Rx, Gx etc.

Using this model, the rotation components can be easily extracted an applied to the B-matrix.

The parameters are ordered as follows: [ AngleX AngleY AngleZ ShearX ShearY ShearZ ScaleX ScaleY ScaleZ TranslationX TranslationY TranslationZ ]

The serialization of the fixed parameters is an array of 3 elements defining the center of rotation.

Definition at line 80 of file itkAffineDTI3DTransform.h.

Inheritance diagram for itk::AffineDTI3DTransform< TScalarType >:

Public Types
typedef Superclass::ScalarType	AngleType

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::InternalMatrixType	InternalMatrixType

typedef Superclass::InverseMatrixType	InverseMatrixType

typedef Superclass::JacobianOfSpatialHessianType	JacobianOfSpatialHessianType

typedef Superclass::JacobianOfSpatialJacobianType	JacobianOfSpatialJacobianType

typedef Superclass::JacobianType	JacobianType

typedef Superclass::MatrixType	MatrixType

typedef Superclass::NonZeroJacobianIndicesType	NonZeroJacobianIndicesType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

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 FixedArray< ScalarType >	ScalarArrayType

typedef Superclass::ScalarType	ScalarType

typedef AffineDTI3DTransform	Self

typedef Superclass::SpatialHessianType	SpatialHessianType

typedef Superclass::SpatialJacobianType	SpatialJacobianType

typedef AdvancedMatrixOffsetTransformBase< TScalarType, 3, 3 >	Superclass

typedef Superclass::TranslationType	TranslationType

Public Types inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
typedef InputPointType	CenterType

typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::FixedParametersType	FixedParametersType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef Superclass::InternalMatrixType	InternalMatrixType

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

typedef Superclass::JacobianOfSpatialHessianType	JacobianOfSpatialHessianType

typedef Superclass::JacobianOfSpatialJacobianType	JacobianOfSpatialJacobianType

typedef Superclass::JacobianType	JacobianType

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

typedef Superclass::NonZeroJacobianIndicesType	NonZeroJacobianIndicesType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef OutputVectorType	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 AdvancedMatrixOffsetTransformBase	Self

typedef Superclass::SpatialHessianType	SpatialHessianType

typedef Superclass::SpatialJacobianType	SpatialJacobianType

typedef AdvancedTransform< double, NInputDimensions, NOutputDimensions >	Superclass

typedef Superclass::TransformCategoryEnum	TransformCategoryEnum

typedef OutputVectorType	TranslationType

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

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::FixedParametersType	FixedParametersType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef SpatialJacobianType::InternalMatrixType	InternalMatrixType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::InverseTransformBaseType	InverseTransformBaseType

typedef std::vector< SpatialHessianType >	JacobianOfSpatialHessianType

typedef std::vector< SpatialJacobianType >	JacobianOfSpatialJacobianType

typedef Superclass::JacobianType	JacobianType

typedef OutputCovariantVectorType	MovingImageGradientType

typedef MovingImageGradientType::ValueType	MovingImageGradientValueType

typedef std::vector< unsigned long >	NonZeroJacobianIndicesType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef AdvancedTransform	Self

typedef FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension >	SpatialHessianType

typedef Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension >	SpatialJacobianType

typedef Transform< double, NInputDimensions, NOutputDimensions >	Superclass

typedef Transform< double, NInputDimensions, NOutputDimensions >	TransformType

typedef TransformType::ConstPointer	TransformTypeConstPointer

typedef TransformType::Pointer	TransformTypePointer

Public Member Functions
virtual const char *	GetClassName () const

void	GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const override

const ParametersType &	GetParameters (void) const override

	itkStaticConstMacro (InputSpaceDimension, unsigned int, 3)

	itkStaticConstMacro (OutputSpaceDimension, unsigned int, 3)

	itkStaticConstMacro (ParametersDimension, unsigned int, 12)

	itkStaticConstMacro (SpaceDimension, unsigned int, 3)

void	SetIdentity (void) override

void	SetParameters (const ParametersType &parameters) override

Public Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
void	Compose (const Self *other, bool pre=0)

const InputPointType &	GetCenter (void) const

virtual const char *	GetClassName () const

const FixedParametersType &	GetFixedParameters (void) const override

bool	GetInverse (Self *inverse) const

const InverseMatrixType &	GetInverseMatrix (void) const

void	GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const override

void	GetJacobianOfSpatialHessian (const InputPointType &, JacobianOfSpatialHessianType &, NonZeroJacobianIndicesType &) const override

void	GetJacobianOfSpatialHessian (const InputPointType &ipp, SpatialHessianType &sh, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const override

void	GetJacobianOfSpatialJacobian (const InputPointType &, JacobianOfSpatialJacobianType &, NonZeroJacobianIndicesType &) const override

void	GetJacobianOfSpatialJacobian (const InputPointType &, SpatialJacobianType &, JacobianOfSpatialJacobianType &, NonZeroJacobianIndicesType &) const override

const MatrixType &	GetMatrix (void) const

const OutputVectorType &	GetOffset (void) const

const ParametersType &	GetParameters (void) const override

void	GetSpatialHessian (const InputPointType &, SpatialHessianType &) const override

void	GetSpatialJacobian (const InputPointType &, SpatialJacobianType &) const override

TransformCategoryEnum	GetTransformCategory () const override

const OutputVectorType &	GetTranslation (void) const

bool	IsLinear (void) const override

	itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)

	itkStaticConstMacro (OutputSpaceDimension, unsigned int, NOutputDimensions)

	itkStaticConstMacro (ParametersDimension, unsigned int, NOutputDimensions *(NInputDimensions+1))

void	SetCenter (const InputPointType &center)

void	SetFixedParameters (const FixedParametersType &) override

virtual void	SetIdentity (void)

virtual void	SetMatrix (const MatrixType &matrix)

void	SetOffset (const OutputVectorType &offset)

void	SetParameters (const ParametersType &parameters) override

void	SetTranslation (const OutputVectorType &translation)

OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector) const override

OutputPointType	TransformPoint (const InputPointType &point) const override

OutputVectorType	TransformVector (const InputVectorType &vector) const override

OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector) const override

Public Member Functions inherited from itk::AdvancedTransform< double, NInputDimensions, NOutputDimensions >
void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const override

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

virtual const char *	GetClassName () const

virtual bool	GetHasNonZeroJacobianOfSpatialHessian () const

virtual bool	GetHasNonZeroSpatialHessian () const

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

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

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

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

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

virtual NumberOfParametersType	GetNumberOfNonZeroJacobianIndices (void) const

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

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

	itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)

	itkStaticConstMacro (OutputSpaceDimension, unsigned int, NOutputDimensions)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
static Pointer	New ()

Protected Member Functions
	AffineDTI3DTransform ()

	AffineDTI3DTransform (const MatrixType &matrix, const OutputPointType &offset)

	AffineDTI3DTransform (unsigned int outputSpaceDims, unsigned int paramsSpaceDims)

void	ComputeMatrix (void) override

void	ComputeMatrixParameters (void) override

virtual void	PrecomputeJacobianOfSpatialJacobian (void)

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

void	SetVarAngleScaleShear (ScalarArrayType angle, ScalarArrayType shear, ScalarArrayType scale)

	~AffineDTI3DTransform ()

Protected Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
	AdvancedMatrixOffsetTransformBase ()

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

	AdvancedMatrixOffsetTransformBase (unsigned int paramDims)

virtual void	ComputeMatrix (void)

virtual void	ComputeMatrixParameters (void)

virtual void	ComputeOffset (void)

virtual void	ComputeTranslation (void)

const InverseMatrixType &	GetVarInverseMatrix (void) const

bool	InverseMatrixIsOld (void) const

virtual void	PrecomputeJacobians (unsigned int paramDims)

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

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)

	~AdvancedMatrixOffsetTransformBase () override

Protected Member Functions inherited from itk::AdvancedTransform< double, NInputDimensions, NOutputDimensions >
	AdvancedTransform ()

	AdvancedTransform (NumberOfParametersType numberOfParameters)

	~AdvancedTransform () override

Private Member Functions
	AffineDTI3DTransform (const Self &)

void	operator= (const Self &)

Private Attributes
ScalarArrayType	m_Angle

ScalarArrayType	m_Scale

ScalarArrayType	m_Shear

Additional Inherited Members
Protected Attributes inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
JacobianOfSpatialHessianType	m_JacobianOfSpatialHessian

JacobianOfSpatialJacobianType	m_JacobianOfSpatialJacobian

NonZeroJacobianIndicesType	m_NonZeroJacobianIndices

SpatialHessianType	m_SpatialHessian

Protected Attributes inherited from itk::AdvancedTransform< double, NInputDimensions, NOutputDimensions >
bool	m_HasNonZeroJacobianOfSpatialHessian

bool	m_HasNonZeroSpatialHessian