#include <itkAffineDTI3DTransform.h>

Detailed Description

template<typename 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 78 of file itkAffineDTI3DTransform.h.

Inheritance diagram for itk::AffineDTI3DTransform< TScalarType >:

[legend]

Public Types
using	AngleType = typename Superclass::ScalarType
using	ConstPointer = SmartPointer<const Self>
typedef typename SpatialJacobianType::InternalMatrixType	InternalMatrixType
typedef std::vector< SpatialHessianType >	JacobianOfSpatialHessianType
typedef std::vector< SpatialJacobianType >	JacobianOfSpatialJacobianType
typedef std::vector< uint64_t >	NonZeroJacobianIndicesType
using	Pointer = SmartPointer<Self>
using	ScalarArrayType = FixedArray<ScalarType>
using	Self = AffineDTI3DTransform
typedef FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension >	SpatialHessianType
typedef Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension >	SpatialJacobianType
using	Superclass = AdvancedMatrixOffsetTransformBase<TScalarType, 3, 3>
Public Types inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
using	CenterType
using	ConstPointer
typedef typename SpatialJacobianType::InternalMatrixType	InternalMatrixType
using	InverseMatrixType
typedef std::vector< SpatialHessianType >	JacobianOfSpatialHessianType
typedef std::vector< SpatialJacobianType >	JacobianOfSpatialJacobianType
using	MatrixType
typedef std::vector< uint64_t >	NonZeroJacobianIndicesType
using	OffsetType
using	Pointer
using	Self
typedef FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension >	SpatialHessianType
typedef Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension >	SpatialJacobianType
using	Superclass
using	TranslationType
Public Types inherited from itk::AdvancedTransform< double, NInputDimensions, NOutputDimensions >
using	ConstPointer
using	InternalMatrixType
using	InverseTransformBaseType
using	JacobianOfSpatialHessianType
using	JacobianOfSpatialJacobianType
using	MovingImageGradientType
using	MovingImageGradientValueType
using	NonZeroJacobianIndicesType
using	Pointer
using	Self
using	SpatialHessianType
using	SpatialJacobianType
using	Superclass
using	TransformType
using	TransformTypeConstPointer
using	TransformTypePointer

Public Member Functions
void	GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const override
const ParametersType &	GetParameters () const override
	ITK_DISALLOW_COPY_AND_MOVE (AffineDTI3DTransform)
	itkOverrideGetNameOfClassMacro (AffineDTI3DTransform)
	itkStaticConstMacro (InputSpaceDimension, unsigned int, 3)
	itkStaticConstMacro (OutputSpaceDimension, unsigned int, 3)
	itkStaticConstMacro (ParametersDimension, unsigned int, 12)
	itkStaticConstMacro (SpaceDimension, unsigned int, 3)
void	SetIdentity () override
void	SetParameters (const ParametersType &parameters) override
Public Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
const InputPointType &	GetCenter () const
const FixedParametersType &	GetFixedParameters () const override
void	GetJacobianOfSpatialHessian (const InputPointType &, JacobianOfSpatialHessianType &, NonZeroJacobianIndicesType &) const override
void	GetJacobianOfSpatialJacobian (const InputPointType &, JacobianOfSpatialJacobianType &, NonZeroJacobianIndicesType &) const override
const MatrixType &	GetMatrix () const
const ParametersType &	GetParameters () const override
void	GetSpatialHessian (const InputPointType &, SpatialHessianType &) const override
void	GetSpatialJacobian (const InputPointType &, SpatialJacobianType &) const override
TransformCategoryEnum	GetTransformCategory () const override
const OutputVectorType &	GetTranslation () const
bool	IsLinear () const override
	itkOverrideGetNameOfClassMacro (AdvancedMatrixOffsetTransformBase)
	itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)
void	SetCenter (const InputPointType &center)
void	SetFixedParameters (const FixedParametersType &) override
virtual void	SetMatrix (const MatrixType &matrix)
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
Public Member Functions inherited from itk::AdvancedTransform< double, NInputDimensions, NOutputDimensions >
void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const override
virtual void	EvaluateJacobianWithImageGradientProduct (const InputPointType &inputPoint, const MovingImageGradientType &movingImageGradient, DerivativeType &imageJacobian, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const
virtual bool	GetHasNonZeroJacobianOfSpatialHessian () const
virtual bool	GetHasNonZeroSpatialHessian () const
virtual NumberOfParametersType	GetNumberOfNonZeroJacobianIndices () const
	ITK_DISALLOW_COPY_AND_MOVE (AdvancedTransform)
	itkOverrideGetNameOfClassMacro (AdvancedTransform)
	itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)

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 () override
void	ComputeMatrixParameters () override
virtual void	PrecomputeJacobianOfSpatialJacobian ()
void	PrintSelf (std::ostream &os, Indent indent) const override
void	SetVarAngleScaleShear (ScalarArrayType angle, ScalarArrayType shear, ScalarArrayType scale)
	~AffineDTI3DTransform () override=default
Protected Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< double, 3, 3 >
	AdvancedMatrixOffsetTransformBase (const unsigned int paramDims=ParametersDimension)
virtual void	ComputeOffset ()
void	ComputeTranslation ()
const OutputVectorType &	GetOffset () const
void	PrintSelf (std::ostream &s, Indent indent) const override
void	SetVarMatrix (const MatrixType &matrix)
void	SetVarTranslation (const OutputVectorType &translation)
	~AdvancedMatrixOffsetTransformBase () override=default
Protected Member Functions inherited from itk::AdvancedTransform< double, NInputDimensions, NOutputDimensions >
	AdvancedTransform ()=default
	~AdvancedTransform () override=default

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