ITK  4.13.0
Insight Segmentation and Registration Toolkit
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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 ValueTypeconst_pointer
 
typedef const ValueTypeconst_reference
 
typedef const ValueTypeConstIterator
 
typedef ValueTypeIterator
 
typedef ValueTypepointer
 
typedef ValueTypereference
 
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
 
ValueTypeoperator() (unsigned int row, unsigned int col)
 
const ValueTypeoperator() (unsigned int row, unsigned int col) const
 
Self operator* (const RealValueType &scalar) const
 
const Selfoperator*= (const RealValueType &scalar)
 
Self operator+ (const Self &vec) const
 
const Selfoperator+= (const Self &vec)
 
Self operator- (const Self &vec) const
 
const Selfoperator-= (const Self &vec)
 
Self operator/ (const RealValueType &scalar) const
 
const Selfoperator/= (const RealValueType &scalar)
 
Selfoperator= (const ComponentType &r)
 
Selfoperator= (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 >
Selfoperator= (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)
 
ValueTypeGetDataPointer ()
 
const ValueTypeGetDataPointer () const
 
bool operator!= (const FixedArray &r) const
 
FixedArrayoperator= (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)
 
FixedArrayoperator= (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()

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.


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