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

#include <itkSymmetricSecondRankTensor.h>

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

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

Detailed Description

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

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:

typedef itk::SymmetricSecondRankTensor< float > TensorPixelType; 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) (http://www.na-mic.org). A discussion on the design of this class can be found in the WIKI pages of NAMIC:

http://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.

Public Types
typedef NumericTraits < ValueType >::RealType	AccumulateValueType
typedef FixedArray< TComponent, itkGetStaticConstMacro(InternalDimension) >	BaseArray
typedef ComponentType	ComponentArrayType [itkGetStaticConstMacro(InternalDimension)]
typedef TComponent	ComponentType
typedef FixedArray< TComponent, NDimension >	EigenValuesArrayType
typedef Matrix< TComponent, NDimension, NDimension >	EigenVectorsMatrixType
typedef Matrix< TComponent, NDimension, NDimension >	MatrixType
typedef NumericTraits < ValueType >::RealType	RealValueType
typedef SymmetricSecondRankTensor	Self
typedef FixedArray< TComponent, NDimension *(NDimension+1)/2 >	Superclass
typedef SymmetricEigenAnalysis < MatrixType, EigenValuesArrayType, EigenVectorsMatrixType >	SymmetricEigenAnalysisType
typedef Superclass::ValueType	ValueType
Public Types inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
typedef ValueType	CArray [VLength]
typedef const ValueType *	const_pointer
typedef const ValueType &	const_reference
typedef const ValueType *	ConstIterator
typedef ValueType *	Iterator
typedef ValueType *	pointer
typedef ValueType &	reference
typedef unsigned int	SizeType
typedef TComponent	ValueType

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 &scalar) const
const Self &	operator*= (const RealValueType &scalar)
Self	operator+ (const Self &vec) const
const Self &	operator+= (const Self &vec)
Self	operator- (const Self &vec) const
const Self &	operator-= (const Self &vec)
Self	operator/ (const RealValueType &scalar) const
const Self &	operator/= (const RealValueType &scalar)
Self &	operator= (const ComponentType &r)
Self &	operator= (const ComponentArrayType r)
MatrixType	PostMultiply (const MatrixType &m) const
MatrixType	PreMultiply (const MatrixType &m) const
void	SetIdentity ()
void	SetNthComponent (int c, const ComponentType &v)
	SymmetricSecondRankTensor ()
	SymmetricSecondRankTensor (const ComponentType &r)
template<typename TCoordRepB >
	SymmetricSecondRankTensor (const SymmetricSecondRankTensor< TCoordRepB, NDimension > &pa)
	SymmetricSecondRankTensor (const ComponentArrayType r)
template<typename TCoordRepB >
Self &	operator= (const SymmetricSecondRankTensor< TCoordRepB, NDimension > &pa)
template<typename TMatrixValueType >
Self	Rotate (const Matrix< TMatrixValueType, NDimension, NDimension > &m) const
template<typename TMatrixValueType >
Self	Rotate (const vnl_matrix_fixed< TMatrixValueType, NDimension, NDimension > &m) const
template<typename TMatrixValueType >
Self	Rotate (const vnl_matrix< TMatrixValueType > &m) const
Public Member Functions inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
Iterator	Begin ()
ConstIterator	Begin () const
Iterator	End ()
ConstIterator	End () const
void	Fill (const ValueType &)
	FixedArray (const TScalarValue *r)
ValueType *	GetDataPointer ()
const ValueType *	GetDataPointer () const
bool	operator!= (const FixedArray &r) const
FixedArray &	operator= (const ValueType r[VLength])
bool	operator== (const FixedArray &r) const
ReverseIterator	rBegin ()
ConstReverseIterator	rBegin () const
ReverseIterator	rEnd ()
ConstReverseIterator	rEnd () const
SizeType	Size () const
	FixedArray ()
	FixedArray (const ValueType r[VLength])
	FixedArray (const ValueType &r)
	FixedArray (const FixedArray< TFixedArrayValueType, VLength > &r)
FixedArray &	operator= (const FixedArray< TFixedArrayValueType, VLength > &r)
reference	operator[] (short index)
const_reference	operator[] (short index) const
reference	operator[] (unsigned short index)
const_reference	operator[] (unsigned short index) const
reference	operator[] (int index)
const_reference	operator[] (int index) const
reference	operator[] (unsigned int index)
const_reference	operator[] (unsigned int index) const
reference	operator[] (long index)
const_reference	operator[] (long index) const
reference	operator[] (unsigned long index)
const_reference	operator[] (unsigned long index) const
reference	operator[] (long long index)
const_reference	operator[] (long long index) const
reference	operator[] (unsigned long long index)
const_reference	operator[] (unsigned long long index) const
void	SetElement (unsigned short index, const_reference value)
const_reference	GetElement (unsigned short index) const

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

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

Member Typedef Documentation

template<typename TComponent, unsigned int NDimension = 3>

typedef NumericTraits< ValueType >::RealType itk::SymmetricSecondRankTensor< TComponent, NDimension >::AccumulateValueType

Definition at line 102 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef FixedArray< TComponent, itkGetStaticConstMacro(InternalDimension) > itk::SymmetricSecondRankTensor< TComponent, NDimension >::BaseArray

Convenience typedefs.

Definition at line 90 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef ComponentType itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComponentArrayType[itkGetStaticConstMacro(InternalDimension)]

Definition at line 118 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef TComponent itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComponentType

Define the component type.

Definition at line 100 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef FixedArray< TComponent, NDimension > itk::SymmetricSecondRankTensor< TComponent, NDimension >::EigenValuesArrayType

Array of eigen-values.

Definition at line 93 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef Matrix< TComponent, NDimension, NDimension > itk::SymmetricSecondRankTensor< TComponent, NDimension >::EigenVectorsMatrixType

Definition at line 97 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef Matrix< TComponent, NDimension, NDimension > itk::SymmetricSecondRankTensor< TComponent, NDimension >::MatrixType

Matrix of eigen-vectors.

Definition at line 96 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef NumericTraits< ValueType >::RealType itk::SymmetricSecondRankTensor< TComponent, NDimension >::RealValueType

Definition at line 103 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef SymmetricSecondRankTensor itk::SymmetricSecondRankTensor< TComponent, NDimension >::Self

Standard class typedefs.

Definition at line 80 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef FixedArray< TComponent, NDimension *( NDimension + 1 ) / 2 > itk::SymmetricSecondRankTensor< TComponent, NDimension >::Superclass

Definition at line 81 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef SymmetricEigenAnalysis< MatrixType, EigenValuesArrayType, EigenVectorsMatrixType > itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricEigenAnalysisType

Definition at line 106 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef Superclass::ValueType itk::SymmetricSecondRankTensor< TComponent, NDimension >::ValueType

Definition at line 101 of file itkSymmetricSecondRankTensor.h.

Constructor & Destructor Documentation

template<typename TComponent, unsigned int NDimension = 3>

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

inline

Default constructor has nothing to do.

Definition at line 109 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

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

inline

Definition at line 111 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

template<typename TCoordRepB >

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

inline

Constructor to enable casting...

Definition at line 115 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

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

inline

Pass-through constructor for the Array base class.

Definition at line 121 of file itkSymmetricSecondRankTensor.h.

Member Function Documentation

template<typename TComponent, unsigned int NDimension = 3>

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

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

template<typename TComponent, unsigned int NDimension = 3>

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

(

EigenValuesArrayType &

eigenValues

)

const

Return an array containing EigenValues.

template<typename TComponent, unsigned int NDimension = 3>

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

inline

Return the value for the Nth component.

Definition at line 163 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

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

inlinestatic

Return the number of components.

Definition at line 157 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

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

(

)

const

Get Trace value

template<typename TComponent, unsigned int NDimension = 3>

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

Matrix notation, in const and non-const forms.

template<typename TComponent, unsigned int NDimension = 3>

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

template<typename TComponent, unsigned int NDimension = 3>

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

(

const RealValueType &

scalar

)

const

Arithmetic operations between tensors and scalars

template<typename TComponent, unsigned int NDimension = 3>

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

(

const RealValueType &

scalar

)

template<typename TComponent, unsigned int NDimension = 3>

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

(

const Self &

vec

)

const

Aritmetic operations between pixels. Return a new SymmetricSecondRankTensor.

template<typename TComponent, unsigned int NDimension = 3>

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

(

const Self &

vec

)

template<typename TComponent, unsigned int NDimension = 3>

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

(

const Self &

vec

)

const

template<typename TComponent, unsigned int NDimension = 3>

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

(

const Self &

vec

)

template<typename TComponent, unsigned int NDimension = 3>

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

(

const RealValueType &

scalar

)

const

template<typename TComponent, unsigned int NDimension = 3>

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

(

const RealValueType &

scalar

)

template<typename TComponent, unsigned int NDimension = 3>

template<typename TCoordRepB >

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

inline

Templated Pass-through assignment for the Array base class.

Definition at line 125 of file itkSymmetricSecondRankTensor.h.

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

template<typename TComponent, unsigned int NDimension = 3>

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

(

const ComponentType &

r

)

Pass-through assignment operator for the Array base class.

template<typename TComponent, unsigned int NDimension = 3>

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

(

const ComponentArrayType

r

)

template<typename TComponent, unsigned int NDimension = 3>

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

(

const MatrixType &

m

)

const

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

template<typename TComponent, unsigned int NDimension = 3>

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

(

const MatrixType &

m

)

const

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

template<typename TComponent, unsigned int NDimension = 3>

template<typename TMatrixValueType >

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

(

const Matrix< TMatrixValueType, NDimension, NDimension > &

m

)

const

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

Referenced by itk::SymmetricSecondRankTensor< TComponent, 3 >::Rotate().

template<typename TComponent, unsigned int NDimension = 3>

template<typename TMatrixValueType >

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

inline

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

Definition at line 194 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

template<typename TMatrixValueType >

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

inline

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

Definition at line 199 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

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

(

)

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

template<typename TComponent, unsigned int NDimension = 3>

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

inline

Set the Nth component to v.

Definition at line 166 of file itkSymmetricSecondRankTensor.h.

Member Data Documentation

template<typename TComponent, unsigned int NDimension = 3>

const unsigned int itk::SymmetricSecondRankTensor< TComponent, NDimension >::Dimension = NDimension

static

Dimension of the vector space.

Definition at line 84 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

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

static

Dimension of the vector space.

Definition at line 85 of file itkSymmetricSecondRankTensor.h.

Referenced by itk::SymmetricSecondRankTensor< TComponent, 3 >::GetNumberOfComponents().

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

• itkSymmetricSecondRankTensor.h