itk::SymmetricSecondRankTensor< TComponent, NDimension > Class Template Reference
[Image Representation Objects]

#include <itkSymmetricSecondRankTensor.h>

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

[legend]Collaboration diagram for itk::SymmetricSecondRankTensor< TComponent, NDimension >:

[legend]List of all members.

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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

TensorObjects Geometry

Definition at line 74 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 Member Functions
void	ComputeEigenAnalysis (EigenValuesArrayType &eigenValues, EigenVectorsMatrixType &eigenVectors) const
void	ComputeEigenValues (EigenValuesArrayType &eigenValues) const
ComponentType	GetNthComponent (int c) const
AccumulateValueType	GetTrace () const
	itkStaticConstMacro (InternalDimension, unsigned int, NDimension *(NDimension+1)/2)
Dimension of the vector space *	itkStaticConstMacro (Dimension, unsigned int, NDimension)
Arithmetic operations between tensors and scalars *Self	operator * (const RealValueType &scalar) const
const Self &	operator *= (const RealValueType &scalar)
Pass through assignment	operator for the Array base class.*/Self &operator= (const Self &r)
const ValueType &	operator() (unsigned int row, unsigned int col) const
Matrix in const and non const forms *ValueType &	operator() (unsigned int row, unsigned int col)
Aritmetic operations between pixels Return a new SymmetricSecondRankTensor *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 ComponentArrayType r)
Self &	operator= (const ComponentType &r)
void	SetIdentity ()
void	SetNthComponent (int c, const ComponentType &v)
	SymmetricSecondRankTensor (const ComponentArrayType r)
Pass through constructor for the Array base class *	SymmetricSecondRankTensor (const Self &r)
	SymmetricSecondRankTensor (const ComponentType &r)
	SymmetricSecondRankTensor ()
Static Public Member Functions
static unsigned int	GetNumberOfComponents ()
Public Attributes
Matrix	notation

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Member Typedef Documentation

template<typename TComponent, unsigned int NDimension = 3> typedef NumericTraits<ValueType>::RealType itk::SymmetricSecondRankTensor< TComponent, NDimension >::AccumulateValueType

Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 101 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 89 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef ComponentType itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComponentArrayType[itkGetStaticConstMacro(InternalDimension)]

Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 112 of file itkSymmetricSecondRankTensor.h.

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

Define the component type. Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 99 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef FixedArray<TComponent, NDimension> itk::SymmetricSecondRankTensor< TComponent, NDimension >::EigenValuesArrayType

Array of eigen-values. Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 92 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef Matrix<TComponent, NDimension, NDimension> itk::SymmetricSecondRankTensor< TComponent, NDimension >::EigenVectorsMatrixType

Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 96 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 95 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef NumericTraits<ValueType>::RealType itk::SymmetricSecondRankTensor< TComponent, NDimension >::RealValueType

Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 102 of file itkSymmetricSecondRankTensor.h.

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

Standard class typedefs. Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 79 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef FixedArray<TComponent,NDimension*(NDimension+1)/2 itk::SymmetricSecondRankTensor< TComponent, NDimension >::Superclass)

Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 80 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef SymmetricEigenAnalysis< MatrixType, EigenValuesArrayType, EigenVectorsMatrixType > itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricEigenAnalysisType

Definition at line 105 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> typedef Superclass::ValueType itk::SymmetricSecondRankTensor< TComponent, NDimension >::ValueType

Reimplemented in itk::DiffusionTensor3D< TComponent >. Definition at line 100 of file itkSymmetricSecondRankTensor.h.

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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 108 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor (  const ComponentType &  r  )  [inline]

Definition at line 110 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> Pass through constructor for the Array base class* itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor (  const Self &  r  )  [inline]

Definition at line 115 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor (  const ComponentArrayType  r  )  [inline]

Definition at line 116 of file itkSymmetricSecondRankTensor.h.

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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 146 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> static unsigned int itk::SymmetricSecondRankTensor< TComponent, NDimension >::GetNumberOfComponents (   )  [inline, static]

Return the number of components. Definition at line 140 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3> AccumulateValueType itk::SymmetricSecondRankTensor< TComponent, NDimension >::GetTrace (   )  const

Get Trace value Reimplemented in itk::DiffusionTensor3D< TComponent >.

template<typename TComponent, unsigned int NDimension = 3> itk::SymmetricSecondRankTensor< TComponent, NDimension >::itkStaticConstMacro (  InternalDimension  , unsigned  int, NDimension *(NDimension+1)/  2 )

template<typename TComponent, unsigned int NDimension = 3> Dimension of the vector space* itk::SymmetricSecondRankTensor< TComponent, NDimension >::itkStaticConstMacro (  Dimension  , unsigned  int, NDimension  )

template<typename TComponent, unsigned int NDimension = 3> Arithmetic operations between tensors and scalars* 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> Pass through assignment itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator for the Array base class.*/Self &operator= (  const Self &  r  )

Reimplemented in itk::DiffusionTensor3D< TComponent >.

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> Matrix in const and non const forms* ValueType& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator() (  unsigned int  row, unsigned int  col )

template<typename TComponent, unsigned int NDimension = 3> Aritmetic operations between pixels Return a new SymmetricSecondRankTensor* 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 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> Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= (  const ComponentArrayType  r  )

Reimplemented in itk::DiffusionTensor3D< TComponent >.

template<typename TComponent, unsigned int NDimension = 3> Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= (  const ComponentType &  r  )

Reimplemented in itk::DiffusionTensor3D< TComponent >.

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 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 150 of file itkSymmetricSecondRankTensor.h.

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Member Data Documentation

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

Definition at line 153 of file itkSymmetricSecondRankTensor.h.

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

• itkSymmetricSecondRankTensor.h

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