Examples/RegistrationITKv4/ImageRegistrationHistogramPlotter.cxx

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 *
 *  Copyright NumFOCUS
 *
 *  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
 *
 *         https://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.
 *
 *=========================================================================*/
 
//  Software Guide : Begin TODO HACK FIXME CommandLineArgs
//  INPUTS:  {BrainT1SliceBorder20.png}
//  INPUTS:  {BrainProtonDensitySliceShifted13x17y.png}
//  ARGUMENTS:    RegisteredImage.png 0
//  OUTPUTS: {JointEntropyHistogramPriorToRegistration.png}
//  OUTPUTS: {JointEntropyHistogramAfterRegistration.png}
//  ARGUMENTS:    128
//  Software Guide : End TODO HACK FIXME CommandLineArgs
 
//  Software Guide : BeginLatex
//
//  When fine tuning the parameters of an image registration process it is not
//  always clear what factor are having a larger impact on the behavior of the
//  registration. Even plotting the values of the metric and the transform
//  parameters may not provide a clear indication on the best way to modify
//  the optimizer and metric parameters in order to improve the convergence
//  rate and stability. In such circumstances it is useful to take a closer
//  look at the internals of the components involved in computing the
//  registration. One of the critical components is, of course, the image
//  metric. This section illustrates a mechanism that can be used for
//  monitoring the behavior of the Mutual Information metric by continuously
//  looking at the joint histogram at regular intervals during the iterations
//  of the optimizer.
//
//  This particular example shows how to use the
//  \doxygen{HistogramToEntropyImageFilter} class in order to get access to
//  the joint histogram that is internally computed by the metric. This class
//  represents the joint histogram as a $2D$ image and therefore can take
//  advantage of the IO functionalities described in chapter~\ref{sec:IO}. The
//  example registers two images using the gradient descent optimizer.  The
//  transform used here is a simple translation transform. The metric is a
//  \doxygen{MutualInformationHistogramImageToImageMetric}.
//
//  In the code below we create a helper class called the
//  \code{HistogramWriter}.  Its purpose is to save the joint histogram into a
//  file using any of the file formats supported by ITK. This object is
//  invoked after every iteration of the optimizer.  The writer here saves the
//  joint histogram into files with names: \code{JointHistogramXXX.mhd} where
//  \code{XXX} is replaced with the iteration number. The output image
//  contains the joint entropy histogram given by \begin{equation} f_{ij} =
//  -p_{ij} \log_2 ( p_{ij} ) \end{equation}
//
//  where the indices $i$ and $j$ identify the location of a bin in the Joint
//  Histogram of the two images and are in the ranges $i \in [0:N-1]$ and  $j
//  \in [0:M-1]$. The image $f$ representing the joint histogram has $N x M$
//  pixels because the intensities of the Fixed image are quantized into $N$
//  histogram bins and the intensities of the Moving image are quantized into
//  $M$ histogram bins. The probability value $p_{ij}$ is computed from the
//  frequency count of the histogram bins.
//  \begin{equation}
//  p_{ij} = \frac{q_{ij}}{\sum_{i=0}^{N-1} \sum_{j=0}^{M-1} q_{ij}}
//  \end{equation}
//  The value $q_{ij}$ is the frequency of a bin in the histogram and it is
//  computed as the number of pixels where the Fixed image has intensities in
//  the range of bin $i$ and the Moving image has intensities on the range of
//  bin $j$.  The value $p_{ij}$ is therefore the probability of the
//  occurrence of the measurement vector centered in the bin ${ij}$.  The
//  filter produces an output image of pixel type \code{double}. For details
//  on the use of Histograms in ITK please refer to
//  section~\ref{sec:Histogram}.
//
//  Depending on whether you want to see the joint histogram frequencies
//  directly, or the joint probabilities, or log of joint probabilities, you
//  may want to instantiate respectively any of the following classes
//
//  \begin{itemize}
//  \item \doxygen{HistogramToIntensityImageFilter}
//  \item \doxygen{HistogramToProbabilityImageFilter}
//  \item \doxygen{HistogramToLogProbabilityImageFilter}
//  \end{itemize}
//
//  \index{Histogram\-To\-Log\-Probability\-ImageFilter}
//  \index{Histogram\-To\-Intensity\-Image\-Filter}
//  \index{Histogram\-To\-Probability\-Image\-Filter}
//
//  The use of all of these classes is very similar. Note that the log of the
//  probability is equivalent to units of information, also known as
//  \textbf{bits}, more details on this concept can be found in
//  section~\ref{sec:ComputingImageEntropy}
//
//   Software Guide : EndLatex
 
 
#include "itkImageRegistrationMethod.h"
#include "itkTranslationTransform.h"
#include "itkRegularStepGradientDescentOptimizer.h"
#include "itkNormalizeImageFilter.h"
#include "itkDiscreteGaussianImageFilter.h"
#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"
#include "itkResampleImageFilter.h"
#include "itkCastImageFilter.h"
 
#include <iomanip>
 
// Software Guide : BeginLatex
//
// The header files of the classes featured in this example are included as a
// first step.
//
// \index{Histogram\-To\-Probability\-Image\-Filter!Header}
// \index{Mutual\-Information\-Histogram\-Image\-To\-Image\-Metric!Header}
//
// Software Guide : EndLatex
 
// Software Guide : BeginCodeSnippet
#include "itkHistogramToEntropyImageFilter.h"
#include "itkMutualInformationHistogramImageToImageMetric.h"
// Software Guide : EndCodeSnippet
 
#include "itkCommand.h"
 
#include <cstdio>
 
// Functor to rescale plot the histogram on a log scale and invert it.
template <class TInput>
class RescaleDynamicRangeFunctor
{
public:
  using OutputPixelType = unsigned char;
  RescaleDynamicRangeFunctor() = default;
  ~RescaleDynamicRangeFunctor() = default;
  inline OutputPixelType
  operator()(const TInput & A)
  {
    if ((A > 0.0))
    {
      if (-(30.0 * std::log(A)) > 255)
      {
        return static_cast<OutputPixelType>(255);
      }
      else
      {
        return itk::Math::Round<OutputPixelType>(-(30.0 * std::log(A)));
      }
    }
    else
    {
      return static_cast<OutputPixelType>(255);
    }
  }
};
 
// Class to write the joint histograms.
// Software : BeginLatex
//
// Here we will create a simple class to write the joint histograms. This
// class, that we arbitrarily name as \code{HistogramWriter}, uses internally
// the \doxygen{HistogramToEntropyImageFilter} class among others.
//
// Software Guide : EndLatex
 
// Software Guide : BeginCodeSnippet
namespace
{
class HistogramWriter
{
public:
  using InternalPixelType = float;
  static constexpr unsigned int Dimension = 2;
 
  using InternalImageType = itk::Image<InternalPixelType, Dimension>;
 
  using MetricType =
    itk::MutualInformationHistogramImageToImageMetric<InternalImageType,
                                                      InternalImageType>;
  // Software Guide : EndCodeSnippet
 
  using MetricPointer = MetricType::Pointer;
 
  // Software Guide : BeginCodeSnippet
  using HistogramType = MetricType::HistogramType;
 
  using HistogramToEntropyImageFilterType =
    itk::HistogramToEntropyImageFilter<HistogramType, InternalImageType>;
 
  using HistogramToImageFilterPointer =
    HistogramToEntropyImageFilterType::Pointer;
 
  using OutputImageType = HistogramToEntropyImageFilterType::OutputImageType;
 
  using HistogramFileWriterType = itk::ImageFileWriter<OutputImageType>;
  using HistogramFileWriterPointer = HistogramFileWriterType::Pointer;
  // Software Guide : EndCodeSnippet
 
  using OutputPixelType = HistogramToEntropyImageFilterType::OutputPixelType;
 
  HistogramWriter()
    : m_Metric(nullptr)
  {
 
    // Software Guide : BeginLatex
    //
    // The \code{HistogramWriter} has a member variable \code{m\_Filter} of
    // type HistogramToEntropyImageFilter.
    //
    // Software Guide : EndLatex
 
    // Software Guide : BeginCodeSnippet
    this->m_Filter = HistogramToEntropyImageFilterType::New();
    // Software Guide : EndCodeSnippet
 
    // Software Guide : BeginLatex
    //
    // It also has an ImageFileWriter that has been instantiated using the
    // image type that is produced as output from the histogram to image
    // filter. We connect the output of the filter as input to the writer.
    //
    // Software Guide : EndLatex
 
    // Software Guide : BeginCodeSnippet
    this->m_HistogramFileWriter = HistogramFileWriterType::New();
    this->m_HistogramFileWriter->SetInput(this->m_Filter->GetOutput());
    // Software Guide : EndCodeSnippet
  }
 
  ~HistogramWriter() = default;
 
  void
  SetMetric(MetricPointer metric)
  {
    this->m_Metric = metric;
  }
 
  MetricPointer
  GetMetric() const
  {
    return this->m_Metric;
  }
 
  void
  WriteHistogramFile(unsigned int iterationNumber)
  {
    std::string        outputFileBase = "JointHistogram";
    std::ostringstream outputFilename;
    outputFilename << outputFileBase << "." << std::setfill('0')
                   << std::setw(3) << iterationNumber << "."
                   << "mhd";
    m_HistogramFileWriter->SetFileName(outputFilename.str());
    this->m_Filter->SetInput(this->GetMetric()->GetHistogram());
    this->m_Filter->Modified();
 
    try
    {
      m_Filter->Update();
    }
    catch (const itk::ExceptionObject & err)
    {
      std::cerr << "ERROR: ExceptionObject caught !" << std::endl;
      std::cerr << err << std::endl;
    }
 
    try
    {
      m_HistogramFileWriter->Update();
    }
    catch (const itk::ExceptionObject & excp)
    {
      std::cerr << "Exception thrown " << excp << std::endl;
    }
 
    std::cout << "Joint Histogram file: ";
    std::cout << outputFilename.str() << " written" << std::endl;
  }
 
  // Software Guide : BeginLatex
  //
  // The method of this class that is most relevant to our discussion is the
  // one that writes the image into a file. In this method we assign the
  // output histogram of the metric to the input of the histogram to image
  // filter. In this way we construct an ITK $2D$ image where every pixel
  // corresponds to one of the Bins of the joint histogram computed by the
  // Metric.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  void
  WriteHistogramFile(std::string & outputFilename)
  {
    // Software Guide : EndCodeSnippet
 
 
    // Software Guide : BeginCodeSnippet
    this->m_Filter->SetInput(this->GetMetric()->GetHistogram());
    this->m_Filter->Modified();
 
    // Software Guide : EndCodeSnippet
 
    // Software Guide : BeginLatex
    //
    // The output of the filter is connected to a filter that will rescale the
    // intensities in order to improve the visualization of the values. This
    // is done because it is common to find histograms of medical images that
    // have a minority of bins that are largely dominant. Visualizing such
    // histogram in direct values is challenging because only the dominant
    // bins tend to become visible.
    //
    // Software Guide : EndLatex
 
 
    // Write the joint histogram as outputFilename. Also intensity window
    // the image by lower and upper thresholds and rescale the image to
    // 8 bits.
    using RescaledOutputImageType = itk::Image<unsigned char, Dimension>;
 
    using RescaleDynamicRangeFunctorType =
      RescaleDynamicRangeFunctor<OutputPixelType>;
 
    using RescaleDynamicRangeFilterType =
      itk::UnaryFunctorImageFilter<OutputImageType,
                                   RescaledOutputImageType,
                                   RescaleDynamicRangeFunctorType>;
 
    auto rescaler = RescaleDynamicRangeFilterType::New();
 
    rescaler->SetInput(m_Filter->GetOutput());
 
    using RescaledWriterType = itk::ImageFileWriter<RescaledOutputImageType>;
 
    auto rescaledWriter = RescaledWriterType::New();
 
    rescaledWriter->SetInput(rescaler->GetOutput());
 
    rescaledWriter->SetFileName(outputFilename);
 
    try
    {
      m_Filter->Update();
    }
    catch (const itk::ExceptionObject & err)
    {
      std::cerr << "ERROR: ExceptionObject caught !" << std::endl;
      std::cerr << err << std::endl;
    }
 
    try
    {
      rescaledWriter->Update();
    }
    catch (const itk::ExceptionObject & excp)
    {
      std::cerr << "Exception thrown " << excp << std::endl;
    }
 
    std::cout << "Joint Histogram file: " << outputFilename << " written"
              << std::endl;
  }
 
  // Software Guide : BeginLatex
  //
  // The following are the member variables of our \code{HistogramWriter}
  // class.
  //
  // Software Guide : EndLatex
 
 
  // Software Guide : BeginCodeSnippet
 
private:
  MetricPointer                 m_Metric;
  HistogramToImageFilterPointer m_Filter;
  HistogramFileWriterPointer    m_HistogramFileWriter;
  // Software Guide : EndCodeSnippet
  std::string m_OutputFile;
};
 
// Command - observer invoked after every iteration of the optimizer
class CommandIterationUpdate : public itk::Command
{
public:
  using Self = CommandIterationUpdate;
  using Superclass = itk::Command;
  using Pointer = itk::SmartPointer<Self>;
  itkSimpleNewMacro(Self);
 
protected:
  CommandIterationUpdate() { m_WriteHistogramsAfterEveryIteration = false; }
 
public:
  using OptimizerType = itk::RegularStepGradientDescentOptimizer;
  using OptimizerPointer = const OptimizerType *;
 
  void
  Execute(itk::Object * caller, const itk::EventObject & event) override
  {
    Execute((const itk::Object *)caller, event);
  }
 
  void
  Execute(const itk::Object * object, const itk::EventObject & event) override
  {
    auto optimizer = static_cast<OptimizerPointer>(object);
    if (!itk::IterationEvent().CheckEvent(&event) || optimizer == nullptr)
    {
      return;
    }
    std::cout << optimizer->GetCurrentIteration() << "   ";
    std::cout << optimizer->GetValue() << "   ";
    std::cout << optimizer->GetCurrentPosition() << std::endl;
 
    // Write the joint histogram as a file JointHistogramXXX.mhd
    // where \code{XXX} is the iteration number
 
 
    // Write Joint Entropy Histogram prior to registration.
    if (optimizer->GetCurrentIteration() == 0)
    {
      // Software Guide : BeginLatex
      //
      // We invoke the histogram writer within the Command/Observer of the
      // optimizer to write joint histograms after every iteration.
      //
      // Software Guide : EndLatex
 
      // Software Guide : BeginCodeSnippet
      m_JointHistogramWriter.WriteHistogramFile(m_InitialHistogramFile);
      // Software Guide : EndCodeSnippet
    }
    if (m_WriteHistogramsAfterEveryIteration)
    {
      m_JointHistogramWriter.WriteHistogramFile(
        optimizer->GetCurrentIteration());
    }
  }
 
  void
  SetWriteHistogramsAfterEveryIteration(bool value)
  {
    m_WriteHistogramsAfterEveryIteration = value;
  }
 
  void
  SetInitialHistogramFile(const char * filename)
  {
    m_InitialHistogramFile = filename;
  }
 
  HistogramWriter m_JointHistogramWriter;
 
private:
  bool        m_WriteHistogramsAfterEveryIteration;
  std::string m_InitialHistogramFile;
};
 
} // end anonymous namespace
 
 
int
main(int argc, char * argv[])
{
  if (argc < 8)
  {
    std::cerr << "Missing Parameters " << std::endl;
    std::cerr << "Usage: " << argv[0];
    std::cerr << " fixedImageFile  movingImageFile ";
    std::cerr << "outputImagefile WriteJointHistogramsAfterEveryIteration ";
    std::cerr << "JointHistogramPriorToRegistrationFile ";
    std::cerr << "JointHistogramAfterRegistrationFile ";
    std::cerr
      << "NumberOfHistogramBinsForWritingTheMutualInformationHistogramMetric";
    std::cerr << std::endl;
    return EXIT_FAILURE;
  }
 
  using PixelType = unsigned char;
 
  constexpr unsigned int Dimension = 2;
 
  using FixedImageType = itk::Image<PixelType, Dimension>;
  using MovingImageType = itk::Image<PixelType, Dimension>;
  using InternalPixelType = float;
  using InternalImageType = itk::Image<InternalPixelType, Dimension>;
 
  using TransformType = itk::TranslationTransform<double, Dimension>;
  using OptimizerType = itk::RegularStepGradientDescentOptimizer;
  using InterpolatorType =
    itk::LinearInterpolateImageFunction<InternalImageType, double>;
  using RegistrationType =
    itk::ImageRegistrationMethod<InternalImageType, InternalImageType>;
 
  using MetricType =
    itk::MutualInformationHistogramImageToImageMetric<InternalImageType,
                                                      InternalImageType>;
 
  // Software Guide : BeginLatex
  //
  // We instantiate an optimizer, interpolator and the registration method as
  // shown in previous examples.
  //
  // Software Guide : EndLatex
 
  auto transform = TransformType::New();
  auto optimizer = OptimizerType::New();
  auto interpolator = InterpolatorType::New();
  auto registration = RegistrationType::New();
  auto metric = MetricType::New();
 
 
  registration->SetOptimizer(optimizer);
  registration->SetTransform(transform);
  registration->SetInterpolator(interpolator);
 
  // Software Guide : BeginLatex
  //
  // The number of bins in the metric is set with the
  // \code{SetHistogramSize()} method. This will determine the number of
  // pixels along each dimension of the joint histogram. Note that in this
  // case we arbitrarily decided to use the same number of bins for the
  // intensities of the Fixed image and those of the Moving image. However,
  // this does not have to be the case, we could have selected different
  // numbers of bins for each image.
  //
  // \index{Mutual\-Information\-Histogram\-Image\-To\-Image\-Metric!SetHistogramSize()}
  // \index{SetHistogramSize(),Mutual\-Information\-Histogram\-Image\-To\-Image\-Metric}
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  unsigned int numberOfHistogramBins = std::stoi(argv[7]);
  MetricType::HistogramType::SizeType histogramSize;
  histogramSize.SetSize(2);
  histogramSize[0] = numberOfHistogramBins;
  histogramSize[1] = numberOfHistogramBins;
  metric->SetHistogramSize(histogramSize);
  // Software Guide : EndCodeSnippet
 
  const unsigned int numberOfParameters = transform->GetNumberOfParameters();
  using ScalesType = MetricType::ScalesType;
  ScalesType scales(numberOfParameters);
  scales.Fill(1.0);
  metric->SetDerivativeStepLengthScales(scales);
 
  auto observer = CommandIterationUpdate::New();
 
  // Set the metric for the joint histogram writer
  observer->m_JointHistogramWriter.SetMetric(metric);
 
  registration->SetMetric(metric);
 
  using FixedImageReaderType = itk::ImageFileReader<FixedImageType>;
  using MovingImageReaderType = itk::ImageFileReader<MovingImageType>;
 
  auto fixedImageReader = FixedImageReaderType::New();
  auto movingImageReader = MovingImageReaderType::New();
 
  fixedImageReader->SetFileName(argv[1]);
  movingImageReader->SetFileName(argv[2]);
 
 
  using FixedNormalizeFilterType =
    itk::NormalizeImageFilter<FixedImageType, InternalImageType>;
 
  using MovingNormalizeFilterType =
    itk::NormalizeImageFilter<MovingImageType, InternalImageType>;
 
  auto fixedNormalizer = FixedNormalizeFilterType::New();
 
  auto movingNormalizer = MovingNormalizeFilterType::New();
  using GaussianFilterType =
    itk::DiscreteGaussianImageFilter<InternalImageType, InternalImageType>;
 
  auto fixedSmoother = GaussianFilterType::New();
  auto movingSmoother = GaussianFilterType::New();
 
  fixedSmoother->SetVariance(2.0);
  movingSmoother->SetVariance(2.0);
  fixedNormalizer->SetInput(fixedImageReader->GetOutput());
  movingNormalizer->SetInput(movingImageReader->GetOutput());
 
  fixedSmoother->SetInput(fixedNormalizer->GetOutput());
  movingSmoother->SetInput(movingNormalizer->GetOutput());
 
  registration->SetFixedImage(fixedSmoother->GetOutput());
  registration->SetMovingImage(movingSmoother->GetOutput());
 
 
  try
  {
    fixedNormalizer->Update();
  }
  catch (const itk::ExceptionObject & err)
  {
    std::cout << "ExceptionObject caught !" << std::endl;
    std::cout << err << std::endl;
    return EXIT_FAILURE;
  }
 
  registration->SetFixedImageRegion(
    fixedNormalizer->GetOutput()->GetBufferedRegion());
 
  using ParametersType = RegistrationType::ParametersType;
  ParametersType initialParameters(transform->GetNumberOfParameters());
 
  initialParameters[0] = 0.0; // Initial offset in mm along X
  initialParameters[1] = 0.0; // Initial offset in mm along Y
 
  registration->SetInitialTransformParameters(initialParameters);
 
 
  optimizer->SetMaximumStepLength(4.00);
  optimizer->SetMinimumStepLength(0.01);
  optimizer->SetRelaxationFactor(0.90);
  optimizer->SetNumberOfIterations(200);
  optimizer->MaximizeOn();
 
  optimizer->AddObserver(itk::IterationEvent(), observer);
 
 
  observer->SetInitialHistogramFile(argv[5]);
 
  if (std::stoi(argv[4]))
  {
    observer->SetWriteHistogramsAfterEveryIteration(true);
  }
 
 
  try
  {
    registration->Update();
    std::cout << "Optimizer stop condition: "
              << registration->GetOptimizer()->GetStopConditionDescription()
              << std::endl;
  }
  catch (const itk::ExceptionObject & err)
  {
    std::cout << "ExceptionObject caught !" << std::endl;
    std::cout << err << std::endl;
    return EXIT_FAILURE;
  }
 
  ParametersType finalParameters = registration->GetLastTransformParameters();
 
  double TranslationAlongX = finalParameters[0];
  double TranslationAlongY = finalParameters[1];
 
  unsigned int numberOfIterations = optimizer->GetCurrentIteration();
 
  double bestValue = optimizer->GetValue();
 
 
  std::cout << "Result = " << std::endl;
  std::cout << " Translation X = " << TranslationAlongX << std::endl;
  std::cout << " Translation Y = " << TranslationAlongY << std::endl;
  std::cout << " Iterations    = " << numberOfIterations << std::endl;
  std::cout << " Metric value  = " << bestValue << std::endl;
 
  // Write Joint Entropy Histogram after registration.
  std::string histogramAfter(argv[6]);
  try
  {
    observer->m_JointHistogramWriter.WriteHistogramFile(histogramAfter);
  }
  catch (const itk::ExceptionObject & err)
  {
    std::cerr << "ERROR: ExceptionObject caught !" << std::endl;
    std::cerr << err << std::endl;
    return EXIT_FAILURE;
  }
 
  using ResampleFilterType =
    itk::ResampleImageFilter<MovingImageType, FixedImageType>;
 
  auto finalTransform = TransformType::New();
 
  finalTransform->SetParameters(finalParameters);
  finalTransform->SetFixedParameters(transform->GetFixedParameters());
 
  auto resample = ResampleFilterType::New();
 
  resample->SetTransform(finalTransform);
  resample->SetInput(movingImageReader->GetOutput());
 
  FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
 
  resample->SetSize(fixedImage->GetLargestPossibleRegion().GetSize());
  resample->SetOutputOrigin(fixedImage->GetOrigin());
  resample->SetOutputSpacing(fixedImage->GetSpacing());
  resample->SetOutputDirection(fixedImage->GetDirection());
  resample->SetDefaultPixelValue(100);
 
 
  using OutputPixelType = unsigned char;
 
  using OutputImageType = itk::Image<OutputPixelType, Dimension>;
 
  using CastFilterType =
    itk::CastImageFilter<FixedImageType, OutputImageType>;
 
  using WriterType = itk::ImageFileWriter<OutputImageType>;
 
 
  auto writer = WriterType::New();
  auto caster = CastFilterType::New();
 
 
  writer->SetFileName(argv[3]);
 
 
  caster->SetInput(resample->GetOutput());
  writer->SetInput(caster->GetOutput());
  try
  {
    writer->Update();
  }
  catch (const itk::ExceptionObject & err)
  {
    std::cerr << "ERROR: ExceptionObject caught !" << std::endl;
    std::cerr << err << std::endl;
  }
 
  return EXIT_SUCCESS;
}
 
// Software Guide : BeginLatex
//
// Mutual information attempts to re-group the joint entropy histograms into a
// more ``meaningful'' formation. An optimizer that minimizes the joint
// entropy seeks a transform that produces a small number of high value bins
// and a large majority of almost zero bins. Multi-modality registration seeks
// such a transform while also attempting to maximize the information
// contribution by the fixed and the moving images in the overall region of
// the metric.
//
// A T1 MRI (fixed image) and a proton density MRI (moving image) as shown in
// Figure \ref{fig:FixedMovingImageRegistration2} are provided as input to
// this example.
//
// Figure \ref{fig:JointEntropyHistograms} shows the joint histograms before
// and after registration. \begin{figure} \center
// \includegraphics[width=0.44\textwidth]{JointEntropyHistogramPriorToRegistration}
// \includegraphics[width=0.44\textwidth]{JointEntropyHistogramAfterRegistration}
// \itkcaption[Multi-modality joint histograms]{Joint entropy histograms
// before and after registration. The final transform was within half a pixel
// of true misalignment.} \label{fig:JointEntropyHistograms} \end{figure}
//  Software Guide : EndLatex