libinsighttoolkit3-dev 3.20.1-1 / usr / include / InsightToolkit / Review / itkOptMattesMutualInformationImageToImageMetric.txx

/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    itkOptMattesMutualInformationImageToImageMetric.txx
  Language:  C++
  Date:      $Date$
  Version:   $Revision$

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef __itkOptMattesMutualInformationImageToImageMetric_txx
#define __itkOptMattesMutualInformationImageToImageMetric_txx

#include "itkOptMattesMutualInformationImageToImageMetric.h"
#include "itkCovariantVector.h"
#include "itkImageRandomConstIteratorWithIndex.h"
#include "itkImageRegionConstIterator.h"
#include "itkImageRegionIterator.h"
#include "itkImageIterator.h"
#include "vnl/vnl_math.h"
#include "itkStatisticsImageFilter.h"

#include "vnl/vnl_vector.txx"
#include "vnl/vnl_c_vector.txx"

namespace itk
{

/**
 * Constructor
 */
template < class TFixedImage, class TMovingImage >
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::MattesMutualInformationImageToImageMetric()
{
  m_NumberOfHistogramBins = 50;

  this->SetComputeGradient(false); // don't use the default gradient for now

  // Initialize PDFs to NULL
  m_JointPDF = NULL;
  m_JointPDFDerivatives = NULL;

  // Initialize memory
  m_FixedImageMarginalPDF = NULL;
  m_MovingImageMarginalPDF = NULL;

  m_MovingImageNormalizedMin = 0.0;
  m_FixedImageNormalizedMin = 0.0;
  m_MovingImageTrueMin = 0.0;
  m_MovingImageTrueMax = 0.0;
  m_FixedImageBinSize = 0.0;
  m_MovingImageBinSize = 0.0;

  m_CubicBSplineDerivativeKernel = NULL;

  // For multi-threading the metric
  m_ThreaderFixedImageMarginalPDF = NULL;
  m_ThreaderJointPDF = NULL;
  m_ThreaderJointPDFDerivatives = NULL;
  m_ThreaderJointPDFStartBin = NULL;
  m_ThreaderJointPDFEndBin = NULL;
  m_ThreaderJointPDFSum = NULL;
  this->m_WithinThreadPreProcess = true;
  this->m_WithinThreadPostProcess = false;

  this->m_ThreaderMetricDerivative = NULL;
  this->m_UseExplicitPDFDerivatives = true;
  this->m_ImplicitDerivativesSecondPass = false;
}

template < class TFixedImage, class TMovingImage >
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::~MattesMutualInformationImageToImageMetric()
{

  if(m_FixedImageMarginalPDF != NULL)
    {
    delete [] m_FixedImageMarginalPDF;
    }
  m_FixedImageMarginalPDF = NULL;
  if(m_MovingImageMarginalPDF != NULL)
    {
    delete [] m_MovingImageMarginalPDF;
    }
  m_MovingImageMarginalPDF = NULL;
  if(m_ThreaderJointPDF != NULL)
    {
    delete [] m_ThreaderJointPDF;
    }
  m_ThreaderJointPDF = NULL;

  if(m_ThreaderJointPDFDerivatives != NULL)
    {
    delete [] m_ThreaderJointPDFDerivatives;
    }
  m_ThreaderJointPDFDerivatives = NULL;

  if(m_ThreaderFixedImageMarginalPDF != NULL)
    {
    delete [] m_ThreaderFixedImageMarginalPDF;
    }
  m_ThreaderFixedImageMarginalPDF = NULL;

  if(m_ThreaderJointPDFStartBin != NULL)
    {
    delete [] m_ThreaderJointPDFStartBin;
    }
  m_ThreaderJointPDFStartBin = NULL;

  if(m_ThreaderJointPDFEndBin != NULL)
    {
    delete [] m_ThreaderJointPDFEndBin;
    }
  m_ThreaderJointPDFEndBin = NULL;

  if(m_ThreaderJointPDFSum != NULL)
    {
    delete [] m_ThreaderJointPDFSum;
    }
  m_ThreaderJointPDFSum = NULL;

  if( this->m_ThreaderMetricDerivative != NULL )
    {
    delete [] this->m_ThreaderMetricDerivative;
    }
  this->m_ThreaderMetricDerivative = NULL;
}

/**
 * Print out internal information about this class
 */
template < class TFixedImage, class TMovingImage  >
void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::PrintSelf(std::ostream& os, Indent indent) const
{

  Superclass::PrintSelf(os, indent);

  os << indent << "NumberOfHistogramBins: ";
  os << this->m_NumberOfHistogramBins << std::endl;

  // Debugging information
  os << indent << "FixedImageNormalizedMin: ";
  os << this->m_FixedImageNormalizedMin << std::endl;
  os << indent << "MovingImageNormalizedMin: ";
  os << this->m_MovingImageNormalizedMin << std::endl;
  os << indent << "MovingImageTrueMin: ";
  os << this->m_MovingImageTrueMin << std::endl;
  os << indent << "MovingImageTrueMax: ";
  os << this->m_MovingImageTrueMax << std::endl;
  os << indent << "FixedImageBinSize: ";
  os << this->m_FixedImageBinSize << std::endl;
  os << indent << "MovingImageBinSize: ";
  os << this->m_MovingImageBinSize << std::endl;
  os << indent << "UseExplicitPDFDerivatives: ";
  os << this->m_UseExplicitPDFDerivatives << std::endl;
  os << indent << "ImplicitDerivativesSecondPass: ";
  os << this->m_ImplicitDerivativesSecondPass << std::endl;

}


/**
 * Initialize
 */
template <class TFixedImage, class TMovingImage>
void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::Initialize(void) throw ( ExceptionObject )
{
  this->Superclass::Initialize();
  this->Superclass::MultiThreadingInitialize();

  typedef StatisticsImageFilter<FixedImageType> FixedImageStatisticsFilterType;
  typename FixedImageStatisticsFilterType::Pointer fixedImageStats =
                                         FixedImageStatisticsFilterType::New();
  fixedImageStats->SetInput( this->m_FixedImage );
  fixedImageStats->SetNumberOfThreads( this->m_NumberOfThreads );
  fixedImageStats->Update();

  m_FixedImageTrueMin = fixedImageStats->GetMinimum();
  m_FixedImageTrueMax = fixedImageStats->GetMaximum();
  double fixedImageMin = m_FixedImageTrueMin;
  double fixedImageMax = m_FixedImageTrueMax;

  typedef StatisticsImageFilter<MovingImageType>
                                                MovingImageStatisticsFilterType;
  typename MovingImageStatisticsFilterType::Pointer movingImageStats =
                                         MovingImageStatisticsFilterType::New();
  movingImageStats->SetInput( this->m_MovingImage );
  movingImageStats->SetNumberOfThreads( this->m_NumberOfThreads );
  movingImageStats->Update();

  m_MovingImageTrueMin = movingImageStats->GetMinimum();
  m_MovingImageTrueMax = movingImageStats->GetMaximum();
  double movingImageMin = m_MovingImageTrueMin;
  double movingImageMax = m_MovingImageTrueMax;

  itkDebugMacro( " FixedImageMin: " << fixedImageMin <<
                 " FixedImageMax: " << fixedImageMax << std::endl );
  itkDebugMacro( " MovingImageMin: " << movingImageMin <<
                 " MovingImageMax: " << movingImageMax << std::endl );


  /**
   * Compute binsize for the histograms.
   *
   * The binsize for the image intensities needs to be adjusted so that
   * we can avoid dealing with boundary conditions using the cubic
   * spline as the Parzen window.  We do this by increasing the size
   * of the bins so that the joint histogram becomes "padded" at the
   * borders. Because we are changing the binsize,
   * we also need to shift the minimum by the padded amount in order to
   * avoid minimum values filling in our padded region.
   *
   * Note that there can still be non-zero bin values in the padded region,
   * it's just that these bins will never be a central bin for the Parzen
   * window.
   *
   */
  const int padding = 2;  // this will pad by 2 bins

  m_FixedImageBinSize = ( fixedImageMax - fixedImageMin )
                        / static_cast<double>( m_NumberOfHistogramBins
                                               - 2 * padding );
  m_FixedImageNormalizedMin = fixedImageMin / m_FixedImageBinSize
                              - static_cast<double>( padding );

  m_MovingImageBinSize = ( movingImageMax - movingImageMin )
                         / static_cast<double>( m_NumberOfHistogramBins
                                                - 2 * padding );
  m_MovingImageNormalizedMin = movingImageMin / m_MovingImageBinSize
                               - static_cast<double>( padding );

  itkDebugMacro( "FixedImageNormalizedMin: " << m_FixedImageNormalizedMin );
  itkDebugMacro( "MovingImageNormalizedMin: " << m_MovingImageNormalizedMin );
  itkDebugMacro( "FixedImageBinSize: " << m_FixedImageBinSize );
  itkDebugMacro( "MovingImageBinSize; " << m_MovingImageBinSize );


  /**
   * Allocate memory for the marginal PDF and initialize values
   * to zero. The marginal PDFs are stored as std::vector.
   */
  if(m_FixedImageMarginalPDF != NULL)
    {
    delete [] m_FixedImageMarginalPDF;
    }
  m_FixedImageMarginalPDF = new PDFValueType[m_NumberOfHistogramBins];
  if(m_MovingImageMarginalPDF != NULL)
    {
    delete [] m_MovingImageMarginalPDF;
    }
  m_MovingImageMarginalPDF = new PDFValueType[m_NumberOfHistogramBins];

  /**
   * Allocate memory for the joint PDF and joint PDF derivatives.
   * The joint PDF and joint PDF derivatives are store as itk::Image.
   */
  m_JointPDF = JointPDFType::New();
  m_JointPDFDerivatives = JointPDFDerivativesType::New();

  // Instantiate a region, index, size
  JointPDFRegionType             jointPDFRegion;
  JointPDFIndexType              jointPDFIndex;
  JointPDFSizeType               jointPDFSize;

  // Deallocate the memory that may have been allocated for 
  // previous runs of the metric.
  this->m_JointPDFDerivatives = NULL;  // by destroying the dynamic array
  this->m_PRatioArray.SetSize( 1, 1 ); // and by allocating very small the static ones
  this->m_MetricDerivative = DerivativeType( 1 );

  JointPDFDerivativesRegionType  jointPDFDerivativesRegion;
     
  // 
  // Now allocate memory according to the user-selected method.
  //
  if( this->m_UseExplicitPDFDerivatives )
    {
    this->m_JointPDFDerivatives = JointPDFDerivativesType::New();

    JointPDFDerivativesIndexType  jointPDFDerivativesIndex;
    JointPDFDerivativesSizeType    jointPDFDerivativesSize;

    // For the derivatives of the joint PDF define a region starting from {0,0,0} 
    // with size {m_NumberOfParameters,m_NumberOfHistogramBins, 
    // m_NumberOfHistogramBins}. The dimension represents transform parameters,
    // fixed image parzen window index and moving image parzen window index,
    // respectively. 
    jointPDFDerivativesIndex.Fill( 0 ); 
    jointPDFDerivativesSize[0] = this->m_NumberOfParameters;
    jointPDFDerivativesSize[1] = this->m_NumberOfHistogramBins;
    jointPDFDerivativesSize[2] = this->m_NumberOfHistogramBins;

    jointPDFDerivativesRegion.SetIndex( jointPDFDerivativesIndex );
    jointPDFDerivativesRegion.SetSize( jointPDFDerivativesSize );

    // Set the regions and allocate
    m_JointPDFDerivatives->SetRegions( jointPDFDerivativesRegion );
    m_JointPDFDerivatives->Allocate();
    m_JointPDFDerivativesBufferSize = jointPDFDerivativesSize[0]
                                    * jointPDFDerivativesSize[1]
                                    * jointPDFDerivativesSize[2]
                                    * sizeof(JointPDFDerivativesValueType);

    }
  else
    {
    /** Allocate memory for helper array that will contain the pRatios
     *  for each bin of the joint histogram. This is part of the effort
     *  for flattening the computation of the PDF Jacobians.
     */
    this->m_PRatioArray.SetSize( this->m_NumberOfHistogramBins, this->m_NumberOfHistogramBins );
    this->m_MetricDerivative = DerivativeType( this->GetNumberOfParameters() );
    }

  // For the joint PDF define a region starting from {0,0}
  // with size {m_NumberOfHistogramBins, m_NumberOfHistogramBins}.
  // The dimension represents fixed image parzen window index
  // and moving image parzen window index, respectively.
  jointPDFIndex.Fill( 0 );
  jointPDFSize.Fill( m_NumberOfHistogramBins );

  jointPDFRegion.SetIndex( jointPDFIndex );
  jointPDFRegion.SetSize( jointPDFSize );

  // Set the regions and allocate
  m_JointPDF->SetRegions( jointPDFRegion );
  m_JointPDF->Allocate();

  m_JointPDFBufferSize = jointPDFSize[0] * jointPDFSize[1] * sizeof(PDFValueType);


  /**
   * Setup the kernels used for the Parzen windows.
   */
  m_CubicBSplineKernel = CubicBSplineFunctionType::New();
  m_CubicBSplineDerivativeKernel = CubicBSplineDerivativeFunctionType::New();

  /**
   * Pre-compute the fixed image parzen window index for
   * each point of the fixed image sample points list.
   */
  this->ComputeFixedImageParzenWindowIndices( this->m_FixedImageSamples );


  if(m_ThreaderFixedImageMarginalPDF != NULL)
    {
    delete [] m_ThreaderFixedImageMarginalPDF;
    }
  // Assumes number of threads doesn't change between calls to Initialize
  m_ThreaderFixedImageMarginalPDF = new
                                    PDFValueType[(this->m_NumberOfThreads-1)
                                                 * m_NumberOfHistogramBins];

  if(m_ThreaderJointPDF != NULL)
    {
    delete [] m_ThreaderJointPDF;
    }
  m_ThreaderJointPDF = new typename
                               JointPDFType::Pointer[this->m_NumberOfThreads-1];

  if(m_ThreaderJointPDFStartBin != NULL)
    {
    delete [] m_ThreaderJointPDFStartBin;
    }
  m_ThreaderJointPDFStartBin = new int[this->m_NumberOfThreads];

  if(m_ThreaderJointPDFEndBin != NULL)
    {
    delete [] m_ThreaderJointPDFEndBin;
    }
  m_ThreaderJointPDFEndBin = new int[this->m_NumberOfThreads];

  if(m_ThreaderJointPDFSum != NULL)
    {
    delete [] m_ThreaderJointPDFSum;
    }
  m_ThreaderJointPDFSum = new double[this->m_NumberOfThreads];

  unsigned int threadID;

  int binRange = m_NumberOfHistogramBins / this->m_NumberOfThreads;

  for(threadID = 0; threadID < this->m_NumberOfThreads-1; threadID++)
    {
    m_ThreaderJointPDF[threadID] = JointPDFType::New();
    m_ThreaderJointPDF[threadID]->SetRegions( jointPDFRegion );
    m_ThreaderJointPDF[threadID]->Allocate();

    m_ThreaderJointPDFStartBin[threadID] = threadID * binRange;
    m_ThreaderJointPDFEndBin[threadID] = (threadID + 1) * binRange - 1;
    }

  m_ThreaderJointPDFStartBin[this->m_NumberOfThreads-1] = 
    (this->m_NumberOfThreads - 1 ) * binRange;

  m_ThreaderJointPDFEndBin[this->m_NumberOfThreads-1] = m_NumberOfHistogramBins - 1;

  // Release memory of arrays that may have been used for 
  // previous executions of this metric with different settings
  // of the memory caching flags.
  if(m_ThreaderJointPDFDerivatives != NULL)
    {
    delete [] m_ThreaderJointPDFDerivatives;
    }
  m_ThreaderJointPDFDerivatives = NULL;

  if(m_ThreaderMetricDerivative != NULL)
    {
    delete [] m_ThreaderMetricDerivative;
    }
  m_ThreaderMetricDerivative = NULL;


  if( this->m_UseExplicitPDFDerivatives )
    {
    m_ThreaderJointPDFDerivatives = new typename
                      JointPDFDerivativesType::Pointer[this->m_NumberOfThreads-1];

    for(threadID = 0; threadID < this->m_NumberOfThreads-1; threadID++)
      {
      m_ThreaderJointPDFDerivatives[threadID] = JointPDFDerivativesType::New();
      m_ThreaderJointPDFDerivatives[threadID]->SetRegions(
                                                   jointPDFDerivativesRegion );
      m_ThreaderJointPDFDerivatives[threadID]->Allocate();
      }
    }
   else
    {
    m_ThreaderMetricDerivative = new DerivativeType[this->m_NumberOfThreads-1];

    for(threadID = 0; threadID < this->m_NumberOfThreads-1; threadID++)
      {
      this->m_ThreaderMetricDerivative[threadID] = DerivativeType( this->GetNumberOfParameters() );
      }
    }
}

/**
 * Uniformly sample the fixed image domain using a random walk
 */
template < class TFixedImage, class TMovingImage >
void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::ComputeFixedImageParzenWindowIndices(
           FixedImageSampleContainer& samples )
{

  typename FixedImageSampleContainer::iterator iter;
  typename FixedImageSampleContainer::const_iterator end=samples.end();

  for( iter=samples.begin(); iter != end; ++iter )
    {

    // Determine parzen window arguments (see eqn 6 of Mattes paper [2]).
    double windowTerm = static_cast<double>( (*iter).value )
                        / m_FixedImageBinSize
                        - m_FixedImageNormalizedMin;
    OffsetValueType pindex = static_cast<OffsetValueType>( windowTerm );

    // Make sure the extreme values are in valid bins
    if ( pindex < 2 )
      {
      pindex = 2;
      }
    else 
      {
      const OffsetValueType nindex = 
        static_cast< OffsetValueType >( this->m_NumberOfHistogramBins ) - 3;
      if ( pindex > nindex )
        {
        pindex = nindex;
        }
      }

    (*iter).valueIndex = pindex;
    }

}

template < class TFixedImage, class TMovingImage  >
inline void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueThreadPreProcess( unsigned int threadID,
                            bool withinSampleThread ) const
{

  this->Superclass::GetValueThreadPreProcess( threadID, withinSampleThread );

  if(threadID > 0)
    {
    memset( m_ThreaderJointPDF[threadID-1]->GetBufferPointer(),
            0,
            m_JointPDFBufferSize );
    memset( &(m_ThreaderFixedImageMarginalPDF[(threadID-1)
                                              *m_NumberOfHistogramBins]),
            0,
            m_NumberOfHistogramBins*sizeof(PDFValueType) );
    }
  else
    {
    // zero-th thread uses the variables directly
    memset( m_JointPDF->GetBufferPointer(),
            0,
            m_JointPDFBufferSize );
    memset( m_FixedImageMarginalPDF,
            0,
            m_NumberOfHistogramBins*sizeof(PDFValueType) );
    }
}

template < class TFixedImage, class TMovingImage  >
inline bool
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueThreadProcessSample( unsigned int threadID,
                               unsigned long fixedImageSample,
                               const MovingImagePointType & itkNotUsed(mappedPoint),
                               double movingImageValue) const
{
  /**
   * Compute this sample's contribution to the marginal and
   * joint distributions.
   *
   */

  if(movingImageValue < m_MovingImageTrueMin)
    {
    return false;
    }
  else if(movingImageValue > m_MovingImageTrueMax)
    {
    return false;
    }

  // Determine parzen window arguments (see eqn 6 of Mattes paper [2]).
  double movingImageParzenWindowTerm = movingImageValue
                                       / m_MovingImageBinSize
                                       - m_MovingImageNormalizedMin;
  // Same as floor
  OffsetValueType movingImageParzenWindowIndex =
    static_cast<OffsetValueType>( movingImageParzenWindowTerm );
  if( movingImageParzenWindowIndex < 2 )
    {
    movingImageParzenWindowIndex = 2;
    }
  else 
    {
    const OffsetValueType nindex = 
      static_cast< OffsetValueType >( this->m_NumberOfHistogramBins ) - 3;
    if( movingImageParzenWindowIndex > nindex )
      {
      movingImageParzenWindowIndex = nindex;
      }
    }

  unsigned int fixedImageParzenWindowIndex =
                      this->m_FixedImageSamples[fixedImageSample].valueIndex;
  if(threadID > 0)
    {
    m_ThreaderFixedImageMarginalPDF[(threadID-1)*m_NumberOfHistogramBins
                                    + fixedImageParzenWindowIndex] += 1;
    }
  else
    {
    m_FixedImageMarginalPDF[fixedImageParzenWindowIndex] += 1;
    }

  // Pointer to affected bin to be updated
  JointPDFValueType *pdfPtr;
  if(threadID > 0)
    {
    pdfPtr = m_ThreaderJointPDF[threadID-1]->GetBufferPointer() +
                               ( fixedImageParzenWindowIndex
                                 * m_ThreaderJointPDF[threadID-1]
                                    ->GetOffsetTable()[1] );
    }
  else
    {
    pdfPtr = m_JointPDF->GetBufferPointer() +
                               ( fixedImageParzenWindowIndex
                                 * m_JointPDF->GetOffsetTable()[1] );
    }

  // Move the pointer to the first affected bin
  int pdfMovingIndex = static_cast<int>( movingImageParzenWindowIndex ) - 1;
  pdfPtr += pdfMovingIndex;
  int pdfMovingIndexMax = static_cast<int>(movingImageParzenWindowIndex) + 2;

  double movingImageParzenWindowArg =
                    static_cast<double>( pdfMovingIndex )
                     - movingImageParzenWindowTerm;

  while( pdfMovingIndex <= pdfMovingIndexMax )
    {
    *(pdfPtr++) += static_cast<PDFValueType>( m_CubicBSplineKernel
                                              ->Evaluate(
                                                movingImageParzenWindowArg ) );
    movingImageParzenWindowArg += 1;
    ++pdfMovingIndex;
    }

  return true;
}

template < class TFixedImage, class TMovingImage  >
inline void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueThreadPostProcess( unsigned int threadID,
                             bool itkNotUsed(withinSampleThread) ) const
{
    unsigned int t;
    int i;
    int maxI;
    maxI = m_NumberOfHistogramBins
           * ( m_ThreaderJointPDFEndBin[threadID]
               - m_ThreaderJointPDFStartBin[threadID] + 1);
    JointPDFValueType *pdfPtr;
    JointPDFValueType *pdfPtrStart;
    pdfPtrStart = m_JointPDF->GetBufferPointer()
                  + ( m_ThreaderJointPDFStartBin[threadID]
                      * m_JointPDF->GetOffsetTable()[1] );
    JointPDFValueType *tPdfPtr;
    JointPDFValueType *tPdfPtrEnd;
    unsigned int       tPdfPtrOffset;
    tPdfPtrOffset = ( m_ThreaderJointPDFStartBin[threadID]
                      * m_JointPDF->GetOffsetTable()[1] );
    for(t=0; t<this->m_NumberOfThreads-1; t++)
      {
      pdfPtr = pdfPtrStart;
      tPdfPtr = m_ThreaderJointPDF[t]->GetBufferPointer() + tPdfPtrOffset;
      tPdfPtrEnd = tPdfPtr + maxI;
      //for(i=0; i < maxI; i++)
      while(tPdfPtr < tPdfPtrEnd)
        {
        *(pdfPtr++) += *(tPdfPtr++);
        }
      for(i = m_ThreaderJointPDFStartBin[threadID];
          i <= m_ThreaderJointPDFEndBin[threadID];
          i++)
        {
        m_FixedImageMarginalPDF[i] += m_ThreaderFixedImageMarginalPDF[
                                          (t*m_NumberOfHistogramBins) + i];
        }
      }
    double jointPDFSum = 0.0;
    pdfPtr = pdfPtrStart;
    for(i = 0; i < maxI; i++)
      {
      jointPDFSum += *(pdfPtr++);
      }
    if(threadID > 0)
      {
      m_ThreaderJointPDFSum[threadID-1] = jointPDFSum;
      }
    else
      {
      m_JointPDFSum = jointPDFSum;
      }
}

template < class TFixedImage, class TMovingImage  >
typename MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::MeasureType
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValue( const ParametersType & parameters ) const
{
  // Set up the parameters in the transform
  this->m_Transform->SetParameters( parameters );
  this->m_Parameters = parameters;

  // MUST BE CALLED TO INITIATE PROCESSING
  this->GetValueMultiThreadedInitiate();

  // MUST BE CALLED TO INITIATE PROCESSING
  this->GetValueMultiThreadedPostProcessInitiate();

  for(unsigned int threadID = 0; threadID<this->m_NumberOfThreads-1; threadID++)
    {
    m_JointPDFSum += m_ThreaderJointPDFSum[threadID];
    }
  if ( m_JointPDFSum == 0.0 )
    {
    itkExceptionMacro( "Joint PDF summed to zero" );
    }

  memset( m_MovingImageMarginalPDF,
          0,
          m_NumberOfHistogramBins*sizeof(PDFValueType) );

  JointPDFValueType * pdfPtr;
  PDFValueType * movingMarginalPtr;
  unsigned int i, j;
  double fixedPDFSum = 0.0;
  double nFactor = 1.0 / m_JointPDFSum;
  pdfPtr = m_JointPDF->GetBufferPointer();
  for(i=0; i<m_NumberOfHistogramBins; i++)
    {
    fixedPDFSum += m_FixedImageMarginalPDF[i];
    movingMarginalPtr = m_MovingImageMarginalPDF;
    for(j=0; j<m_NumberOfHistogramBins; j++)
      {
      *(pdfPtr) *= nFactor;
      *(movingMarginalPtr++) += *(pdfPtr++);
      }
    }

  if( this->m_NumberOfPixelsCounted <
      this->m_NumberOfFixedImageSamples / 16 )
    {
    itkExceptionMacro( "Too many samples map outside moving image buffer: "
                       << this->m_NumberOfPixelsCounted << " / "
                       << this->m_NumberOfFixedImageSamples
                       << std::endl );
    }

  // Normalize the fixed image marginal PDF
  if ( fixedPDFSum == 0.0 )
    {
    itkExceptionMacro( "Fixed image marginal PDF summed to zero" );
    }
  for( unsigned int bin=0; bin < m_NumberOfHistogramBins; bin++ )
    {
    m_FixedImageMarginalPDF[bin] /= fixedPDFSum;
    }

  /**
   * Compute the metric by double summation over histogram.
   */

  // Setup pointer to point to the first bin
  JointPDFValueType * jointPDFPtr = m_JointPDF->GetBufferPointer();

  double sum = 0.0;

  for( unsigned int fixedIndex = 0;
       fixedIndex < m_NumberOfHistogramBins;
       ++fixedIndex )
    {
    double fixedImagePDFValue = m_FixedImageMarginalPDF[fixedIndex];

    for( unsigned int movingIndex = 0;
         movingIndex < m_NumberOfHistogramBins;
         ++movingIndex, jointPDFPtr++ )
      {
      double movingImagePDFValue = m_MovingImageMarginalPDF[movingIndex];
      double jointPDFValue = *(jointPDFPtr);

      // check for non-zero bin contribution
      if( jointPDFValue > 1e-16 &&  movingImagePDFValue > 1e-16 )
        {

        double pRatio = vcl_log(jointPDFValue / movingImagePDFValue );
        if( fixedImagePDFValue > 1e-16)
          {
          sum += jointPDFValue * ( pRatio - vcl_log(fixedImagePDFValue ) );
          }

        }  // end if-block to check non-zero bin contribution
      }  // end for-loop over moving index
    }  // end for-loop over fixed index

  return static_cast<MeasureType>( -1.0 * sum );

}


template < class TFixedImage, class TMovingImage  >
inline void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueAndDerivativeThreadPreProcess( unsigned int threadID,
                                         bool itkNotUsed(withinSampleThread) ) const
{
  if(threadID > 0)
    {
    memset( m_ThreaderJointPDF[threadID-1]->GetBufferPointer(),
            0,
            m_JointPDFBufferSize );

    memset( &(m_ThreaderFixedImageMarginalPDF[(threadID-1)
                                              * m_NumberOfHistogramBins]),
            0,
            m_NumberOfHistogramBins*sizeof(PDFValueType) );

    if( this->m_UseExplicitPDFDerivatives )
      {
      memset( m_ThreaderJointPDFDerivatives[threadID-1]->GetBufferPointer(),
              0,
              m_JointPDFDerivativesBufferSize );
      }
    }
  else
    {
    memset( m_JointPDF->GetBufferPointer(),
            0,
            m_JointPDFBufferSize );
    memset( m_FixedImageMarginalPDF,
            0,
            m_NumberOfHistogramBins*sizeof(PDFValueType) );

    if( this->m_UseExplicitPDFDerivatives )
      {
      memset( m_JointPDFDerivatives->GetBufferPointer(),
              0,
              m_JointPDFDerivativesBufferSize );
      }
    }
}

template < class TFixedImage, class TMovingImage  >
inline bool
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueAndDerivativeThreadProcessSample( unsigned int threadID,
                         unsigned long fixedImageSample,
                         const MovingImagePointType & itkNotUsed(mappedPoint),
                         double movingImageValue,
                         const ImageDerivativesType &
                         movingImageGradientValue) const
{
  /**
   * Compute this sample's contribution to the marginal
   *   and joint distributions.
   *
   */
  if(movingImageValue < m_MovingImageTrueMin)
    {
    return false;
    }
  else if(movingImageValue > m_MovingImageTrueMax)
    {
    return false;
    }

  unsigned int fixedImageParzenWindowIndex =
                      this->m_FixedImageSamples[fixedImageSample].valueIndex;

  // Determine parzen window arguments (see eqn 6 of Mattes paper [2]).
  double movingImageParzenWindowTerm = movingImageValue
                                       / m_MovingImageBinSize
                                       - m_MovingImageNormalizedMin;
  OffsetValueType movingImageParzenWindowIndex =
    static_cast<OffsetValueType>( movingImageParzenWindowTerm );

  // Make sure the extreme values are in valid bins
  if ( movingImageParzenWindowIndex < 2 )
    {
    movingImageParzenWindowIndex = 2;
    }
  else
    {
    const OffsetValueType nindex = 
      static_cast< OffsetValueType >( this->m_NumberOfHistogramBins ) - 3;
    if ( movingImageParzenWindowIndex > nindex )
      {
      movingImageParzenWindowIndex = nindex;
      }
    }

  // Since a zero-order BSpline (box car) kernel is used for
  // the fixed image marginal pdf, we need only increment the
  // fixedImageParzenWindowIndex by value of 1.0.
  if(threadID > 0)
    {
    ++m_ThreaderFixedImageMarginalPDF[(threadID-1)*m_NumberOfHistogramBins
                                      + fixedImageParzenWindowIndex];
    }
  else
    {
    ++m_FixedImageMarginalPDF[fixedImageParzenWindowIndex];
    }

  /**
    * The region of support of the parzen window determines which bins
    * of the joint PDF are effected by the pair of image values.
    * Since we are using a cubic spline for the moving image parzen
    * window, four bins are effected.  The fixed image parzen window is
    * a zero-order spline (box car) and thus effects only one bin.
    *
    *  The PDF is arranged so that moving image bins corresponds to the
    * zero-th (column) dimension and the fixed image bins corresponds
    * to the first (row) dimension.
    *
    */

  // Pointer to affected bin to be updated
  JointPDFValueType *pdfPtr;
  if(threadID > 0)
    {
    pdfPtr = m_ThreaderJointPDF[threadID-1]
                               ->GetBufferPointer() +
                               ( fixedImageParzenWindowIndex
                                 * m_NumberOfHistogramBins );
    }
  else
    {
    pdfPtr = m_JointPDF->GetBufferPointer() +
                               ( fixedImageParzenWindowIndex
                                 * m_NumberOfHistogramBins );
    }

  // Move the pointer to the fist affected bin
  int pdfMovingIndex = static_cast<int>( movingImageParzenWindowIndex ) - 1;
  pdfPtr += pdfMovingIndex;
  int pdfMovingIndexMax = static_cast<int>(movingImageParzenWindowIndex) + 2;

  double movingImageParzenWindowArg = static_cast<double>( pdfMovingIndex )
                          - static_cast<double>( movingImageParzenWindowTerm );

  while( pdfMovingIndex <= pdfMovingIndexMax )
    {
    *(pdfPtr++) += static_cast<PDFValueType>( m_CubicBSplineKernel
                                              ->Evaluate(
                                                movingImageParzenWindowArg ) );

    if( this->m_UseExplicitPDFDerivatives || this->m_ImplicitDerivativesSecondPass )
      {
      // Compute the cubicBSplineDerivative for later repeated use.
      double cubicBSplineDerivativeValue = 
        m_CubicBSplineDerivativeKernel->Evaluate( movingImageParzenWindowArg );

      // Compute PDF derivative contribution.
      this->ComputePDFDerivatives( threadID,
                                   fixedImageSample,
                                   pdfMovingIndex,
                                   movingImageGradientValue,
                                   cubicBSplineDerivativeValue );
       }

    movingImageParzenWindowArg += 1;
    ++pdfMovingIndex;
    }

  return true;
}

template < class TFixedImage, class TMovingImage  >
inline void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueAndDerivativeThreadPostProcess( unsigned int threadID,
                                          bool withinSampleThread ) const
{
  this->GetValueThreadPostProcess( threadID, withinSampleThread );

  if( this->m_UseExplicitPDFDerivatives )
    {
    const unsigned int rowSize = this->m_NumberOfParameters * m_NumberOfHistogramBins;
   
    const unsigned int maxI =
      rowSize * ( m_ThreaderJointPDFEndBin[threadID]
                - m_ThreaderJointPDFStartBin[threadID] + 1 );

    JointPDFDerivativesValueType *pdfDPtr;
    JointPDFDerivativesValueType *pdfDPtrStart;
    pdfDPtrStart = m_JointPDFDerivatives->GetBufferPointer()
                   + ( m_ThreaderJointPDFStartBin[threadID] * rowSize );
    JointPDFDerivativesValueType *tPdfDPtr;
    JointPDFDerivativesValueType *tPdfDPtrEnd;
    unsigned int tPdfDPtrOffset;
    tPdfDPtrOffset = m_ThreaderJointPDFStartBin[threadID] *  rowSize;
    for(unsigned int t=0; t<this->m_NumberOfThreads-1; t++)
      {
      pdfDPtr = pdfDPtrStart;
      tPdfDPtr = m_ThreaderJointPDFDerivatives[t]->GetBufferPointer()
                 + tPdfDPtrOffset;
      tPdfDPtrEnd = tPdfDPtr + maxI;
      // for(i = 0; i < maxI; i++)
      while(tPdfDPtr < tPdfDPtrEnd)
        {
        *(pdfDPtr++) += *(tPdfDPtr++);
        }
      }

    double nFactor = 1.0 / (m_MovingImageBinSize
                            * this->m_NumberOfPixelsCounted);

    pdfDPtr = pdfDPtrStart;
    tPdfDPtrEnd = pdfDPtrStart + maxI;
    //for(int i = 0; i < maxI; i++)
    while(pdfDPtr < tPdfDPtrEnd)
      {
      *(pdfDPtr++) *= nFactor;
      }
    }
}

/**
 * Get the both Value and Derivative Measure
 */
template < class TFixedImage, class TMovingImage  >
void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetValueAndDerivative( const ParametersType & parameters,
                         MeasureType & value,
                         DerivativeType & derivative) const
{
  // Set output values to zero
  value = NumericTraits< MeasureType >::Zero;

  if( this->m_UseExplicitPDFDerivatives )
    {
    // Set output values to zero
    if(derivative.GetSize() != this->m_NumberOfParameters)
      {
      derivative = DerivativeType( this->m_NumberOfParameters );
      }
    memset( derivative.data_block(),
            0,
            this->m_NumberOfParameters * sizeof(double) );
    }
  else
    {
    this->m_PRatioArray.Fill( 0.0 );
    this->m_MetricDerivative.Fill( NumericTraits< MeasureType >::Zero );
    for(unsigned int threadID = 0; threadID < this->m_NumberOfThreads-1; threadID++ )
      {
      this->m_ThreaderMetricDerivative[threadID].Fill( NumericTraits< MeasureType >::Zero );
      }
    this->m_ImplicitDerivativesSecondPass = false;
    }

  // Set up the parameters in the transform
  this->m_Transform->SetParameters( parameters );
  this->m_Parameters = parameters;

  // MUST BE CALLED TO INITIATE PROCESSING ON SAMPLES
  this->GetValueAndDerivativeMultiThreadedInitiate();

  // CALL IF DOING THREADED POST PROCESSING
  this->GetValueAndDerivativeMultiThreadedPostProcessInitiate();

  for(unsigned int threadID = 0; threadID<this->m_NumberOfThreads-1; threadID++)
    {
    m_JointPDFSum += m_ThreaderJointPDFSum[threadID];
    }
  if ( m_JointPDFSum == 0.0 )
    {
    itkExceptionMacro( "Joint PDF summed to zero" );
    }

  memset( m_MovingImageMarginalPDF,
          0,
          m_NumberOfHistogramBins*sizeof(PDFValueType) );

  JointPDFValueType * pdfPtr;
  PDFValueType * movingMarginalPtr;
  unsigned int i, j;
  double fixedPDFSum = 0.0;
  const double normalizationFactor = 1.0 / m_JointPDFSum;

  pdfPtr = m_JointPDF->GetBufferPointer();
  for(i=0; i<m_NumberOfHistogramBins; i++)
    {
    fixedPDFSum += m_FixedImageMarginalPDF[i];
    movingMarginalPtr = m_MovingImageMarginalPDF;
    for(j=0; j<m_NumberOfHistogramBins; j++)
      {
      *(pdfPtr) *= normalizationFactor;
      *(movingMarginalPtr++) += *(pdfPtr++);
      }
    }

  if( this->m_NumberOfPixelsCounted <
      this->m_NumberOfFixedImageSamples / 16 )
    {
    itkExceptionMacro( "Too many samples map outside moving image buffer: "
                       << this->m_NumberOfPixelsCounted << " / "
                       << this->m_NumberOfFixedImageSamples
                       << std::endl );
    }

  // Normalize the fixed image marginal PDF
  if ( fixedPDFSum == 0.0 )
    {
    itkExceptionMacro( "Fixed image marginal PDF summed to zero" );
    }
  for( unsigned int bin=0; bin < m_NumberOfHistogramBins; bin++ )
    {
    m_FixedImageMarginalPDF[bin] /= fixedPDFSum;
    }

  /**
   * Compute the metric by double summation over histogram.
   */

  // Setup pointer to point to the first bin
  JointPDFValueType * jointPDFPtr = m_JointPDF->GetBufferPointer();

  // Initialize sum to zero
  double sum = 0.0;

  const double nFactor = 1.0 / (m_MovingImageBinSize
                            * this->m_NumberOfPixelsCounted);

  for( unsigned int fixedIndex = 0;
       fixedIndex < m_NumberOfHistogramBins;
       ++fixedIndex )
    {
    double fixedImagePDFValue = m_FixedImageMarginalPDF[fixedIndex];

    for( unsigned int movingIndex = 0;
         movingIndex < m_NumberOfHistogramBins;
         ++movingIndex, jointPDFPtr++ )
      {
      double movingImagePDFValue = m_MovingImageMarginalPDF[movingIndex];
      double jointPDFValue = *(jointPDFPtr);

      // check for non-zero bin contribution
      if( jointPDFValue > 1e-16 &&  movingImagePDFValue > 1e-16 )
        {

        double pRatio = vcl_log(jointPDFValue / movingImagePDFValue );

        if( fixedImagePDFValue > 1e-16)
          {
          sum += jointPDFValue * ( pRatio - vcl_log(fixedImagePDFValue ) );
          }

        if( this->m_UseExplicitPDFDerivatives )
          {
          // move joint pdf derivative pointer to the right position
          JointPDFValueType * derivPtr = m_JointPDFDerivatives->GetBufferPointer()
             + ( fixedIndex  * m_JointPDFDerivatives->GetOffsetTable()[2] )
             + ( movingIndex * m_JointPDFDerivatives->GetOffsetTable()[1] );

          for( unsigned int parameter=0; parameter < this->m_NumberOfParameters; ++parameter, derivPtr++ )
            {

            // Ref: eqn 23 of Thevenaz & Unser paper [3]
            derivative[parameter] -= (*derivPtr) * pRatio;

            }  // end for-loop over parameters
          }
        else
          {
          this->m_PRatioArray[fixedIndex][movingIndex] = pRatio * nFactor;
          }
        }  // end if-block to check non-zero bin contribution
      }  // end for-loop over moving index
    }  // end for-loop over fixed index

  if( !(this->m_UseExplicitPDFDerivatives ) )
    {
    // Second pass: This one is done for accumulating the contributions
    //              to the derivative array.
    //
    this->m_ImplicitDerivativesSecondPass = true;
    //
    // MUST BE CALLED TO INITIATE PROCESSING ON SAMPLES
    this->GetValueAndDerivativeMultiThreadedInitiate();

    // CALL IF DOING THREADED POST PROCESSING
    this->GetValueAndDerivativeMultiThreadedPostProcessInitiate();

    // Consolidate the contributions from each one of the threads to the total
    // derivative.
    for(unsigned int t = 0; t < this->m_NumberOfThreads-1; t++ )
      {
      DerivativeType * source = &(this->m_ThreaderMetricDerivative[t]);
      for(unsigned int pp=0; pp < this->m_NumberOfParameters; pp++ )
        {
        this->m_MetricDerivative[pp] += (*source)[pp];
        }
      }

    derivative = this->m_MetricDerivative;
    }

  value = static_cast<MeasureType>( -1.0 * sum );

}

/**
 * Get the match measure derivative
 */
template < class TFixedImage, class TMovingImage  >
void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::GetDerivative( const ParametersType & parameters,
                 DerivativeType & derivative ) const
{
  MeasureType value;
  // call the combined version
  this->GetValueAndDerivative( parameters, value, derivative );
}


/**
 * Compute PDF derivatives contribution for each parameter
 */
template < class TFixedImage, class TMovingImage >
void
MattesMutualInformationImageToImageMetric<TFixedImage,TMovingImage>
::ComputePDFDerivatives( unsigned int threadID,
                         unsigned int sampleNumber,
                         int pdfMovingIndex,
                         const ImageDerivativesType & movingImageGradientValue,
                         double cubicBSplineDerivativeValue ) const
{
  // Update bins in the PDF derivatives for the current intensity pair
  // Could pre-compute
  JointPDFDerivativesValueType * derivPtr;

  double precomputedWeight = 0.0;

  const int pdfFixedIndex = this->m_FixedImageSamples[sampleNumber].valueIndex;

  DerivativeType * derivativeHelperArray = NULL;

  if( this->m_UseExplicitPDFDerivatives )
    {
    if(threadID > 0)
      {
      derivPtr = m_ThreaderJointPDFDerivatives[threadID-1]->GetBufferPointer()
        + ( pdfFixedIndex  * m_JointPDFDerivatives->GetOffsetTable()[2] )
        + ( pdfMovingIndex * m_JointPDFDerivatives->GetOffsetTable()[1] );
      }
    else
      {
      derivPtr = m_JointPDFDerivatives->GetBufferPointer()
        + ( pdfFixedIndex  * m_JointPDFDerivatives->GetOffsetTable()[2] )
        + ( pdfMovingIndex * m_JointPDFDerivatives->GetOffsetTable()[1] );
      }
    }
  else
    {
    derivPtr = 0;
    // Recover the precomputed weight for this specific PDF bin
    precomputedWeight = this->m_PRatioArray[pdfFixedIndex][pdfMovingIndex];
    if(threadID > 0)
      {
      derivativeHelperArray = &(this->m_ThreaderMetricDerivative[threadID-1]);
      }
    else
      {
      derivativeHelperArray = &(this->m_MetricDerivative);
      }

    }

  if( !this->m_TransformIsBSpline )
    {
    /**
     * Generic version which works for all transforms.
     */

    // Compute the transform Jacobian.
    // Should pre-compute
    typedef typename TransformType::JacobianType JacobianType;

    // Need to use one of the threader transforms if we're
    // not in thread 0.
    //
    // Use a raw pointer here to avoid the overhead of smart pointers.
    // For instance, Register and UnRegister have mutex locks around
    // the reference counts.
    TransformType* transform;

    if (threadID > 0)
      {
      transform = this->m_ThreaderTransform[threadID - 1];
      }
    else
      {
      transform = this->m_Transform;
      }

    const JacobianType& jacobian = 
      transform->GetJacobian( this->m_FixedImageSamples[sampleNumber].point );

    for ( unsigned int mu = 0; mu < this->m_NumberOfParameters; mu++ )
      {
      double innerProduct = 0.0;
      for ( unsigned int dim = 0; dim < Superclass::FixedImageDimension; dim++ )
        {
        innerProduct += jacobian[dim][mu] * movingImageGradientValue[dim];
        }

      const double derivativeContribution = innerProduct * cubicBSplineDerivativeValue;

      if( this->m_UseExplicitPDFDerivatives )
        {
        *(derivPtr) -= derivativeContribution;
        ++derivPtr; 
        }
      else
        {
        (*derivativeHelperArray)[mu] += precomputedWeight * derivativeContribution;
        }
      }
    }
  else
    {
    const WeightsValueType * weights = NULL;
    const IndexValueType   * indices = NULL;

    
    BSplineTransformWeightsType    * weightsHelper = NULL;
    BSplineTransformIndexArrayType * indicesHelper = NULL; 

    if( this->m_UseCachingOfBSplineWeights )
      {
      // 
      // If the transform is of type BSplineDeformableTransform, we can obtain
      // a speed up by only processing the affected parameters.  Note that
      // these pointers are just pointing to pre-allocated rows of the caching
      // arrays. There is therefore, no need to free this memory.
      // 
      weights = this->m_BSplineTransformWeightsArray[sampleNumber];
      indices = this->m_BSplineTransformIndicesArray[sampleNumber];
      }
    else
      {
      if( threadID > 0 )
        {
        weightsHelper = &(this->m_ThreaderBSplineTransformWeights[threadID-1]);
        indicesHelper = &(this->m_ThreaderBSplineTransformIndices[threadID-1]);
        }
      else
        {
        weightsHelper = &(this->m_BSplineTransformWeights);
        indicesHelper = &(this->m_BSplineTransformIndices);
        }

      this->m_BSplineTransform->GetJacobian(  
        this->m_FixedImageSamples[sampleNumber].point, 
        *weightsHelper, *indicesHelper );
      }

    for( unsigned int dim = 0; dim < Superclass::FixedImageDimension; dim++ )
      {

      double innerProduct;
      int parameterIndex;

      for( unsigned int mu = 0; mu < this->m_NumBSplineWeights; mu++ )
        {

        /* The array weights contains the Jacobian values in a 1-D array 
         * (because for each parameter the Jacobian is non-zero in only 1 of the
         * possible dimensions) which is multiplied by the moving image 
         * gradient. */
        if( this->m_UseCachingOfBSplineWeights )
          {
          innerProduct = movingImageGradientValue[dim] * weights[mu];
          parameterIndex = indices[mu] + this->m_BSplineParametersOffset[dim];
          }
        else
          {
          innerProduct = movingImageGradientValue[dim] * (*weightsHelper)[mu];
          parameterIndex = (*indicesHelper)[mu] + this->m_BSplineParametersOffset[dim];
          }

        const double derivativeContribution = innerProduct * cubicBSplineDerivativeValue;

        if( this->m_UseExplicitPDFDerivatives )
          {
          JointPDFValueType * ptr = derivPtr + parameterIndex;
          *(ptr) -= derivativeContribution;
          }
        else
          {
          (*derivativeHelperArray)[parameterIndex] += precomputedWeight * derivativeContribution;
          }

        } //end mu for loop
      } //end dim for loop

    } // end if-block transform is BSpline

}


} // end namespace itk


#endif