itk::SymmetricSecondRankTensor< TComponent, VDimension > Class Template Reference

#include <itkSymmetricSecondRankTensor.h>

Detailed Description

template<typename TComponent, unsigned int VDimension = 3>
class itk::SymmetricSecondRankTensor< TComponent, VDimension >

Represent a symmetric tensor of second rank.

This class implements a ND symmetric tensor of second rank.

Since SymmetricSecondRankTensor is a subclass of FixedArray, you can access its components as:

using TensorPixelType = itk::SymmetricSecondRankTensor< float >; TensorPixelType tensor;

tensor[0] = 1.233; tensor[1] = 1.456;

for convenience the indexed access is also available as

tensor(0,0) = 1.233; tensor(2,0) = 1.233;

The Tensor in principle represents a NxN matrix, but given that it is always symmetric the representation can be compacted into a N*(N+1)/2 elements array that derives from the itk::FixedArray<T>

Author

Jeffrey Duda from School of Engineering at University of Pennsylvania

Torsten Rohlfing from SRI International Neuroscience Program.

This class was mostly based on files that Jeffrey Duda, Torsten Rohlfing and Martin Styner contributed to the ITK users list during a discussion on support for DiffusionTensorImages. The funding for creating this class was largely provided by NAMIC (National Alliance for Medical Image Computing) (https://www.na-mic.org). A discussion on the design of this class can be found in the WIKI pages of NAMIC:

https://www.na-mic.org/Wiki/index.php/NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType

See also

DiffusionTensor3D

Examples

SphinxExamples/src/Nonunit/Review/SegmentBloodVesselsWithMultiScaleHessianBasedMeasure/Code.cxx.

Definition at line 75 of file itkSymmetricSecondRankTensor.h.

Inheritance diagram for itk::SymmetricSecondRankTensor< TComponent, VDimension >:

Collaboration diagram for itk::SymmetricSecondRankTensor< TComponent, VDimension >:

Public Types
using	AccumulateValueType = typename NumericTraits< ValueType >::RealType
using	BaseArray = FixedArray< TComponent, Self::InternalDimension >
using	ComponentArrayType = ComponentType[Self::InternalDimension]
using	ComponentType = TComponent
using	EigenValuesArrayType = FixedArray< TComponent, VDimension >
using	EigenVectorsMatrixType = Matrix< TComponent, VDimension, VDimension >
using	MatrixType = Matrix< TComponent, VDimension, VDimension >
using	RealValueType = typename NumericTraits< ValueType >::RealType
using	Self = SymmetricSecondRankTensor
using	Superclass = FixedArray< TComponent, VDimension *(VDimension+1)/2 >
using	SymmetricEigenAnalysisType = SymmetricEigenAnalysisFixedDimension< Dimension, MatrixType, EigenValuesArrayType, EigenVectorsMatrixType >
Public Types inherited from itk::FixedArray< TComponent, VDimension *(VDimension+1)/2 >
using	CArray = ValueType[VLength]
using	const_iterator = const ValueType *
using	const_pointer = const ValueType *
using	const_reference = const ValueType &
using	const_reverse_iterator = std::reverse_iterator< const_iterator >
using	ConstIterator = const ValueType *
using	Iterator = ValueType *
using	iterator = ValueType *
using	pointer = ValueType *
using	reference = ValueType &
using	reverse_iterator = std::reverse_iterator< iterator >
using	SizeType = unsigned int
using	ValueType = TComponent

Public Member Functions
void	ComputeEigenAnalysis (EigenValuesArrayType &eigenValues, EigenVectorsMatrixType &eigenVectors) const
void	ComputeEigenValues (EigenValuesArrayType &eigenValues) const
ComponentType	GetNthComponent (int c) const
AccumulateValueType	GetTrace () const
ValueType &	operator() (unsigned int row, unsigned int col)
const ValueType &	operator() (unsigned int row, unsigned int col) const
Self	operator* (const RealValueType &r) const
const Self &	operator*= (const RealValueType &r)
Self	operator+ (const Self &r) const
const Self &	operator+= (const Self &r)
Self	operator- (const Self &r) const
const Self &	operator-= (const Self &r)
Self	operator/ (const RealValueType &r) const
const Self &	operator/= (const RealValueType &r)
Self &	operator= (const ComponentArrayType r)
Self &	operator= (const ComponentType &r)
MatrixType	PostMultiply (const MatrixType &m) const
MatrixType	PreMultiply (const MatrixType &m) const
void	SetIdentity ()
void	SetNthComponent (int c, const ComponentType &v)
	SymmetricSecondRankTensor (const ComponentArrayType r)
	SymmetricSecondRankTensor (const ComponentType &r)
template<typename TCoordRepB >
	SymmetricSecondRankTensor (const SymmetricSecondRankTensor< TCoordRepB, VDimension > &pa)
	SymmetricSecondRankTensor ()=default
template<typename TCoordRepB >
Self &	operator= (const SymmetricSecondRankTensor< TCoordRepB, VDimension > &pa)
template<typename TMatrixValueType >
Self	Rotate (const Matrix< TMatrixValueType, VDimension, VDimension > &m) const
template<typename TMatrixValueType >
Self	Rotate (const vnl_matrix_fixed< TMatrixValueType, VDimension, VDimension > &m) const
template<typename TMatrixValueType >
Self	Rotate (const vnl_matrix< TMatrixValueType > &m) const
Public Member Functions inherited from itk::FixedArray< TComponent, VDimension *(VDimension+1)/2 >
Iterator	Begin ()
ConstIterator	Begin () const
constexpr const_iterator	begin () const noexcept
constexpr iterator	begin () noexcept
constexpr const_iterator	cbegin () const noexcept
constexpr const_iterator	cend () const noexcept
const_reverse_iterator	crbegin () const
const_reverse_iterator	crend () const
ValueType *	data ()
const ValueType *	data () const
Iterator	End ()
ConstIterator	End () const
constexpr const_iterator	end () const noexcept
constexpr iterator	end () noexcept
void	Fill (const ValueType &)
	FixedArray ()=default
	FixedArray (const FixedArray< TFixedArrayValueType, VLength > &r)
	FixedArray (const std::array< ValueType, VLength > &stdArray)
	FixedArray (const TScalarValue *r)
ValueType *	GetDataPointer ()
const ValueType *	GetDataPointer () const
	ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION (FixedArray)
	itkLegacyMacro (ReverseIterator rBegin();) itkLegacyMacro(ConstReverseIterator rBegin() const
	itkLegacyMacro (ReverseIterator rEnd();) itkLegacyMacro(ConstReverseIterator rEnd() const
FixedArray &	operator= (const FixedArray< TFixedArrayValueType, VLength > &r)
FixedArray &	operator= (const ValueType r[VLength])
bool	operator== (const FixedArray &r) const
reverse_iterator	rbegin ()
const_reverse_iterator	rbegin () const
reverse_iterator	rend ()
const_reverse_iterator	rend () const
SizeType	Size () const
constexpr SizeType	size () const
void	swap (FixedArray &other)
	FixedArray (const ValueType r[VLength])
	FixedArray (const ValueType &)
ITK_GCC_PRAGMA_PUSH constexpr ITK_GCC_SUPPRESS_Warray_bounds reference	operator[] (unsigned int index)
constexpr const_reference	operator[] (unsigned int index) const
ITK_GCC_PRAGMA_POP void	SetElement (unsigned int index, const_reference value)
const_reference	GetElement (unsigned int index) const

Static Public Member Functions
static unsigned int	GetNumberOfComponents ()
Static Public Member Functions inherited from itk::FixedArray< TComponent, VDimension *(VDimension+1)/2 >
static constexpr FixedArray	Filled (const ValueType &value)

Static Public Attributes
static constexpr unsigned int	Dimension = VDimension
static constexpr unsigned int	InternalDimension = VDimension * (VDimension + 1) / 2
Static Public Attributes inherited from itk::FixedArray< TComponent, VDimension *(VDimension+1)/2 >
static constexpr unsigned int	Dimension
static constexpr unsigned int	Length

Member Typedef Documentation

AccumulateValueType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::AccumulateValueType = typename NumericTraits<ValueType>::RealType

Definition at line 99 of file itkSymmetricSecondRankTensor.h.

BaseArray

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::BaseArray = FixedArray<TComponent, Self::InternalDimension>

Convenience type alias.

Definition at line 87 of file itkSymmetricSecondRankTensor.h.

ComponentArrayType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::ComponentArrayType = ComponentType[Self::InternalDimension]

Definition at line 122 of file itkSymmetricSecondRankTensor.h.

ComponentType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::ComponentType = TComponent

Define the component type.

Definition at line 97 of file itkSymmetricSecondRankTensor.h.

EigenValuesArrayType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::EigenValuesArrayType = FixedArray<TComponent, VDimension>

Array of eigen-values.

Definition at line 90 of file itkSymmetricSecondRankTensor.h.

EigenVectorsMatrixType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::EigenVectorsMatrixType = Matrix<TComponent, VDimension, VDimension>

Definition at line 94 of file itkSymmetricSecondRankTensor.h.

MatrixType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::MatrixType = Matrix<TComponent, VDimension, VDimension>

Matrix of eigen-vectors.

Definition at line 93 of file itkSymmetricSecondRankTensor.h.

RealValueType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::RealValueType = typename NumericTraits<ValueType>::RealType

Definition at line 100 of file itkSymmetricSecondRankTensor.h.

Self

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::Self = SymmetricSecondRankTensor

Standard class type aliases.

Definition at line 79 of file itkSymmetricSecondRankTensor.h.

Superclass

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::Superclass = FixedArray<TComponent, VDimension *(VDimension + 1) / 2>

Definition at line 80 of file itkSymmetricSecondRankTensor.h.

SymmetricEigenAnalysisType

template<typename TComponent, unsigned int VDimension = 3>

using itk::SymmetricSecondRankTensor< TComponent, VDimension >::SymmetricEigenAnalysisType = SymmetricEigenAnalysisFixedDimension<Dimension, MatrixType, EigenValuesArrayType, EigenVectorsMatrixType>

Definition at line 103 of file itkSymmetricSecondRankTensor.h.

Constructor & Destructor Documentation

SymmetricSecondRankTensor() [1/4]

template<typename TComponent, unsigned int VDimension = 3>

itk::SymmetricSecondRankTensor< TComponent, VDimension >::SymmetricSecondRankTensor ( )

default

Default-constructor.

Note

The other five "special member functions" are defaulted implicitly, following the C++ "Rule of Zero".

SymmetricSecondRankTensor() [2/4]

template<typename TComponent, unsigned int VDimension = 3>

itk::SymmetricSecondRankTensor< TComponent, VDimension >::SymmetricSecondRankTensor ( const ComponentType &  r )

inline

Definition at line 114 of file itkSymmetricSecondRankTensor.h.

SymmetricSecondRankTensor() [3/4]

template<typename TComponent, unsigned int VDimension = 3>

template<typename TCoordRepB >

itk::SymmetricSecondRankTensor< TComponent, VDimension >::SymmetricSecondRankTensor ( const SymmetricSecondRankTensor< TCoordRepB, VDimension > &  pa )

inline

Constructor to enable casting...

Definition at line 118 of file itkSymmetricSecondRankTensor.h.

SymmetricSecondRankTensor() [4/4]

template<typename TComponent, unsigned int VDimension = 3>

itk::SymmetricSecondRankTensor< TComponent, VDimension >::SymmetricSecondRankTensor ( const ComponentArrayType  r )

inline

Pass-through constructor for the Array base class.

Definition at line 125 of file itkSymmetricSecondRankTensor.h.

Member Function Documentation

ComputeEigenAnalysis()

template<typename TComponent, unsigned int VDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, VDimension >::ComputeEigenAnalysis	(	EigenValuesArrayType &	eigenValues,
		EigenVectorsMatrixType &	eigenVectors
	)		const

Return an array containing EigenValues, and a matrix containing Eigen vectors.

ComputeEigenValues()

template<typename TComponent, unsigned int VDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, VDimension >::ComputeEigenValues

(

EigenValuesArrayType &

eigenValues

)

const

Return an array containing EigenValues.

GetNthComponent()

template<typename TComponent, unsigned int VDimension = 3>

ComponentType itk::SymmetricSecondRankTensor< TComponent, VDimension >::GetNthComponent ( int  c ) const

inline

Return the value for the Nth component.

Definition at line 181 of file itkSymmetricSecondRankTensor.h.

GetNumberOfComponents()

template<typename TComponent, unsigned int VDimension = 3>

static unsigned int itk::SymmetricSecondRankTensor< TComponent, VDimension >::GetNumberOfComponents ( )

inlinestatic

Return the number of components.

Definition at line 174 of file itkSymmetricSecondRankTensor.h.

GetTrace()

template<typename TComponent, unsigned int VDimension = 3>

AccumulateValueType itk::SymmetricSecondRankTensor< TComponent, VDimension >::GetTrace

(

)

const

Get Trace value

operator()() [1/2]

template<typename TComponent, unsigned int VDimension = 3>

ValueType& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator()	(	unsigned int	row,
		unsigned int	col
	)

Matrix notation, in const and non-const forms.

operator()() [2/2]

template<typename TComponent, unsigned int VDimension = 3>

const ValueType& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator()	(	unsigned int	row,
		unsigned int	col
	)		const

operator*()

template<typename TComponent, unsigned int VDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator*

(

const RealValueType &

r

)

const

Arithmetic operations between tensors and scalars

operator*=()

template<typename TComponent, unsigned int VDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator*=

(

const RealValueType &

r

)

operator+()

template<typename TComponent, unsigned int VDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator+

(

const Self &

r

)

const

Arithmetic operations between pixels. Return a new SymmetricSecondRankTensor.

operator+=()

template<typename TComponent, unsigned int VDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator+=

(

const Self &

r

)

operator-()

template<typename TComponent, unsigned int VDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator-

(

const Self &

r

)

const

operator-=()

template<typename TComponent, unsigned int VDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator-=

(

const Self &

r

)

operator/()

template<typename TComponent, unsigned int VDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator/

(

const RealValueType &

r

)

const

operator/=()

template<typename TComponent, unsigned int VDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator/=

(

const RealValueType &

r

)

operator=() [1/3]

template<typename TComponent, unsigned int VDimension = 3>

Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator=

(

const ComponentArrayType

r

)

operator=() [2/3]

template<typename TComponent, unsigned int VDimension = 3>

Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator=

(

const ComponentType &

r

)

Pass-through assignment operator for the Array base class.

operator=() [3/3]

template<typename TComponent, unsigned int VDimension = 3>

template<typename TCoordRepB >

Self& itk::SymmetricSecondRankTensor< TComponent, VDimension >::operator= ( const SymmetricSecondRankTensor< TCoordRepB, VDimension > &  pa )

inline

Templated Pass-through assignment for the Array base class.

Definition at line 132 of file itkSymmetricSecondRankTensor.h.

Referenced by itk::DiffusionTensor3D< TComponent >::operator=().

PostMultiply()

template<typename TComponent, unsigned int VDimension = 3>

MatrixType itk::SymmetricSecondRankTensor< TComponent, VDimension >::PostMultiply

(

const MatrixType &

m

)

const

Post-Multiply by a Matrix as ResultingMatrix = ThisTensor * Matrix.

PreMultiply()

template<typename TComponent, unsigned int VDimension = 3>

MatrixType itk::SymmetricSecondRankTensor< TComponent, VDimension >::PreMultiply

(

const MatrixType &

m

)

const

Pre-Multiply by a Matrix as ResultingMatrix = Matrix * ThisTensor.

Rotate() [1/3]

template<typename TComponent, unsigned int VDimension = 3>

template<typename TMatrixValueType >

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::Rotate

(

const Matrix< TMatrixValueType, VDimension, VDimension > &

m

)

const

Returns the tensor rotated by the provided matrix. ResultingTensor = Matrix * ThisTensor * Matrix.GetTranspose()

Rotate() [2/3]

template<typename TComponent, unsigned int VDimension = 3>

template<typename TMatrixValueType >

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::Rotate ( const vnl_matrix< TMatrixValueType > &  m ) const

inline

Returns the tensor rotated by the provided matrix. ResultingTensor = Matrix * ThisTensor * Matrix.GetTranspose()

Definition at line 232 of file itkSymmetricSecondRankTensor.h.

Rotate() [3/3]

template<typename TComponent, unsigned int VDimension = 3>

template<typename TMatrixValueType >

Self itk::SymmetricSecondRankTensor< TComponent, VDimension >::Rotate ( const vnl_matrix_fixed< TMatrixValueType, VDimension, VDimension > &  m ) const

inline

Returns the tensor rotated by the provided matrix. ResultingTensor = Matrix * ThisTensor * Matrix.GetTranspose()

Definition at line 226 of file itkSymmetricSecondRankTensor.h.

SetIdentity()

template<typename TComponent, unsigned int VDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, VDimension >::SetIdentity

(

)

Set the tensor to an identity tensor. This has 1 in its diagonal elements and zero elsewhere.

SetNthComponent()

template<typename TComponent, unsigned int VDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, VDimension >::SetNthComponent ( int  c, const ComponentType &  v  )

inline

Set the Nth component to v.

Definition at line 188 of file itkSymmetricSecondRankTensor.h.

Member Data Documentation

Dimension

template<typename TComponent, unsigned int VDimension = 3>

constexpr unsigned int itk::SymmetricSecondRankTensor< TComponent, VDimension >::Dimension = VDimension

staticconstexpr

Dimension of the vector space.

Definition at line 83 of file itkSymmetricSecondRankTensor.h.

InternalDimension

template<typename TComponent, unsigned int VDimension = 3>

constexpr unsigned int itk::SymmetricSecondRankTensor< TComponent, VDimension >::InternalDimension = VDimension * (VDimension + 1) / 2

staticconstexpr

Definition at line 84 of file itkSymmetricSecondRankTensor.h.

---

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

• itkSymmetricSecondRankTensor.h