libinsighttoolkit4-dev 4.5.0-3 / usr / include / ITK-4.5 / itkFEMImageMetricLoad.hxx

/*=========================================================================
 *
 *  Copyright Insight Software Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
#ifndef __itkFEMImageMetricLoad_hxx
#define __itkFEMImageMetricLoad_hxx

#include "itkFEMImageMetricLoad.h"

namespace itk
{
namespace fem
{
// Overload the CreateAnother() method.
template <typename TMoving, typename TFixed>
::itk::LightObject::Pointer
ImageMetricLoad<TMoving, TFixed>
::CreateAnother(void) const
{
  ::itk::LightObject::Pointer smartPtr;
  Pointer copyPtr = Self::New();

  // Copy Load Contents
  copyPtr->m_MetricGradientImage = this->m_MetricGradientImage;
  copyPtr->m_RefImage = this->m_RefImage;
  copyPtr->m_TarImage = this->m_TarImage;
  copyPtr->m_MetricRadius = this->m_MetricRadius;
  copyPtr->m_RefSize = this->m_RefSize;
  copyPtr->m_TarSize = this->m_TarSize;

  copyPtr->m_NumberOfIntegrationPoints = this->m_NumberOfIntegrationPoints;
  copyPtr->m_SolutionIndex = this->m_SolutionIndex;
  copyPtr->m_SolutionIndex2 = this->m_SolutionIndex2;
  copyPtr->m_Sign = this->m_Sign;
  copyPtr->m_Temp = this->m_Temp;
  copyPtr->m_Gamma = this->m_Gamma;

  copyPtr->m_Solution = this->m_Solution;
  copyPtr->m_Metric = this->m_Metric;
  copyPtr->m_Transform = this->m_Transform;
  copyPtr->m_Interpolator = this->m_Interpolator;
  copyPtr->m_Energy = this->m_Energy;

  smartPtr = static_cast<Pointer>(copyPtr);

  return smartPtr;
}

template <typename TMoving, typename TFixed>
void
ImageMetricLoad<TMoving, TFixed>
::InitializeMetric(void)
{
  if( !m_Transform )
    {
    m_Transform = DefaultTransformType::New();
    }
  if( !m_Metric )
    {
    m_Metric = DefaultMetricType::New();
    }

  m_Temp = 0.0;
  m_Gamma = 1.0;
  m_Energy = 0.0;

// ------------------------------------------------------------
// Set up the metric -- see MetricTest in Testing
// ------------------------------------------------------------

  m_Metric->SetMovingImage(m_RefImage);
  m_Metric->SetFixedImage(m_TarImage);

  typename FixedType::RegionType requestedRegion;
  typename FixedType::SizeType   size;
  typename FixedType::IndexType  tindex;
//  typename MovingType::IndexType rindex;
// initialize the offset/vector part
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    // Set the size of the image region
    size[k] = 1;
    tindex[k] = 0;
    }

  // Set the number of integration points to zero (default for an element)

  m_NumberOfIntegrationPoints = 0;

  // Set the associated region
  requestedRegion.SetSize(size);
  requestedRegion.SetIndex(tindex);
  m_TarImage->SetRequestedRegion(requestedRegion);
  m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );

  m_Metric->SetTransform( m_Transform.GetPointer() );
  m_Interpolator = InterpolatorType::New();
  m_Interpolator->SetInputImage(m_RefImage);
  m_Metric->SetInterpolator( m_Interpolator.GetPointer() );

  // ------------------------------------------------------------
  // This call is mandatory before start querying the Metric
  // This method do all the necessary connections between the
  // internal components: Interpolator, Transform and Images
  // ------------------------------------------------------------
  try
    {
    m_Metric->Initialize();
    }
  catch( ExceptionObject & e )
    {
    std::cout << "Metric initialization failed" << std::endl;
    std::cout << "Reason " << e.GetDescription() << std::endl;
    }
}

template <typename TMoving, typename TFixed>
ImageMetricLoad<TMoving, TFixed>
::ImageMetricLoad()
{
  m_Metric = NULL;
  m_Transform = NULL;
  m_SolutionIndex = 1;
  m_SolutionIndex2 = 0;
  m_Sign = 1.0;
  for( unsigned int i = 0; i < ImageDimension; i++ )
    {
    m_MetricRadius[i] = 1;
    }
  m_MetricGradientImage = NULL;
}

template <typename TMoving, typename TFixed>
typename ImageMetricLoad<TMoving, TFixed>::Float
ImageMetricLoad<TMoving, TFixed>
::EvaluateMetricGivenSolution(Element::ArrayType *element, Float step)
{
  Float energy = 0.0, defe = 0.0;

  vnl_vector_fixed<Float, 2 *ImageDimension> InVec(0.0);

  Element::VectorType ip, shapef;
  Element::MatrixType solmat;
  Element::Float      w;

  Element::ArrayType::iterator elt = element->begin();
  const unsigned int           Nnodes = ( *elt )->GetNumberOfNodes();

  solmat.set_size(Nnodes * ImageDimension, 1);
  for(; elt != element->end(); elt++ )
    {
    for( unsigned int i = 0; i < m_NumberOfIntegrationPoints; i++ )
      {
      static_cast<Element *>( ( *elt ) )->GetIntegrationPointAndWeight(i, ip, w, m_NumberOfIntegrationPoints);
      // FIXME REMOVE WHEN ELEMENT NEW IS BASE CLASS
      shapef = ( *elt )->ShapeFunctions(ip);

      float solval, posval;
      Float detJ = ( *elt )->JacobianDeterminant(ip);
      for( unsigned int f = 0; f < ImageDimension; f++ )
        {
        solval = 0.0;
        posval = 0.0;
        for( unsigned int n = 0; n < Nnodes; n++ )
          {
          posval += shapef[n] * ( ( ( *elt )->GetNodeCoordinates(n) )[f] );
          float nodeval =
            ( ( m_Solution )->GetSolutionValue( ( *elt )->GetNode(n)->GetDegreeOfFreedom(f), m_SolutionIndex )
              + ( m_Solution )->GetSolutionValue( ( *elt )->GetNode(n)->GetDegreeOfFreedom(f),
                                                  m_SolutionIndex2 ) * step );

          solval += shapef[n] * nodeval;
          solmat[( n * ImageDimension ) + f][0] = nodeval;
          }
        InVec[f] = posval;
        InVec[f + ImageDimension] = solval;
        }

      float tempe = 0.0;
      try
        {
        tempe = vcl_fabs( GetMetric(InVec) );
        }
      catch( itk::ExceptionObject & )
        {
        // do nothing we dont care if the metric region is outside the image
        // std::cerr << e << std::endl;
        }
      for( unsigned int n = 0; n < Nnodes; n++ )
        {
        itk::fem::Element::Float temp = shapef[n] * tempe * w * detJ;
        energy += temp;
        }
      }

    defe += 0.0; // (double)(*elt)->GetElementDeformationEnergy( solmat );
    }

  // std::cout << " def e " << defe << " sim e " << energy*m_Gamma << std::endl;
  return vcl_fabs( (double)energy * (double)m_Gamma - (double)defe );
}

template <typename TMoving, typename TFixed>
typename ImageMetricLoad<TMoving, TFixed>::Float
ImageMetricLoad<TMoving, TFixed>
::EvaluateMetricGivenSolution1(Element::ArrayType *element, Float step)
{
  Float energy = 0.0, defe = 0.0;

  vnl_vector_fixed<Float, 2 *ImageDimension> InVec(0.0);

  Element::VectorType ip, shapef;
  Element::MatrixType solmat;
  Element::Float      w;

  Element::ArrayType::iterator elt = element->begin();
  const unsigned int           Nnodes = ( *elt )->GetNumberOfNodes();

  solmat.set_size(Nnodes * ImageDimension, 1);
  for(; elt != element->end(); elt++ )
    {
    for( unsigned int i = 0; i < m_NumberOfIntegrationPoints; i++ )
      {
      static_cast<Element *>( ( *elt ) )->GetIntegrationPointAndWeight(i, ip, w, m_NumberOfIntegrationPoints);
      //FIXME REMOVE WHEN ELEMENT NEW IS BASE CLASS
      shapef = ( *elt )->ShapeFunctions(ip);

      Float detJ = ( *elt )->JacobianDeterminant(ip);
      for( unsigned int f = 0; f < ImageDimension; f++ )
        {
        float solval = 0.0;
        float posval = 0.0;
        for( unsigned int n = 0; n < Nnodes; n++ )
          {
          posval += shapef[n] * ( ( ( *elt )->GetNodeCoordinates(n) )[f] );
          float nodeval =
            ( ( m_Solution )->GetSolutionValue( ( *elt )->GetNode(n)->GetDegreeOfFreedom(f), m_SolutionIndex )
              + ( m_Solution )->GetSolutionValue( ( *elt )->GetNode(n)->GetDegreeOfFreedom(f),
                                                  m_SolutionIndex2 ) * step );

          solval += shapef[n] * nodeval;
          solmat[( n * ImageDimension ) + f][0] = nodeval;
          }
        InVec[f] = posval;
        InVec[f + ImageDimension] = solval;
        }

      float tempe = 0.0;
      try
        {
        tempe = vcl_fabs( GetMetric(InVec) );
        }
      catch( itk::ExceptionObject & )
        {
        // do nothing we dont care if the metric region is outside the image
        // std::cerr << e << std::endl;
        }
      for( unsigned int n = 0; n < Nnodes; n++ )
        {
        itk::fem::Element::Float temp = shapef[n] * tempe * w * detJ;
        energy += temp;
        }
      }

    defe += 0.0; // (double)(*elt)->GetElementDeformationEnergy( solmat );
    }

  // std::cout << " def e " << defe << " sim e " << energy*m_Gamma << std::endl;
  return vcl_fabs( (double)energy * (double)m_Gamma - (double)defe );
}

template <typename TMoving, typename TFixed>
typename ImageMetricLoad<TMoving, TFixed>::VectorType
ImageMetricLoad<TMoving, TFixed>
::Fe(VectorType Gpos, VectorType Gsol)
{
  // We assume the vector input is of size 2*ImageDimension.
  // The 0 to ImageDimension-1 elements contain the position, p,
  // in the reference image.  The next ImageDimension to 2*ImageDimension-1
  // elements contain the value of the vector field at that point, v(p).
  //
  // Thus, we evaluate the derivative at the point p+v(p) with respect to
  // some region of the target (fixed) image by calling the metric with
  // the translation parameters as provided by the vector field at p.
  // ------------------------------------------------------------
  // Set up transform parameters
  // ------------------------------------------------------------

  VectorType OutVec;
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    if( vnl_math_isnan(Gpos[k])  || vnl_math_isinf(Gpos[k])
        || vnl_math_isnan(Gsol[k])  || vnl_math_isinf(Gsol[k])
        || vcl_fabs(Gpos[k]) > 1.e33  || vcl_fabs(Gsol[k]) > 1.e33  )
      {
      OutVec.set_size(ImageDimension);  OutVec.fill(0.0);  return OutVec;
      }
    }

  ParametersType parameters( m_Transform->GetNumberOfParameters() );

  typename FixedType::RegionType requestedRegion;
  FixedRadiusType regionRadius;
  typename FixedType::IndexType  tindex;
  typename MovingType::IndexType rindex;
  OutVec.set_size(ImageDimension);

  int lobordercheck = 0, hibordercheck = 0;
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    // Set the size of the image region
    parameters[k] = Gsol[k];
    //this gives the translation by the vector field
    //where the piece of reference image currently lines up under the above translation
    //position in reference image
    rindex[k] = (long)( Gpos[k] + Gsol[k] + 0.5 );
    tindex[k] = (long)( Gpos[k] + 0.5 ) - (long)m_MetricRadius[k] / 2;
    hibordercheck = (int)tindex[k] + (int)m_MetricRadius[k] - (int)m_TarSize[k];
    lobordercheck = (int)tindex[k] - (int)m_MetricRadius[k];
    if( hibordercheck >= 0 )
      {
      regionRadius[k] = m_MetricRadius[k] - (long)hibordercheck - 1;
      }
    else if( lobordercheck < 0 )
      {
      regionRadius[k] = m_MetricRadius[k] + (long)lobordercheck;
      }
    else
      {
      regionRadius[k] = m_MetricRadius[k];
      }
    //position in reference image
    tindex[k] = (long)( Gpos[k] + 0.5 ) - (long)regionRadius[k] / 2;
    }

  // Set the associated region

  requestedRegion.SetSize(regionRadius);
  requestedRegion.SetIndex(tindex);

  m_TarImage->SetRequestedRegion(requestedRegion);
  m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );

  // --------------------------------------------------------
  // Get metric values

  typename MetricBaseType::MeasureType    measure;
  typename MetricBaseType::DerivativeType derivative;

  try
    {
    m_Metric->GetValueAndDerivative(parameters, measure, derivative);
    //  m_Metric->GetDerivative( parameters, derivative );
    }
  catch( ... )
    {
    // do nothing we don't care if the metric lies outside the image sometimes
    // std::cerr << e << std::endl;
    }

  m_Energy += (double)measure;
  float gmag = 0.0;
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    if( lobordercheck < 0 || hibordercheck >= 0
        || vnl_math_isnan(derivative[k])  || vnl_math_isinf(derivative[k]) )
      {
      OutVec[k] = 0.0;
      }
    else
      {
      OutVec[k] = m_Sign * m_Gamma * derivative[k];
      }
    gmag += OutVec[k] * OutVec[k];
    }
  if( gmag == 0.0 )
    {
    gmag = 1.0;
    }
  // NOTE : POSSIBLE THAT DERIVATIVE DIRECTION POINTS UP OR DOWN HILL!
  // IN FACT, IT SEEMS MEANSQRS AND NCC POINT IN DIFFT DIRS
  // std::cout   << " deriv " << derivative <<  " val " << measure << endl;
  // if (m_Temp !=0.0)
  // return OutVec * vcl_exp(-1.*OutVec.magnitude()/m_Temp);
  // else
  return OutVec / vcl_sqrt(gmag);
}

template <typename TMoving, typename TFixed>
typename ImageMetricLoad<TMoving, TFixed>::Float
ImageMetricLoad<TMoving, TFixed>
::GetMetric(VectorType InVec)
{
  // We assume the vector input is of size 2*ImageDimension.
  // The 0 to ImageDimension-1 elements contain the position, p,
  // in the reference image.  The next ImageDimension to 2*ImageDimension-1
  // elements contain the value of the vector field at that point, v(p).
  //
  // Thus, we evaluate the derivative at the point p+v(p) with respect to
  // some region of the target (fixed) image by calling the metric with
  // the translation parameters as provided by the vector field at p.
  // ------------------------------------------------------------
  // Set up transform parameters
  // ------------------------------------------------------------
  ParametersType parameters( m_Transform->GetNumberOfParameters() );

  typename FixedType::RegionType requestedRegion;
  typename FixedType::IndexType  tindex;
  typename MovingType::IndexType rindex;
  FixedRadiusType regionRadius;
  VectorType      OutVec(ImageDimension, 0.0); // gradient direction
  // std::cout << " pos   translation " << InVec  << endl;
  // initialize the offset/vector part
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    // Set the size of the image region
    parameters[k] = InVec[k + ImageDimension];                          // this
                                                                        // gives
                                                                        // the
                                                                        // translation
                                                                        // by
                                                                        // the
                                                                        // vector
                                                                        // field
    rindex[k] = (long)( InVec[k] + InVec[k + ImageDimension] + 0.5 );   // where
                                                                        // the
                                                                        // piece
                                                                        // of
                                                                        // reference
                                                                        // image
                                                                        // currently
                                                                        // lines
                                                                        // up
                                                                        // under
                                                                        // the
                                                                        // above
                                                                        // translation
    tindex[k] = (long)( InVec[k] + 0.5 ) - (long)m_MetricRadius[k] / 2; //
                                                                        // position
                                                                        // in
                                                                        // reference
                                                                        // image
    int hibordercheck = (int)tindex[k] + (int)m_MetricRadius[k] - (int)m_TarSize[k];
    int lobordercheck = (int)tindex[k] - (int)m_MetricRadius[k];
    if( hibordercheck > 0 )
      {
      regionRadius[k] = m_MetricRadius[k] - (long)hibordercheck - 1;
      }
    else if( lobordercheck < 0 )
      {
      regionRadius[k] = m_MetricRadius[k] + (long)lobordercheck;
      }
    else
      {
      regionRadius[k] = m_MetricRadius[k];
      }
    tindex[k] = (long)( InVec[k] + 0.5 ) - (long)regionRadius[k] / 2;  //
                                                                       // position
                                                                       // in
                                                                       // reference
                                                                       // image
    }

  // Set the associated region

  requestedRegion.SetSize(regionRadius);
  requestedRegion.SetIndex(tindex);

  m_TarImage->SetRequestedRegion(requestedRegion);
  m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );

  // --------------------------------------------------------
  // Get metric values

  typename MetricBaseType::MeasureType measure = 0.0;
  try
    {
    measure = m_Metric->GetValue(parameters);
    }
  catch( ... )
    {
    // do nothing we dont care if the metric lies outside the image sometimes
    // std::cerr << e << std::endl;
    }

  return (Float)measure;
}

template <typename TMoving, typename TFixed>
typename ImageMetricLoad<TMoving, TFixed>::VectorType
ImageMetricLoad<TMoving, TFixed>
::MetricFiniteDiff(VectorType Gpos, VectorType Gsol)
{
  typename MetricBaseType::MeasureType measure;

  ParametersType parameters(ImageDimension);

  typename FixedType::RegionType requestedRegion;
  typename FixedType::IndexType  tindex;
  FixedRadiusType regionRadius;

  VectorType OutVec;
  OutVec.set_size(ImageDimension);
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    parameters[k] = Gsol[k];                                           // this
                                                                       // gives
                                                                       // the
                                                                       // translation
                                                                       // by the
                                                                       // vector
                                                                       // field
    tindex[k] = (long)( Gpos[k] + 0.5 ) - (long)m_MetricRadius[k] / 2; //
                                                                       // position
                                                                       // in
                                                                       // reference
                                                                       // image
    if( tindex[k] > m_TarSize[k] - 1 || tindex[k] < 0 )
      {
      tindex[k] = (long)( Gpos[k] + 0.5 );
      }
    int hibordercheck = (int)tindex[k] + (int)m_MetricRadius[k] - (int)m_TarSize[k];
    int lobordercheck = (int)tindex[k] - (int)m_MetricRadius[k];
    if( hibordercheck >= 0 )
      {
      regionRadius[k] = m_MetricRadius[k] - (long)hibordercheck - 1;
      }
    else if( lobordercheck < 0 )
      {
      regionRadius[k] = m_MetricRadius[k] + (long)lobordercheck;
      }
    else
      {
      regionRadius[k] = m_MetricRadius[k];
      }
    tindex[k] = (long)( Gpos[k] + 0.5 ) - (long)regionRadius[k] / 2;  //
                                                                      // position
                                                                      // in
                                                                      // reference
                                                                      // image
    }

  unsigned int row;
  typename ImageType::IndexType difIndex[ImageDimension][2];

  typename MetricBaseType::MeasureType dPixL, dPixR;
  for( row = 0; row < ImageDimension; row++ )
    {
    difIndex[row][0] = tindex;
    difIndex[row][1] = tindex;
    if( tindex[row] < m_TarSize[row] - 1 )
      {
      difIndex[row][0][row] = tindex[row] + 1;
      }
    if( tindex[row] > 0 )
      {
      difIndex[row][1][row] = tindex[row] - 1;
      }
    try
      {
      requestedRegion.SetIndex(difIndex[row][1]);
      requestedRegion.SetSize(regionRadius);
      m_TarImage->SetRequestedRegion(requestedRegion);
      m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );
      dPixL = m_Metric->GetValue(parameters);
      }
    catch( ... )
      {
      dPixL = 0.0;
      }
    try
      {
      requestedRegion.SetIndex(difIndex[row][0]);
      requestedRegion.SetSize(regionRadius);
      m_TarImage->SetRequestedRegion(requestedRegion);
      m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );
      dPixR = m_Metric->GetValue(parameters);
      }
    catch( ... )
      {
      dPixR = 0.0;
      }

    OutVec[row] = dPixL - dPixR;
    }
  return OutVec;
}

template <typename TMoving, typename TFixed>
typename ImageMetricLoad<TMoving, TFixed>::VectorType
ImageMetricLoad<TMoving, TFixed>
::GetPolynomialFitToMetric(VectorType Gpos, VectorType Gsol)
{
  // discrete orthogonal polynomial fitting
  // see p.394-403 haralick computer and robot vision
  //
  // here, use chebyshev polynomials for fitting a plane to the data
  //
  // f(x,y,z) = a0 + a1*x + a2*y + a3*z
  //
  ParametersType parameters(ImageDimension);

  typename FixedType::RegionType requestedRegion;
  typename FixedType::IndexType  tindex;
  FixedRadiusType regionRadius;

  typename ImageType::IndexType temp;

  VectorType chebycoefs; // gradient direction
  chebycoefs.set_size(ImageDimension);
  double chebycoefs0 = 0.0;  // the constant term
  double datatotal = 0.0;
  double a0norm = 1.0;
  double a1norm = 1.0 / 2.0;

  double met, ind1, ind2;
  double inds[3]; inds[0] = -1.0;  inds[1] = 0.0;  inds[2] = 1.0;
  for( unsigned int k = 0; k < ImageDimension; k++ )
    {
    a0norm /= 3.0;
    if( k < ImageDimension - 1 )
      {
      a1norm /= 3.0;
      }
    chebycoefs[k] = 0.0;
    parameters[k] = Gsol[k];                                           // this
                                                                       // gives
                                                                       // the
                                                                       // translation
                                                                       // by the
                                                                       // vector
                                                                       // field
    tindex[k] = (long)( Gpos[k] + 0.5 ) - (long)m_MetricRadius[k] / 2; //
                                                                       // position
                                                                       // in
                                                                       // reference
                                                                       // image
    if( tindex[k] > m_TarSize[k] - 1 || tindex[k] < 0 )
      {
      tindex[k] = (long)( Gpos[k] + 0.5 );
      }
    int hibordercheck = (int)tindex[k] + (int)m_MetricRadius[k] - (int)m_TarSize[k];
    int lobordercheck = (int)tindex[k] - (int)m_MetricRadius[k];
    if( hibordercheck >= 0 )
      {
      regionRadius[k] = m_MetricRadius[k] - (long)hibordercheck - 1;
      }
    else if( lobordercheck < 0 )
      {
      regionRadius[k] = m_MetricRadius[k] + (long)lobordercheck;
      }
    else
      {
      regionRadius[k] = m_MetricRadius[k];
      }
    tindex[k] = (long)( Gpos[k] + 0.5 ) - (long)regionRadius[k] / 2;  //
                                                                      // position
                                                                      // in
                                                                      // reference
                                                                      // image
    }

  if( ImageDimension == 2 )
    {
    double measure[3][3];
    for( int row = -1; row < 2; row++ )
      {
      for( int col = -1; col < 2; col++ )
        {
        temp[0] = tindex[0] + (long)row;
        temp[1] = tindex[1] + (long)col;
        for( unsigned int i = 0; i < ImageDimension; i++ )
          {
          if( temp[i] > m_TarSize[i] - 1 )
            {
            temp[i] = m_TarSize[i] - 1;
            }
          else if( temp[i] < 0 )
            {
            temp[i] = 0;
            }
          }

        requestedRegion.SetIndex(temp);
        requestedRegion.SetSize(regionRadius);
        m_TarImage->SetRequestedRegion(requestedRegion);
        m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );
        measure[row + 1][col + 1] = 0.0;

        try
          {
          measure[row + 1][col + 1] = m_Metric->GetValue(parameters);
          }
        catch( ... )
          {
          }

        datatotal += measure[row + 1][col + 1];
        }
      }
    for( unsigned int cb1 = 0; cb1 < 3; cb1++ )
      {
      for( unsigned int cb2 = 0; cb2 < 3; cb2++ )
        {
        met = measure[cb1][cb2];
        ind1 = inds[cb1] * a1norm;
        ind2 = inds[cb2] * a1norm;
        chebycoefs[0] += met * ind1;
        chebycoefs[1] += met * ind2;
        }
      }
    }
  else if( ImageDimension == 3 )
    {
    double measure3D[3][3][3];
    for( int row = -1; row < 2; row++ )
      {
      for( int col = -1; col < 2; col++ )
        {
        for( int z = -1; z < 2; z++ )
          {
          temp[0] = tindex[0] + (long)row;
          temp[1] = tindex[1] + (long)col;
          temp[2] = tindex[2] + (long)z;
          for( unsigned int i = 0; i < ImageDimension; i++ )
            {
            if( temp[i] > m_TarSize[i] - 1 )
              {
              temp[i] = m_TarSize[i] - 1;
              }
            else if( temp[i] < 0 )
              {
              temp[i] = 0;
              }
            }

          requestedRegion.SetIndex(temp);
          requestedRegion.SetSize(regionRadius);
          m_TarImage->SetRequestedRegion(requestedRegion);
          m_Metric->SetFixedImageRegion( m_TarImage->GetRequestedRegion() );
          measure3D[row + 1][col + 1][z + 1] = 0.0;

          try
            {
            measure3D[row + 1][col + 1][z + 1] = m_Metric->GetValue(parameters);
            }
          catch( ... )
            {
            }

          datatotal += measure3D[row + 1][col + 1][z + 1];
          }
        }
      }
    for( unsigned int cb1 = 0; cb1 < 2; cb1++ )
      {
      for( unsigned int cb2 = 0; cb2 < 2; cb2++ )
        {
        for( unsigned int cb3 = 0; cb3 < 2; cb3++ )
          {
          chebycoefs[0] += measure3D[cb1][cb2][cb3] * inds[cb1] * a1norm;
          chebycoefs[1] += measure3D[cb1][cb2][cb3] * inds[cb2] * a1norm;
          chebycoefs[2] += measure3D[cb1][cb2][cb3] * inds[cb3] * a1norm;
          }
        }
      }
    }

  chebycoefs0 = a0norm * datatotal;
//  std::cout << " cb " << chebycoefs << std::endl;
  return chebycoefs;
}

template <typename TMoving, typename TFixed>
void
ImageMetricLoad<TMoving, TFixed>
::ApplyLoad(Element::ConstPointer element, Element::VectorType & _Fe)
{
  const unsigned int TotalSolutionIndex = 1; /* Need to change if the index
                                              * changes in CrankNicolsonSolver
                                              */

  // has current solution state
  const typename Solution::ConstPointer S = this->GetSolution();

  // Order of integration
  // FIXME: Allow changing the order of integration by setting a
  //        static member within an element base class.
  const unsigned int order = this->GetNumberOfIntegrationPoints();

  const unsigned int Nip = element->GetNumberOfIntegrationPoints(order);
  const unsigned int Nnodes = element->GetNumberOfNodes();

  const unsigned int Ndofs = element->GetNumberOfDegreesOfFreedomPerNode();

  Element::VectorType ip;

  _Fe.set_size( element->GetNumberOfDegreesOfFreedom() );
  _Fe.fill(0.0);

  Element::VectorType shapef;
  shapef.set_size(Nnodes);

  Element::VectorType gsol(Ndofs,0.0);
  Element::VectorType gip(Ndofs, 0.0);

  //Element::VectorType force_tmp;
  //
  Element::Float w;
  Element::VectorType force(Ndofs, 0.0);
  for( unsigned int i = 0; i < Nip; i++ )
    {
    element->GetIntegrationPointAndWeight(i, ip, w, order);
    if( Ndofs == 3 )
      {
#define FASTHEX
#ifdef FASTHEX
      float r = ip[0]; float s = ip[1]; float t = ip[2];
      // FIXME temporarily using hexahedron shape f for speed
      shapef[0] = ( 1 - r ) * ( 1 - s ) * ( 1 - t ) * 0.125;
      shapef[1] = ( 1 + r ) * ( 1 - s ) * ( 1 - t ) * 0.125;
      shapef[2] = ( 1 + r ) * ( 1 + s ) * ( 1 - t ) * 0.125;
      shapef[3] = ( 1 - r ) * ( 1 + s ) * ( 1 - t ) * 0.125;
      shapef[4] = ( 1 - r ) * ( 1 - s ) * ( 1 + t ) * 0.125;
      shapef[5] = ( 1 + r ) * ( 1 - s ) * ( 1 + t ) * 0.125;
      shapef[6] = ( 1 + r ) * ( 1 + s ) * ( 1 + t ) * 0.125;
      shapef[7] = ( 1 - r ) * ( 1 + s ) * ( 1 + t ) * 0.125;
#else
      shapef = element->ShapeFunctions(ip);
#endif
      }
    else if( Ndofs == 2 )
      {
      shapef = element->ShapeFunctions(ip);
      }
    const Element::Float detJ = element->JacobianDeterminant(ip);
    for( unsigned int f = 0; f < Ndofs; f++ )
      {
      float solval = 0.0;
      float posval = 0.0;
      for( unsigned int n = 0; n < Nnodes; n++ )
        {
        posval += shapef[n] * ( ( element->GetNodeCoordinates(n) )[f] );
        solval += shapef[n] * S->GetSolutionValue(element->GetNode(n)->GetDegreeOfFreedom(f), TotalSolutionIndex);
        }
      gsol[f] = solval;
      gip[f] = posval;
      }

    // Adjust the size of a force vector returned from the load object so
    // that it is equal to the number of DOFs per node. If the Fg returned
    // a vector with less dimensions, we add zero elements. If the Fg
    // returned a vector with more dimensions, we remove the extra dimensions.
    force.fill(0.0); //HACK:  Is this setting to all zeros necessary given that the next line overwrites the values anyway
    force = this->Fe(gip, gsol);
    // Calculate the equivalent nodal loads
    for( unsigned int n = 0; n < Nnodes; n++ )
      {
      for( unsigned int d = 0; d < Ndofs; d++ )
        {
        itk::fem::Element::Float temp = shapef[n] * force[d] * w * detJ;
        _Fe[n * Ndofs + d] += temp;
        }
      }
    }
}

template <typename TMoving, typename TFixed>
void
ImageMetricLoad<TMoving, TFixed>
::PrintSelf(std::ostream& os, Indent indent) const
{
  Superclass::PrintSelf(os, indent);
  os << indent << "Metric Gradient Image: " << this->m_MetricGradientImage << std::endl;
  os << indent << "Moving Image: " << this->m_RefImage << std::endl;
  os << indent << "Fixed Image: " << this->m_TarImage << std::endl;
  os << indent << "Metric Radius: " << this->m_MetricRadius << std::endl;
  os << indent << "Reference Size: " << this->m_RefSize << std::endl;
  os << indent << "Target Size: " << this->m_TarSize << std::endl;
  os << indent << "Number Of Integration Points: " << this->m_NumberOfIntegrationPoints << std::endl;
  os << indent << "Solution Index: " << this->m_SolutionIndex << std::endl;
  os << indent << "Solution Index 2: " << this->m_SolutionIndex2 << std::endl;
  os << indent << "Sign: " << this->m_Sign << std::endl;
  os << indent << "Temp: " << this->m_Temp << std::endl;
  os << indent << "Gamma: " << this->m_Gamma << std::endl;
  os << indent << "Solution: " << this->m_Solution << std::endl;
  os << indent << "Metric: " << this->m_Metric << std::endl;
  os << indent << "Transform: " << this->m_Transform << std::endl;
  os << indent << "Interpolator: " << this->m_Interpolator << std::endl;
  os << indent << "Energy: " << this->m_Energy << std::endl;
}

} // end namespace fem
} // end namespace itk

#endif