NAMIC Wiki:DTI:ITK-DiffusionTensorPixelType:Header

The DiffusionTensorPixel type derives from the itk::FixedArray<> instantiated for a fixed size of 6 elements. The rationale behind it is that we are dealing with symmetric tensors in this particular case, therefore for the sake of memory use we only store 6 components. The type however will also implement a matrix-like notation in order to provide a natural notation for tensor operations.

A short version of the class essentials is below, a full compilable version is at the end of this page

template < typename TComponent = float >
class DiffusionTensorPixel: public FixedArray<TComponent,6>
{
public:
  typedef DiffusionTensorPixel  Self;
  typedef FixedArray<TComponent, 6> SuperClass;
  itkStaticConstMacro(Dimension, unsigned int, 6);
  itkStaticConstMacro(Length, unsigned int, 6);
  typedef FixedArray<TComponent, 6> BaseArray;

  /** Array of eigen-values. */
  typedef FixedArray<TComponent, 3> EigenValuesArray;
  typedef Matrix<TComponent, 3, 3>  EigenVectorsMatrix;

  /** Matrix notation, in const and non-const forms. */
  ValueType & operator()( unsigned int i, unsigned int j);
  const ValueType & operator()( unsigned int i, unsigned int j) const;
};

Here is the full version of the class. This code is compilable using ITK 2.0.

 #ifndef __itkDiffusionTensorPixel_h
 #define __itkDiffusionTensorPixel_h
 
 // Undefine an eventual DiffusionTensorPixel macro
 #ifdef DiffusionTensorPixel
 #undef DiffusionTensorPixel
 #endif
 
 #include <itkIndent.h>
 #include <itkFixedArray.h>
 #include <itkMatrix.h>
 #include "vnl/vnl_math.h"
 
 namespace itk
 {
 
 /** \class DiffusionTensorPixel
  * \brief Represent a diffusion tensor as used in DTI images.
  *
  * This class implements a 3D symmetric tensor as it is used for representing
  * diffusion of water molecules in Diffusion Tensor Images.
  *
  * Since DiffusionTensorPixel is a subclass of Array, you can access its components as:
  *
  * typedef itk::DiffusionTensorPixel< 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 3x3 matrix, but given that it is
  * always symmetric the representation can be compacted into a 6-elements
  * array that derives from the itk::FixedArray<T>
  *
  * \ingroup ImageObjects
  */
 
 template < typename TComponent = float >
 class DiffusionTensorPixel: public FixedArray<TComponent,6>
 {
 public:
   /** Standard class typedefs. */
   typedef DiffusionTensorPixel  Self;
   typedef FixedArray<TComponent, 6> SuperClass;
 
   /** Dimension of the vector space. */
   itkStaticConstMacro(Dimension, unsigned int, 6);
   itkStaticConstMacro(Length, unsigned int, 6);
 
   /** Convenience typedefs. */
   typedef FixedArray<TComponent, 6> BaseArray;
 
   /** Array of eigen-values. */
   typedef FixedArray<TComponent, 3> EigenValuesArray;
 
   /** Matrix of eigen-vectors. */
   typedef Matrix<TComponent, 3, 3> EigenVectorsMatrix;
 
   /**  Define the component type. */
   typedef TComponent ComponentType;
   typedef typename SuperClass::ValueType ValueType;
 
   /** Default constructor has nothing to do. */
   DiffusionTensorPixel() {this->Fill(0);}
   DiffusionTensorPixel (const ComponentType& r) { this->Fill(r); }
 
   /** Pass-through constructor for the Array base class. */
   DiffusionTensorPixel(const Self& r): BaseArray(r) {}
   DiffusionTensorPixel(const ComponentType  r[6]): BaseArray(r) {}
 
   /** Pass-through assignment operator for the Array base class. */
   Self& operator= (const Self& r);
   Self& operator= (const ComponentType r[6]);
 
   /** Aritmetic operations between pixels. Return a new DiffusionTensorPixel. */
   Self operator+(const Self &vec) const;
   Self operator-(const Self &vec) const;
   const Self & operator+=(const Self &vec);
   const Self & operator-=(const Self &vec);
   Self operator*(const ComponentType &f) const;
 
 
   /** Return the number of components. */
   static int GetNumberOfComponents(){ return 6;}
 
   /** Return the value for the Nth component. */
   ComponentType GetNthComponent(int c) const
     { return this->operator[](c); }
 
   /** Set the Nth component to v. */
   void SetNthComponent(int c, const ComponentType& v)
     {  this->operator[](c) = v; }
 
   /** Matrix notation, in const and non-const forms. */
   ValueType & operator()( unsigned int i, unsigned int j);
   const ValueType & operator()( unsigned int i, unsigned int j) const;
 
 };
 
 
 template< typename TComponent  >
 ITK_EXPORT std::ostream& operator<<(std::ostream& os,
                                     const DiffusionTensorPixel<TComponent> & c);
 template< typename TComponent  >
 ITK_EXPORT std::istream& operator>>(std::istream& is,
                                           DiffusionTensorPixel<TComponent> & c);
 
 } // end namespace itk
 
 #ifndef ITK_MANUAL_INSTANTIATION
 #include "itkDiffusionTensorPixel.txx"
 #endif
 
 #endif