itkBSplineInterpolateImageFunction.txx

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

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkBSplineInterpolateImageFunction.txx,v $
  Language:  C++
  Date:      $Date: 2009-10-13 07:39:24 $
  Version:   $Revision: 1.22 $

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

  Portions of this code are covered under the VTK copyright.
  See VTKCopyright.txt or http://www.kitware.com/VTKCopyright.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 __itkBSplineInterpolateImageFunction_txx
#define __itkBSplineInterpolateImageFunction_txx

// First, make sure that we include the configuration file.
// This line may be removed once the ThreadSafeTransform gets
// integrated into ITK.
#include "itkConfigure.h"

// Second, redirect to the optimized version if necessary
#ifdef ITK_USE_OPTIMIZED_REGISTRATION_METHODS
#include "itkOptBSplineInterpolateImageFunction.txx"
#else

#include "itkBSplineInterpolateImageFunction.h"
#include "itkImageLinearIteratorWithIndex.h"
#include "itkImageRegionConstIteratorWithIndex.h"
#include "itkImageRegionIterator.h"

#include "itkVector.h"

#include "itkMatrix.h"

namespace itk
{

template <class TImageType, class TCoordRep, class TCoefficientType>
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::BSplineInterpolateImageFunction()
{
  m_SplineOrder = 0;
  unsigned int SplineOrder = 3;
  m_CoefficientFilter = CoefficientFilter::New();
  // ***TODO: Should we store coefficients in a variable or retrieve from filter?
  m_Coefficients = CoefficientImageType::New();
  this->SetSplineOrder(SplineOrder);
#if defined(ITK_IMAGE_BEHAVES_AS_ORIENTED_IMAGE)
  this->m_UseImageDirection = true;
#else
  this->m_UseImageDirection = false;
#endif
}

template <class TImageType, class TCoordRep, class TCoefficientType>
void
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::PrintSelf(
  std::ostream& os, 
  Indent indent) const
{
  Superclass::PrintSelf( os, indent );
  os << indent << "Spline Order: " << m_SplineOrder << std::endl;
  os << indent << "UseImageDirection = " 
     << (this->m_UseImageDirection ? "On" : "Off") << std::endl;

}


template <class TImageType, class TCoordRep, class TCoefficientType>
void 
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::SetInputImage(const TImageType * inputData)
{
  if ( inputData )
    {
    m_CoefficientFilter->SetInput(inputData);

    // the Coefficient Filter requires that the spline order and the input data be set.
    // TODO:  We need to ensure that this is only run once and only after both input and
    //        spline order have been set. Should we force an update after the 
    //        splineOrder has been set also?

    m_CoefficientFilter->Update();
    m_Coefficients = m_CoefficientFilter->GetOutput();

    // Call the Superclass implementation after, in case the filter
    // pulls in  more of the input image
    Superclass::SetInputImage(inputData);

    m_DataLength = inputData->GetBufferedRegion().GetSize();
    }
  else
    {
    m_CoefficientFilter->GetOutput()->DisconnectPipeline();
    m_Coefficients = NULL;
    }
}


template <class TImageType, class TCoordRep, class TCoefficientType>
void 
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::SetSplineOrder(unsigned int SplineOrder)
{
  if (SplineOrder == m_SplineOrder)
    {
    return;
    }
  m_SplineOrder = SplineOrder;
  m_CoefficientFilter->SetSplineOrder( SplineOrder );

  //this->SetPoles();
  m_MaxNumberInterpolationPoints = 1;
  for (unsigned int n=0; n < ImageDimension; n++)
    {
    m_MaxNumberInterpolationPoints *= ( m_SplineOrder + 1);
    } 
  this->GeneratePointsToIndex( );
}


template <class TImageType, class TCoordRep, class TCoefficientType>
typename 
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::OutputType
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::EvaluateAtContinuousIndex( const ContinuousIndexType & x ) const
{
  vnl_matrix<long>        EvaluateIndex(ImageDimension, ( m_SplineOrder + 1 ));

  // compute the interpolation indexes 
  this->DetermineRegionOfSupport(EvaluateIndex, x, m_SplineOrder); 

  // Determine weights
  vnl_matrix<double>        weights(ImageDimension, ( m_SplineOrder + 1 ));
  SetInterpolationWeights( x, EvaluateIndex, weights, m_SplineOrder );

  // Modify EvaluateIndex at the boundaries using mirror boundary conditions
  this->ApplyMirrorBoundaryConditions(EvaluateIndex, m_SplineOrder);
  
  // perform interpolation 
  double interpolated = 0.0;
  IndexType coefficientIndex;
  // Step through eachpoint in the N-dimensional interpolation cube.
  for (unsigned int p = 0; p < m_MaxNumberInterpolationPoints; p++)
    {
    // translate each step into the N-dimensional index.
    //      IndexType pointIndex = PointToIndex( p );

    double w = 1.0;
    for (unsigned int n = 0; n < ImageDimension; n++ )
      {
      w *= weights[n][ m_PointsToIndex[p][n] ];
      coefficientIndex[n] = EvaluateIndex[n][m_PointsToIndex[p][n]];  // Build up ND index for coefficients.
      }
    // Convert our step p to the appropriate point in ND space in the
    // m_Coefficients cube.
    interpolated += w * (m_Coefficients->GetPixel(coefficientIndex));
    }
    
  return(interpolated);
    
}


template <class TImageType, class TCoordRep, class TCoefficientType>
typename 
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
:: CovariantVectorType
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::EvaluateDerivativeAtContinuousIndex( const ContinuousIndexType & x ) const
{
  vnl_matrix<long>        EvaluateIndex(ImageDimension, ( m_SplineOrder + 1 ));

  // compute the interpolation indexes 
  // TODO: Do we need to revisit region of support for the derivatives?
  this->DetermineRegionOfSupport(EvaluateIndex, x, m_SplineOrder);

  // Determine weights
  vnl_matrix<double>        weights(ImageDimension, ( m_SplineOrder + 1 ));
  SetInterpolationWeights( x, EvaluateIndex, weights, m_SplineOrder );

  vnl_matrix<double>        weightsDerivative(ImageDimension, ( m_SplineOrder + 1));
  SetDerivativeWeights( x, EvaluateIndex, weightsDerivative, ( m_SplineOrder ) );

  // Modify EvaluateIndex at the boundaries using mirror boundary conditions
  this->ApplyMirrorBoundaryConditions(EvaluateIndex, m_SplineOrder);
  
  const InputImageType * inputImage = this->GetInputImage();
  const typename InputImageType::SpacingType & spacing = inputImage->GetSpacing();

  // Calculate derivative
  CovariantVectorType derivativeValue;
  double tempValue;
  IndexType coefficientIndex;
  for (unsigned int n = 0; n < ImageDimension; n++)
    {
    derivativeValue[n] = 0.0;
    for (unsigned int p = 0; p < m_MaxNumberInterpolationPoints; p++)
      {
      tempValue = 1.0; 
      for (unsigned int n1 = 0; n1 < ImageDimension; n1++)
        {
        //coefficientIndex[n1] = EvaluateIndex[n1][sp];
        coefficientIndex[n1] = EvaluateIndex[n1][m_PointsToIndex[p][n1]];

        if (n1 == n)
          {
          //w *= weights[n][ m_PointsToIndex[p][n] ];
          tempValue *= weightsDerivative[n1][ m_PointsToIndex[p][n1] ];
          }
        else
          {
          tempValue *= weights[n1][ m_PointsToIndex[p][n1] ];
          }
        }
      derivativeValue[n] += m_Coefficients->GetPixel(coefficientIndex) * tempValue;
      }
    derivativeValue[n] /= spacing[n];   // take spacing into account
    }

#ifdef ITK_USE_ORIENTED_IMAGE_DIRECTION
  if( this->m_UseImageDirection )
    {
    CovariantVectorType orientedDerivative;
    inputImage->TransformLocalVectorToPhysicalVector( derivativeValue, orientedDerivative );
    return orientedDerivative;
    }
#endif

  return(derivativeValue);
}


template <class TImageType, class TCoordRep, class TCoefficientType>
void 
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::SetInterpolationWeights( const ContinuousIndexType & x, const vnl_matrix<long> & EvaluateIndex, 
                           vnl_matrix<double> & weights, unsigned int splineOrder ) const
{
  // For speed improvements we could make each case a separate function and use
  // function pointers to reference the correct weight order.
  // Left as is for now for readability.
  double w, w2, w4, t, t0, t1;
  
  switch (splineOrder)
    {
    case 3:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        w = x[n] - (double) EvaluateIndex[n][1];
        weights[n][3] = (1.0 / 6.0) * w * w * w;
        weights[n][0] = (1.0 / 6.0) + 0.5 * w * (w - 1.0) - weights[n][3];
        weights[n][2] = w + weights[n][0] - 2.0 * weights[n][3];
        weights[n][1] = 1.0 - weights[n][0] - weights[n][2] - weights[n][3];
        }
      break;
    case 0:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        weights[n][0] = 1; // implements nearest neighbor
        }
      break;
    case 1:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        w = x[n] - (double) EvaluateIndex[n][0];
        weights[n][1] = w;
        weights[n][0] = 1.0 - w;
        }
      break;
    case 2:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        /* x */
        w = x[n] - (double)EvaluateIndex[n][1];
        weights[n][1] = 0.75 - w * w;
        weights[n][2] = 0.5 * (w - weights[n][1] + 1.0);
        weights[n][0] = 1.0 - weights[n][1] - weights[n][2];
        }
      break;
    case 4:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        /* x */
        w = x[n] - (double)EvaluateIndex[n][2];
        w2 = w * w;
        t = (1.0 / 6.0) * w2;
        weights[n][0] = 0.5 - w;
        weights[n][0] *= weights[n][0];
        weights[n][0] *= (1.0 / 24.0) * weights[n][0];
        t0 = w * (t - 11.0 / 24.0);
        t1 = 19.0 / 96.0 + w2 * (0.25 - t);
        weights[n][1] = t1 + t0;
        weights[n][3] = t1 - t0;
        weights[n][4] = weights[n][0] + t0 + 0.5 * w;
        weights[n][2] = 1.0 - weights[n][0] - weights[n][1] - weights[n][3] - weights[n][4];
        }
      break;
    case 5:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        /* x */
        w = x[n] - (double)EvaluateIndex[n][2];
        w2 = w * w;
        weights[n][5] = (1.0 / 120.0) * w * w2 * w2;
        w2 -= w;
        w4 = w2 * w2;
        w -= 0.5;
        t = w2 * (w2 - 3.0);
        weights[n][0] = (1.0 / 24.0) * (1.0 / 5.0 + w2 + w4) - weights[n][5];
        t0 = (1.0 / 24.0) * (w2 * (w2 - 5.0) + 46.0 / 5.0);
        t1 = (-1.0 / 12.0) * w * (t + 4.0);
        weights[n][2] = t0 + t1;
        weights[n][3] = t0 - t1;
        t0 = (1.0 / 16.0) * (9.0 / 5.0 - t);
        t1 = (1.0 / 24.0) * w * (w4 - w2 - 5.0);
        weights[n][1] = t0 + t1;
        weights[n][4] = t0 - t1;
        }
      break;
    default:
      // SplineOrder not implemented yet.
      ExceptionObject err(__FILE__, __LINE__);
      err.SetLocation( ITK_LOCATION );
      err.SetDescription( "SplineOrder must be between 0 and 5. Requested spline order has not been implemented yet." );
      throw err;
      break;
    }
    
}

template <class TImageType, class TCoordRep, class TCoefficientType>
void 
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::SetDerivativeWeights( const ContinuousIndexType & x, const vnl_matrix<long> & EvaluateIndex, 
                        vnl_matrix<double> & weights, unsigned int splineOrder ) const
{
  // For speed improvements we could make each case a separate function and use
  // function pointers to reference the correct weight order.
  // Another possiblity would be to loop inside the case statement (reducing the number
  // of switch statement executions to one per routine call.
  // Left as is for now for readability.
  double w, w1, w2, w3, w4, w5, t, t0, t1, t2;
  int derivativeSplineOrder = (int) splineOrder -1;
  
  switch (derivativeSplineOrder)
    {
    
    // Calculates B(splineOrder) ( (x + 1/2) - xi) - B(splineOrder -1) ( (x - 1/2) - xi)
    case -1:
      // Why would we want to do this?
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        weights[n][0] = 0.0;
        }
      break;
    case 0:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        weights[n][0] = -1.0;
        weights[n][1] =  1.0;
        }
      break;
    case 1:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        w = x[n] + 0.5 - (double)EvaluateIndex[n][1];
        // w2 = w;
        w1 = 1.0 - w;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w;
        weights[n][2] = w; 
        }
      break;
    case 2:
      
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        w = x[n] + .5 - (double)EvaluateIndex[n][2];
        w2 = 0.75 - w * w;
        w3 = 0.5 * (w - w2 + 1.0);
        w1 = 1.0 - w2 - w3;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w2;
        weights[n][2] = w2 - w3;
        weights[n][3] = w3; 
        }
      break;
    case 3:
      
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        w = x[n] + 0.5 - (double)EvaluateIndex[n][2];
        w4 = (1.0 / 6.0) * w * w * w;
        w1 = (1.0 / 6.0) + 0.5 * w * (w - 1.0) - w4;
        w3 = w + w1 - 2.0 * w4;
        w2 = 1.0 - w1 - w3 - w4;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w2;
        weights[n][2] = w2 - w3;
        weights[n][3] = w3 - w4;
        weights[n][4] = w4;
        }
      break;
    case 4:
      for (unsigned int n = 0; n < ImageDimension; n++)
        {
        w = x[n] + .5 - (double)EvaluateIndex[n][3];
        t2 = w * w;
        t = (1.0 / 6.0) * t2;
        w1 = 0.5 - w;
        w1 *= w1;
        w1 *= (1.0 / 24.0) * w1;
        t0 = w * (t - 11.0 / 24.0);
        t1 = 19.0 / 96.0 + t2 * (0.25 - t);
        w2 = t1 + t0;
        w4 = t1 - t0;
        w5 = w1 + t0 + 0.5 * w;
        w3 = 1.0 - w1 - w2 - w4 - w5;

        weights[n][0] = 0.0 - w1;
        weights[n][1] = w1 - w2;
        weights[n][2] = w2 - w3;
        weights[n][3] = w3 - w4;
        weights[n][4] = w4 - w5;
        weights[n][5] = w5;
        }
      break;
      
    default:
      // SplineOrder not implemented yet.
      ExceptionObject err(__FILE__, __LINE__);
      err.SetLocation( ITK_LOCATION );
      err.SetDescription( "SplineOrder (for derivatives) must be between 1 and 5. Requested spline order has not been implemented yet." );
      throw err;
      break;
    }
    
}


// Generates m_PointsToIndex;
template <class TImageType, class TCoordRep, class TCoefficientType>
void
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::GeneratePointsToIndex( )
{
  // m_PointsToIndex is used to convert a sequential location to an N-dimension
  // index vector.  This is precomputed to save time during the interpolation routine.
  m_PointsToIndex.resize(m_MaxNumberInterpolationPoints);
  for (unsigned int p = 0; p < m_MaxNumberInterpolationPoints; p++)
    {
    int pp = p;
    unsigned long indexFactor[ImageDimension];
    indexFactor[0] = 1;
    for (int j=1; j< static_cast<int>(ImageDimension); j++)
      {
      indexFactor[j] = indexFactor[j-1] * ( m_SplineOrder + 1 );
      }
    for (int j = (static_cast<int>(ImageDimension) - 1); j >= 0; j--)
      {
      m_PointsToIndex[p][j] = pp / indexFactor[j];
      pp = pp % indexFactor[j];
      }
    }
}

template <class TImageType, class TCoordRep, class TCoefficientType>
void
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::DetermineRegionOfSupport( vnl_matrix<long> & evaluateIndex, 
                            const ContinuousIndexType & x, 
                            unsigned int splineOrder ) const
{ 
  long indx;

// compute the interpolation indexes 
  for (unsigned int n = 0; n< ImageDimension; n++)
    {
    if (splineOrder & 1)     // Use this index calculation for odd splineOrder
      {
      indx = (long)vcl_floor((float)x[n]) - splineOrder / 2;
      for (unsigned int k = 0; k <= splineOrder; k++)
        {
        evaluateIndex[n][k] = indx++;
        }
      }
    else                       // Use this index calculation for even splineOrder
      { 
      indx = (long)vcl_floor((float)(x[n] + 0.5)) - splineOrder / 2;
      for (unsigned int k = 0; k <= splineOrder; k++)
        {
        evaluateIndex[n][k] = indx++;
        }
      }
    }
}

template <class TImageType, class TCoordRep, class TCoefficientType>
void
BSplineInterpolateImageFunction<TImageType,TCoordRep,TCoefficientType>
::ApplyMirrorBoundaryConditions(vnl_matrix<long> & evaluateIndex, 
                                unsigned int splineOrder) const
{
  for (unsigned int n = 0; n < ImageDimension; n++)
    {
    long dataLength2 = 2 * m_DataLength[n] - 2;

    // apply the mirror boundary conditions 
    // TODO:  We could implement other boundary options beside mirror
    if (m_DataLength[n] == 1)
      {
      for (unsigned int k = 0; k <= splineOrder; k++)
        {
        evaluateIndex[n][k] = 0;
        }
      }
    else
      {
      for (unsigned int k = 0; k <= splineOrder; k++)
        {
        // btw - Think about this couldn't this be replaced with a more elagent modulus method?
        evaluateIndex[n][k] = (evaluateIndex[n][k] < 0L) ? (-evaluateIndex[n][k] - dataLength2 * ((-evaluateIndex[n][k]) / dataLength2))
          : (evaluateIndex[n][k] - dataLength2 * (evaluateIndex[n][k] / dataLength2));
        if ((long) m_DataLength[n] <= evaluateIndex[n][k])
          {
          evaluateIndex[n][k] = dataLength2 - evaluateIndex[n][k];
          }
        }
      }
    }
}

} // namespace itk

#endif

#endif