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@@ Line 1: / Line 1: @@
-=== DTITubeSpatialObject and DTITubeSpatialObjectPoint ===
+This page host a discussion on the implementation details of a Tensor class.
-See [[NAMIC_Wiki:DTI:Fiber_format|Fiber format]] for a discussion of the DTITubeSpatialObject as a file format.
+== Tensors and Traits ==
-An itk::DTITubeSpatialObjectPoint represents DTI information at a physical coordinate. DTITubeSpatialObjectPoints are used to build itk::DTITubeSpatialObjects which can be connected into a tube network.
+Torsten Rohlfing for SRI International Neuroscience Program proposed the following for ITK tensor processing:
-DTITubeSpatialObjectPoint stores the following information:
+* Separate the operations which depend on the tensor size from those that do not.
-* Tensor.
+=== A First version of the SymmetricSecondRankTensor class committed to ITK ===
-** Assumed to be a symmetric tensor of dimension 3.
-** 6 floating point values.
+Given that Tensor can have any rank, from zero (scalar), one (vector), two (matrices) to N. It seemed appropriate to specify that this particular class was representing a symmetric tensor of second rank.
-* Eigenvalues
-** 3 floating point values
+The class has been committed into ITK (May 2 2005) and it is expected to evolve in the CVS repository.
-* Eigenvectors
-** 3 vectors each with 3 floating point values
+=== A first version of SymmetricEigenAnalysis class committed to ITK ===
-* FA
-** float
+Serves as a thread safe alternative to vnl_symmetric_eigensystem, which calls netlib C routines is not thread safe. Please use this class in any multi-threaded filters.
-* GA
-** float
+=== A Hessian filter uses the Symmetric second rank tensor class ===
-* ADC
-** float
+A filter for computing the Hessian of an image was also committed to ITK. This filter illustrates the first use of the SymmetricSecondRankTensor class as pixel type of an image.

@@ Line 1: / Line 1: @@
-== ITK Data Structure for DT Images ==
+=== DTITubeSpatialObject and DTITubeSpatialObjectPoint ===
-Since the itk::Image class is templated over pixel type and dimension, specifying a DT image is simply a matter of instantiating the image class over the appropriate tensor pixel type. However, there may be factors that we need to consider to make such an image practical.
+See [[NAMIC_Wiki:DTI:Fiber_format|Fiber format]] for a discussion of the DTITubeSpatialObject as a file format.
-If we are focusing on 3D symmetric tensors, then each pixel at a minimum needs to store 6 floating point values to describe the tensor. To avoid calculating eigenvalues and eigenvectors multiple times for a given tensor during the course of an algorithm or pipeline of algorithms, there is a temptation to cache the eigenvalue and eigenvectors associated with a tensor. Processing DTI could quickly exhaust physical memory.
+An itk::DTITubeSpatialObjectPoint represents DTI information at a physical coordinate. DTITubeSpatialObjectPoints are used to build itk::DTITubeSpatialObjects which can be connected into a tube network.
-Some ideas to consider:
+DTITubeSpatialObjectPoint stores the following information:
-* Does every pixel in an DT image need to be stored? Are there pixels in the DT image that are outside the anatomical region of interest?
+* Tensor.
-** If so, the DT pixel should have minimum storage, perhaps just an internal pointer to the tensor data. That pointer could be null if the tensor for that pixel is not needed.
+** Assumed to be a symmetric tensor of dimension 3.
-* Should the DT pixel be able to cache structure information (eigenvalues and eigenvectors)?
+** 6 floating point values.
-** The DT pixel could cache this information is the algorithm requested.
+* Eigenvalues
-** Tensor::ComputeEigenSystem(cache = true)
+** 3 floating point values
-** Could have methods to destroy cached data
+* Eigenvectors
-** Or should caching this type of information be left to the algorithm developer. An algorithm could separate data structures for caching eigenvalues and eigenvectors.
+** 3 vectors each with 3 floating point values
-* Should the DT pixel type store FA and ADC?
+* FA

@@ Line 1: / Line 1: @@
-Header for proposed itkSymmetricTensorTraits.
+== ITK Data Structure for DT Images ==
- <nowiki>
+Since the itk::Image class is templated over pixel type and dimension, specifying a DT image is simply a matter of instantiating the image class over the appropriate tensor pixel type. However, there may be factors that we need to consider to make such an image practical.
- /*=========================================================================
+If we are focusing on 3D symmetric tensors, then each pixel at a minimum needs to store 6 floating point values to describe the tensor. To avoid calculating eigenvalues and eigenvectors multiple times for a given tensor during the course of an algorithm or pipeline of algorithms, there is a temptation to cache the eigenvalue and eigenvectors associated with a tensor. Processing DTI could quickly exhaust physical memory.
-   Program:   Insight Segmentation & Registration Toolkit
-   Module:    $RCSfile: itkSymmetricTensorTraits.h,v $
+Some ideas to consider:
-   Language:  C++
-   Date:      $Date$
+* Does every pixel in an DT image need to be stored? Are there pixels in the DT image that are outside the anatomical region of interest?
-   Version:   $Revision$
+** If so, the DT pixel should have minimum storage, perhaps just an internal pointer to the tensor data. That pointer could be null if the tensor for that pixel is not needed.
+* Should the DT pixel be able to cache structure information (eigenvalues and eigenvectors)?
-   Copyright (c) Insight Software Consortium. All rights reserved.
+** The DT pixel could cache this information is the algorithm requested.
-   See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.
+** Tensor::ComputeEigenSystem(cache = true)
+** Could have methods to destroy cached data
-      This software is distributed WITHOUT ANY WARRANTY; without even
+** Or should caching this type of information be left to the algorithm developer. An algorithm could separate data structures for caching eigenvalues and eigenvectors.
-      the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+* Should the DT pixel type store FA and ADC?

@@ Line 1: / Line 1: @@
-Header for proposed itkSymmetricTensor.
+Header for proposed itkSymmetricTensorTraits.
   <nowiki>
@@ Line 5: / Line 5: @@
     Program:   Insight Segmentation & Registration Toolkit
-    Module:    $RCSfile: itkSymmetricTensor.txx,v $
+    Module:    $RCSfile: itkSymmetricTensorTraits.h,v $
     Language:  C++
-    Date:      $Date: 2004/04/15 22:37:33 $
+    Date:      $Date$
-    Version:   $Revision: 1.10 $
+    Version:   $Revision$
     Copyright (c) Insight Software Consortium. All rights reserved.
@@ Line 19: / Line 19: @@
   =========================================================================*/
-  #ifndef __itkSymmetricTensor_h
+  #ifndef __itkSymmetricTensorTraits_h
-  #define __itkSymmetricTensor_h
+  #define __itkSymmetricTensorTraits_h
   #include "itkFixedArray.h"
   namespace itk
+  {
-  /** \class itkSymmetricTensor
+  /** \class itkSymmetricTensorTraits
+   *
    */
-  template
+  template<typename TRealType, unsigned int VTensorDimension>
-  < typename TRealType = float, unsigned int VTensorDimension = 3,
+  class ITK_EXPORT SymmetricTensorTraits
+  {
-  public:
+ public:
-    /// The compact linear vector dimension of the tensor.
+    static const unsigned int NTensorDimension = VTensorDimension;
     static const unsigned int NVectorDimension =
-     VTensorDimension*(VTensorDimension+1)/2;
+   VTensorDimension * (VTensorDimension+1) / 2;
     /** Standard class typedefs. */
-    typedef SymmetricTensor Self;
+    typedef SymmetricTensorTraits Self;
-   typedef SmartPointer<Self> Pointer;
+    typedef FixedArray<TRealType,NVectorDimension> SymmetricTensorBaseType;
-    /** Run-time type information (and related methods) */
+    /// Perform eigenvalue computation.
-    itkTypeMacro(SymmetricTensor, FixedArray);
+    static void ComputeEigenvalues( const SymmetricTensorBaseType& tensor,
-   /** Define the data type and the vector of data type used in calculations.
+ /// Specialization for 3D tensors.
-    */
+ template<typename TRealType>
-    typedef TRealType RealType;
+ class ITK_EXPORT SymmetricTensorTraits<TRealType,3>
-   typedef vnl_matrix_fixed<TRealType,VTensorDimension,VTensorDimension> VnlMatrixType;
+    /** Standard class typedefs. */
-    /* Return vnl_matrix object. We do this here, since it's always the same,
+    typedef SymmetricTensorTraits Self;
-    * regardless of tensor size.
+    typedef FixedArray<TRealType,NVectorDimension> SymmetricTensorBaseType;
- protected:
+   /// Perform eigenvalue computation.
-    void PrintSelf(std::ostream& os, Indent indent) const;
+    static void ComputeEigenvalues( const SymmetricTensorBaseType& tensor,
   };
@@ Line 108: / Line 66: @@
   #ifndef ITK_MANUAL_INSTANTIATION
-  #include "itkSymmetricTensor.txx"
+  #include "itkSymmetricTensorTraits.txx"
   #endif

@@ Line 1: / Line 1: @@
-== Draft of Pixel Type implementation ==
+Header for proposed itkSymmetricTensor.
-The following pages contain a proposed implementation (in the spirit of extreme programming) of a pixel type for diffusion tensor images.
+ <nowiki>
+ /*=========================================================================
-* [[NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType:Header|Header ]]
-* [[NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType:Implementation|Implementation ]]
+   Program:   Insight Segmentation & Registration Toolkit
-* [[NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType:Test|Test ]]
+   Module:    $RCSfile: itkSymmetricTensor.txx,v $
+   Language:  C++
-Other proposals have been made to the ITK mailing list.
+   Date:      $Date: 2004/04/15 22:37:33 $
+   Version:   $Revision: 1.10 $
-* [[NAMIC_Wiki:DTI:ITK-TensorsAndTraits|Tensors and Traits]]
-* [[NAMIC_Wiki:DTI:ITK-DTITubeSpatialObjectPoint|DTI Spatial Object]]
+   Copyright (c) Insight Software Consortium. All rights reserved.