| 1 |
|
/*========================================================================= |
| 2 |
|
|
| 3 |
|
Program: Insight Segmentation & Registration Toolkit |
| 4 |
|
Module: $RCSfile: itkSymmetricSecondRankTensor.h.html,v $ |
| 5 |
|
Language: C++ |
| 6 |
|
Date: $Date: 2006/01/17 19:15:48 $ |
| 7 |
|
Version: $Revision: 1.4 $ |
| 8 |
|
|
| 9 |
|
Copyright (c) Insight Software Consortium. All rights reserved. |
| 10 |
|
See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details. |
| 11 |
|
|
| 12 |
|
This software is distributed WITHOUT ANY WARRANTY; without even |
| 13 |
|
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
| 14 |
|
PURPOSE. See the above copyright notices for more information. |
| 15 |
|
|
| 16 |
|
=========================================================================*/ |
| 17 |
|
#ifndef __itkSymmetricSecondRankTensor_h |
| 18 |
|
#define __itkSymmetricSecondRankTensor_h |
| 19 |
|
|
| 20 |
|
// Undefine an eventual SymmetricSecondRankTensor macro |
| 21 |
|
#ifdef SymmetricSecondRankTensor |
| 22 |
|
#undef SymmetricSecondRankTensor |
| 23 |
|
#endif |
| 24 |
|
|
| 25 |
|
#include <itkIndent.h> |
| 26 |
|
#include <itkFixedArray.h> |
| 27 |
|
#include <itkMatrix.h> |
| 28 |
|
#include "itkSymmetricEigenAnalysis.h" |
| 29 |
|
|
| 30 |
|
namespace itk |
| 31 |
|
{ |
| 32 |
|
|
| 33 |
|
/** \class SymmetricSecondRankTensor |
| 34 |
|
* \brief Represent a symmetric tensor of second rank. |
| 35 |
|
* |
| 36 |
|
* This class implements a ND symmetric tensor of second rank. |
| 37 |
|
* |
| 38 |
|
* Since SymmetricSecondRankTensor is a subclass of FixedArray, |
| 39 |
|
* you can access its components as: |
| 40 |
|
* |
| 41 |
|
* typedef itk::SymmetricSecondRankTensor< float > TensorPixelType; |
| 42 |
|
* TensorPixelType tensor; |
| 43 |
|
* |
| 44 |
|
* tensor[0] = 1.233; |
| 45 |
|
* tensor[1] = 1.456; |
| 46 |
|
* |
| 47 |
|
* for convenience the indexed access is also available as |
| 48 |
|
* |
| 49 |
|
* tensor(0,0) = 1.233; |
| 50 |
|
* tensor(2,0) = 1.233; |
| 51 |
|
* |
| 52 |
|
* The Tensor in principle represents a NxN matrix, but given that it is always |
| 53 |
|
* symmetric the representation can be compacted into a N*(N+1)/2 elements |
| 54 |
|
* array that derives from the itk::FixedArray<T> |
| 55 |
|
* |
| 56 |
|
* \author Jeffrey Duda from School of Engineering at University of Pennsylvania |
| 57 |
|
* \author Torsten Rohlfing from SRI International Neuroscience Program. |
| 58 |
|
* |
| 59 |
|
* This class was mostly based on files that Jeffrey Duda, Torsten Rohlfing and |
| 60 |
|
* Martin Styner contributed to the ITK users list during a discussion on |
| 61 |
|
* support for DiffusionTensorImages. The funding for creating this class was |
| 62 |
|
* largely provided by NAMIC (National Alliance for Medical Image Computing) |
| 63 |
|
* (http://www.na-mic.org). A discussion on the design of this class can be |
| 64 |
|
* found in the WIKI pages of NAMIC: |
| 65 |
|
* |
| 66 |
LEN |
* http://www.na-mic.org/Wiki/index.php/NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType |
| 67 |
|
* |
| 68 |
|
* \sa DiffusionTensor3D |
| 69 |
|
* |
| 70 |
|
* \ingroup ImageObjects TensorObjects Geometry |
| 71 |
|
*/ |
| 72 |
|
|
| 73 |
|
template < typename TComponent, unsigned int NDimension=3 > |
| 74 |
|
class SymmetricSecondRankTensor: public |
| 75 |
IND |
********FixedArray<TComponent,NDimension*(NDimension+1)/2> |
| 76 |
|
{ |
| 77 |
|
public: |
| 78 |
|
/** Standard class typedefs. */ |
| 79 |
|
typedef SymmetricSecondRankTensor Self; |
| 80 |
TDA |
typedef FixedArray<TComponent,NDimension*(NDimension+1)/2> Superclass; |
| 81 |
|
|
| 82 |
|
/** Dimension of the vector space. */ |
| 83 |
|
itkStaticConstMacro(Dimension, unsigned int, NDimension); |
| 84 |
LEN |
itkStaticConstMacro(InternalDimension, unsigned int, NDimension*(NDimension+1)/2); |
| 85 |
|
|
| 86 |
|
/** Convenience typedefs. */ |
| 87 |
|
typedef FixedArray<TComponent, |
| 88 |
|
itkGetStaticConstMacro(InternalDimension)> BaseArray; |
| 89 |
|
|
| 90 |
|
/** Array of eigen-values. */ |
| 91 |
|
typedef FixedArray<TComponent, NDimension> EigenValuesArrayType; |
| 92 |
|
|
| 93 |
|
/** Matrix of eigen-vectors. */ |
| 94 |
|
typedef Matrix<TComponent, NDimension, NDimension> MatrixType; |
| 95 |
|
typedef Matrix<TComponent, NDimension, NDimension> EigenVectorsMatrixType; |
| 96 |
|
|
| 97 |
|
/** Define the component type. */ |
| 98 |
|
typedef TComponent ComponentType; |
| 99 |
TDA |
typedef typename Superclass::ValueType ValueType; |
| 100 |
TDA |
typedef typename NumericTraits<ValueType>::RealType AccumulateValueType; |
| 101 |
TDA |
typedef typename NumericTraits<ValueType>::RealType RealValueType; |
| 102 |
|
|
| 103 |
|
typedef SymmetricEigenAnalysis< MatrixType, |
| 104 |
LEN |
EigenValuesArrayType, EigenVectorsMatrixType > SymmetricEigenAnalysisType; |
| 105 |
|
|
| 106 |
|
/** Default constructor has nothing to do. */ |
| 107 |
|
SymmetricSecondRankTensor() {this->Fill(0);} |
| 108 |
|
|
| 109 |
|
SymmetricSecondRankTensor (const ComponentType& r) { this->Fill(r); } |
| 110 |
|
|
| 111 |
LEN,TDR |
typedef ComponentType ComponentArrayType[ itkGetStaticConstMacro(InternalDimension) ]; |
| 112 |
|
|
| 113 |
|
/** Pass-through constructor for the Array base class. */ |
| 114 |
|
SymmetricSecondRankTensor(const Self& r): BaseArray(r) {} |
| 115 |
|
SymmetricSecondRankTensor(const ComponentArrayType r): BaseArray(r) {} |
| 116 |
|
|
| 117 |
|
/** Pass-through assignment operator for the Array base class. */ |
| 118 |
|
Self& operator= (const Self& r); |
| 119 |
|
Self& operator= (const ComponentType& r); |
| 120 |
|
Self& operator= (const ComponentArrayType r); |
| 121 |
|
|
| 122 |
LEN |
/** Aritmetic operations between pixels. Return a new SymmetricSecondRankTensor. */ |
| 123 |
|
Self operator+(const Self &vec) const; |
| 124 |
|
Self operator-(const Self &vec) const; |
| 125 |
|
const Self & operator+=(const Self &vec); |
| 126 |
|
const Self & operator-=(const Self &vec); |
| 127 |
|
|
| 128 |
|
/** Arithmetic operations between tensors and scalars */ |
| 129 |
|
Self operator*(const RealValueType & scalar ) const; |
| 130 |
|
Self operator/(const RealValueType & scalar ) const; |
| 131 |
|
const Self & operator*=(const RealValueType & scalar ); |
| 132 |
|
const Self & operator/=(const RealValueType & scalar ); |
| 133 |
|
|
| 134 |
|
/** Return the number of components. */ |
| 135 |
|
static unsigned int GetNumberOfComponents() |
| 136 |
|
{ |
| 137 |
|
return itkGetStaticConstMacro(InternalDimension); |
| 138 |
|
} |
| 139 |
|
|
| 140 |
|
/** Return the value for the Nth component. */ |
| 141 |
|
ComponentType GetNthComponent(int c) const |
| 142 |
|
{ return this->operator[](c); } |
| 143 |
|
|
| 144 |
|
/** Set the Nth component to v. */ |
| 145 |
|
void SetNthComponent(int c, const ComponentType& v) |
| 146 |
|
{ this->operator[](c) = v; } |
| 147 |
|
|
| 148 |
|
/** Matrix notation, in const and non-const forms. */ |
| 149 |
|
ValueType & operator()( unsigned int row, unsigned int col ); |
| 150 |
|
const ValueType & operator()( unsigned int row, unsigned int col ) const; |
| 151 |
|
|
| 152 |
|
/** Set the tensor to an identity tensor. This has 1 in its diagonal elements |
| 153 |
|
* zero elsewhere */ |
| 154 |
|
void SetIdentity(); |
| 155 |
|
|
| 156 |
|
/** Get Trace value */ |
| 157 |
|
AccumulateValueType GetTrace() const; |
| 158 |
|
|
| 159 |
|
/** Return an array containing EigenValues. */ |
| 160 |
|
void ComputeEigenValues( EigenValuesArrayType & eigenValues ) const; |
| 161 |
|
|
| 162 |
|
/** Return an array containing EigenValues, and a matrix containing Eigen |
| 163 |
|
* vectors. */ |
| 164 |
|
void ComputeEigenAnalysis( EigenValuesArrayType & eigenValues, |
| 165 |
|
EigenVectorsMatrixType & eigenVectors ) const; |
| 166 |
|
|
| 167 |
|
private: |
| 168 |
|
|
| 169 |
|
|
| 170 |
|
}; |
| 171 |
|
|
| 172 |
|
/** This extra typedef is necessary for preventing an Internal Compiler Error in |
| 173 |
LEN |
* Microsoft Visual C++ 6.0. This typedef is not needed for any other compiler. */ |
| 174 |
|
typedef std::ostream OutputStreamType; |
| 175 |
|
typedef std::istream InputStreamType; |
| 176 |
|
|
| 177 |
|
template< typename TComponent, unsigned int NDimension > |
| 178 |
|
ITK_EXPORT OutputStreamType& operator<<(OutputStreamType& os, |
| 179 |
|
const SymmetricSecondRankTensor<TComponent,NDimension> & c); |
| 180 |
|
template< typename TComponent, unsigned int NDimension > |
| 181 |
|
ITK_EXPORT InputStreamType& operator>>(InputStreamType& is, |
| 182 |
|
SymmetricSecondRankTensor<TComponent,NDimension> & c); |
| 183 |
|
|
| 184 |
|
template <typename TValueType, unsigned int VLength> |
| 185 |
|
inline SymmetricSecondRankTensor< TValueType, VLength> operator* |
| 186 |
IND |
****(double d, const SymmetricSecondRankTensor< TValueType, VLength > & f) |
| 187 |
|
{ |
| 188 |
|
return f * d; |
| 189 |
|
} |
| 190 |
|
|
| 191 |
|
|
| 192 |
EML |
|
| 193 |
|
} // end namespace itk |
| 194 |
|
|
| 195 |
|
#ifndef ITK_MANUAL_INSTANTIATION |
| 196 |
|
#include "itkSymmetricSecondRankTensor.txx" |
| 197 |
|
#endif |
| 198 |
|
|
| 199 |
|
#endif |
| 200 |
|
|
