ImageRegistration1.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
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//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySliceBorder20.png}
//    INPUTS:  {BrainProtonDensitySliceShifted13x17y.png}
//    OUTPUTS: {ImageRegistration1Output.png}
//    OUTPUTS: {ImageRegistration1DifferenceAfter.png}
//    OUTPUTS: {ImageRegistration1DifferenceBefore.png}
//  Software Guide : EndCommandLineArgs

// Software Guide : BeginLatex
//
// This example illustrates the use of the image registration framework in
// Insight.  It should be read as a ``Hello World'' for ITK registration.
// Instead of means to an end, this example should be read as a basic
// introduction to the elements typically involved when solving a problem
// of image registration.
//
// \index{itk::Image!Instantiation}
// \index{itk::Image!Header}
//
// A registration method requires the following set of components: two input
// images, a transform, a metric and an optimizer. Some of these components
// are parameterized by the image type for which the registration is intended.
// The following header files provide declarations of common types used for
// these components.
//
// Software Guide : EndLatex


// Software Guide : BeginCodeSnippet
#include "itkImageRegistrationMethodv4.h"
#include "itkTranslationTransform.h"
#include "itkMeanSquaresImageToImageMetricv4.h"
#include "itkRegularStepGradientDescentOptimizerv4.h"
// Software Guide : EndCodeSnippet


#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"

#include "itkResampleImageFilter.h"
#include "itkCastImageFilter.h"
#include "itkRescaleIntensityImageFilter.h"
#include "itkSubtractImageFilter.h"


class CommandIterationUpdate : public itk::Command
{
public:
  using Self = CommandIterationUpdate;
  using Superclass = itk::Command;
  using Pointer = itk::SmartPointer<Self>;
  itkNewMacro(Self);

protected:
  CommandIterationUpdate() = default;

public:
  using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
  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))
    {
      return;
    }

    std::cout << optimizer->GetCurrentIteration() << " = ";
    std::cout << optimizer->GetValue() << " : ";
    std::cout << optimizer->GetCurrentPosition() << std::endl;
  }
};


int
main(int argc, char * argv[])
{
  if (argc < 4)
  {
    std::cerr << "Missing Parameters " << std::endl;
    std::cerr << "Usage: " << argv[0];
    std::cerr << " fixedImageFile  movingImageFile ";
    std::cerr << "outputImagefile [differenceImageAfter]";
    std::cerr << "[differenceImageBefore] [useEstimator]" << std::endl;
    return EXIT_FAILURE;
  }


  // Software Guide : BeginLatex
  //
  // The type of each registration component should
  // be instantiated first. We start by selecting the image
  // dimension and the types to be used for representing image pixels.
  //
  // Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  constexpr unsigned int Dimension = 2;
  using PixelType = float;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The types of the input images are instantiated by the following lines.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using FixedImageType = itk::Image<PixelType, Dimension>;
  using MovingImageType = itk::Image<PixelType, Dimension>;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The transform that will map the fixed image space into the moving image
  //  space is defined below.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using TransformType = itk::TranslationTransform<double, Dimension>;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  An optimizer is required to explore the parameter space of the transform
  //  in search of optimal values of the metric.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The metric will compare how well the two images match each other. Metric
  //  types are usually templated over the image types as seen in
  //  the following type declaration.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using MetricType =
    itk::MeanSquaresImageToImageMetricv4<FixedImageType, MovingImageType>;
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  The registration method type is instantiated using the types of the
  //  fixed and moving images as well as the output transform type. This class
  //  is responsible for interconnecting all the components that we have
  //  described so far.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using RegistrationType = itk::
    ImageRegistrationMethodv4<FixedImageType, MovingImageType, TransformType>;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  Each one of the registration components is created using its
  //  \code{New()} method and is assigned to its respective
  //  \doxygen{SmartPointer}.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  MetricType::Pointer       metric = MetricType::New();
  OptimizerType::Pointer    optimizer = OptimizerType::New();
  RegistrationType::Pointer registration = RegistrationType::New();
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  Each component is now connected to the instance of the registration
  //  method.
  //
  //  \index{itk::RegistrationMethodv4!SetMetric()}
  //  \index{itk::RegistrationMethodv4!SetOptimizer()}
  //  \index{itk::RegistrationMethodv4!SetFixedImage()}
  //  \index{itk::RegistrationMethodv4!SetMovingImage()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  registration->SetMetric(metric);
  registration->SetOptimizer(optimizer);
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  In this example the transform object does not need to be created and
  //  passed to the registration method like above since the registration
  //  filter will instantiate an internal transform object using the transform
  //  type that is passed to it as a template parameter.
  //
  //  Metric needs an interpolator to evaluate the intensities of the fixed
  //  and moving images at non-grid positions. The types of fixed and moving
  //  interpolators are declared here.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using FixedLinearInterpolatorType =
    itk::LinearInterpolateImageFunction<FixedImageType, double>;

  using MovingLinearInterpolatorType =
    itk::LinearInterpolateImageFunction<MovingImageType, double>;
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  Then, fixed and moving interpolators are created and passed to the
  //  metric. Since linear interpolators are used as default, we could skip
  //  the following step in this example.
  //
  //  \index{itk::MeanSquaresImageToImageMetricv4!SetFixedInterpolator()}
  //  \index{itk::MeanSquaresImageToImageMetricv4!SetMovingInterpolator()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  FixedLinearInterpolatorType::Pointer fixedInterpolator =
    FixedLinearInterpolatorType::New();
  MovingLinearInterpolatorType::Pointer movingInterpolator =
    MovingLinearInterpolatorType::New();

  metric->SetFixedInterpolator(fixedInterpolator);
  metric->SetMovingInterpolator(movingInterpolator);
  // Software Guide : EndCodeSnippet

  using FixedImageReaderType = itk::ImageFileReader<FixedImageType>;
  using MovingImageReaderType = itk::ImageFileReader<MovingImageType>;
  FixedImageReaderType::Pointer fixedImageReader =
    FixedImageReaderType::New();
  MovingImageReaderType::Pointer movingImageReader =
    MovingImageReaderType::New();

  fixedImageReader->SetFileName(argv[1]);
  movingImageReader->SetFileName(argv[2]);


  //  Software Guide : BeginLatex
  //
  //  In this example, the fixed and moving images are read from files. This
  //  requires the \doxygen{ImageRegistrationMethodv4} to acquire its inputs
  //  from the output of the readers.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  registration->SetFixedImage(fixedImageReader->GetOutput());
  registration->SetMovingImage(movingImageReader->GetOutput());
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  Now the registration process should be initialized. ITKv4 registration
  //  framework provides initial transforms for both fixed and moving images.
  //  These transforms can be used to setup an initial known correction of the
  //  misalignment between the virtual domain and fixed/moving image spaces.
  //  In this particular case, a translation transform is being used for
  //  initialization of the moving image space.
  //  The array of parameters for the initial moving transform is simply
  //  composed of the translation values along each dimension. Setting the
  //  values of the parameters to zero initializes the transform to an
  //  \emph{Identity} transform. Note that the array constructor requires the
  //  number of elements to be passed as an argument.
  //
  //  \index{itk::TranslationTransform!GetNumberOfParameters()}
  //  \index{itk::RegistrationMethodv4!SetMovingInitialTransform()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  TransformType::Pointer movingInitialTransform = TransformType::New();

  TransformType::ParametersType initialParameters(
    movingInitialTransform->GetNumberOfParameters());
  initialParameters[0] = 0.0; // Initial offset in mm along X
  initialParameters[1] = 0.0; // Initial offset in mm along Y

  movingInitialTransform->SetParameters(initialParameters);

  registration->SetMovingInitialTransform(movingInitialTransform);
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  In the registration filter this moving initial transform will be added
  //  to a composite transform that already includes an instantiation of the
  //  output optimizable transform; then, the resultant composite transform
  //  will be used by the optimizer to evaluate the metric values at each
  //  iteration.
  //
  //  Despite this, the fixed initial transform does not contribute to the
  //  optimization process. It is only used to access the fixed image from the
  //  virtual image space where the metric evaluation happens.
  //
  //  Virtual images are a new concept added to the ITKv4 registration
  //  framework, which potentially lets us to do the registration process in a
  //  physical domain totally different from the fixed and moving image
  //  domains. In fact, the region over which metric evaluation is performed
  //  is called virtual image domain. This domain defines the resolution at
  //  which the evaluation is performed, as well as the physical coordinate
  //  system.
  //
  //  The virtual reference domain is taken from the ``virtual image''
  //  buffered region, and the input images should be accessed from this
  //  reference space using the fixed and moving initial transforms.
  //
  //  The legacy intuitive registration framework can be considered as a
  //  special case where the virtual domain is the same as the fixed image
  //  domain. As this case practically happens in most of the real life
  //  applications, the virtual image is set to be the same as the fixed image
  //  by default. However, the user can define the virtual domain differently
  //  than the fixed image domain by calling either \code{SetVirtualDomain} or
  //  \code{SetVirtualDomainFromImage}.
  //
  //  In this example, like the most examples of this chapter, the virtual
  //  image is considered the same as the fixed image. Since the registration
  //  process happens in the fixed image physical domain, the fixed initial
  //  transform maintains its default value of identity and does not need to
  //  be set.
  //
  //  However, a ``Hello World!'' example should show all the basics, so
  //  all the registration components are explicity set here.
  //
  //  In the next section of this chapter, you will get a better understanding
  //  from behind the scenes of the registration process when the initial
  //  fixed transform is not identity.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  TransformType::Pointer identityTransform = TransformType::New();
  identityTransform->SetIdentity();

  registration->SetFixedInitialTransform(identityTransform);
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  Note that the above process shows only one way of initializing the
  //  registration configuration. Another option is to initialize the output
  //  optimizable transform directly. In this approach, a transform object is
  //  created, initialized, and then passed to the registration method via
  //  \code{SetInitialTransform()}. This approach is shown in
  //  section~\ref{sec:RigidRegistrationIn2D}.
  //
  //  At this point the registration method is ready for execution. The
  //  optimizer is the component that drives the execution of the
  //  registration.  However, the ImageRegistrationMethodv4 class
  //  orchestrates the ensemble to make sure that everything is in place
  //  before control is passed to the optimizer.
  //
  //  It is usually desirable to fine tune the parameters of the optimizer.
  //  Each optimizer has particular parameters that must be interpreted in the
  //  context of the optimization strategy it implements. The optimizer used
  //  in this example is a variant of gradient descent that attempts to
  //  prevent it from taking steps that are too large. At each iteration, this
  //  optimizer will take a step along the direction of the
  //  \doxygen{ImageToImageMetricv4} derivative. Each time the direction of
  //  the derivative abruptly changes, the optimizer assumes that a local
  //  extrema has been passed and reacts by reducing the step length by a
  //  relaxation factor. The reducing factor should have a value between 0
  //  and 1. This factor is set to 0.5 by default, and it can be changed to a
  //  different value via \code{SetRelaxationFactor()}. Also, the default
  //  value for the initial step length is 1, and this value can be changed
  //  manually with the method \code{SetLearningRate()}.
  //
  //  In addition to manual settings, the initial step size can also be
  //  estimated automatically, either at each iteration or only at the first
  //  iteration, by assigning a ScalesEstimator (as will be seen in later
  //  examples).
  //
  //  After several reductions of the step length, the optimizer may be moving
  //  in a very restricted area of the transform parameter space. By the
  //  method \code{SetMinimumStepLength()}, the user can define how small the
  //  step length should be to consider convergence to have been reached. This
  //  is equivalent to defining the precision with which the final transform
  //  should be known. User can also set some other stop criteria manually
  //  like maximum number of iterations.
  //
  //  In other gradient descent-based optimizers of the ITKv4 framework, such
  //  as \doxygen{GradientDescentLineSearchOptimizerv4} and
  //  \doxygen{ConjugateGradientLineSearchOptimizerv4}, the convergence
  //  criteria are set via \code{SetMinimumConvergenceValue()} which is
  //  computed based on the results of the last few iterations. The number of
  //  iterations involved in computations are defined by the convergence
  //  window size via \code{SetConvergenceWindowSize()} which is shown in
  //  later examples of this chapter.
  //
  //  Also note that unlike the previous versions, ITKv4 optimizers do not
  //  have a
  //  ``maximize/minimize'' option to modify the effect of the metric
  //  derivatives. Each assigned metric is assumed to return a parameter
  //  derivative result that "improves" the optimization.
  //
  //  \index{itk::Gradient\-Descent\-Optimizerv4\-Template!SetLearningRate()}
  //  \index{itk::Gradient\-Descent\-Optimizerv4\-Template!SetMinimumStepLength()}
  //  \index{itk::Gradient\-Descent\-Optimizerv4\-Template!SetRelaxationFactor()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  optimizer->SetLearningRate(4);
  optimizer->SetMinimumStepLength(0.001);
  optimizer->SetRelaxationFactor(0.5);
  // Software Guide : EndCodeSnippet

  bool useEstimator = false;
  if (argc > 6)
  {
    useEstimator = std::stoi(argv[6]) != 0;
  }

  if (useEstimator)
  {
    using ScalesEstimatorType =
      itk::RegistrationParameterScalesFromPhysicalShift<MetricType>;
    ScalesEstimatorType::Pointer scalesEstimator = ScalesEstimatorType::New();
    scalesEstimator->SetMetric(metric);
    scalesEstimator->SetTransformForward(true);
    optimizer->SetScalesEstimator(scalesEstimator);
    optimizer->SetDoEstimateLearningRateOnce(true);
  }


  //  Software Guide : BeginLatex
  //
  //  In case the optimizer never succeeds reaching the desired
  //  precision tolerance, it is prudent to establish a limit on the number of
  //  iterations to be performed. This maximum number is defined with the
  //  method \code{SetNumberOfIterations()}.
  //
  //  \index{itk::Gradient\-Descent\-Optimizerv4\-Template!SetNumberOfIterations()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  optimizer->SetNumberOfIterations(200);
  // Software Guide : EndCodeSnippet


  // Connect an observer
  CommandIterationUpdate::Pointer observer = CommandIterationUpdate::New();
  optimizer->AddObserver(itk::IterationEvent(), observer);

  //  Software Guide : BeginLatex
  //
  //  ITKv4 facilitates a multi-level registration framework whereby each
  //  stage is different in the resolution of its virtual space and the
  //  smoothness of the fixed and moving images. These criteria need to be
  //  defined before registration starts. Otherwise, the default values will
  //  be used. In this example, we run a simple registration in one level with
  //  no space shrinking or smoothing on the input data.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  constexpr unsigned int numberOfLevels = 1;

  RegistrationType::ShrinkFactorsArrayType shrinkFactorsPerLevel;
  shrinkFactorsPerLevel.SetSize(1);
  shrinkFactorsPerLevel[0] = 1;

  RegistrationType::SmoothingSigmasArrayType smoothingSigmasPerLevel;
  smoothingSigmasPerLevel.SetSize(1);
  smoothingSigmasPerLevel[0] = 0;

  registration->SetNumberOfLevels(numberOfLevels);
  registration->SetSmoothingSigmasPerLevel(smoothingSigmasPerLevel);
  registration->SetShrinkFactorsPerLevel(shrinkFactorsPerLevel);
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  The registration process is triggered by an invocation of the
  //  \code{Update()} method. If something goes wrong during the
  //  initialization or execution of the registration an exception will be
  //  thrown. We should therefore place the \code{Update()} method
  //  inside a \code{try/catch} block as illustrated in the following lines.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  try
  {
    registration->Update();
    std::cout << "Optimizer stop condition: "
              << registration->GetOptimizer()->GetStopConditionDescription()
              << std::endl;
  }
  catch (const itk::ExceptionObject & err)
  {
    std::cerr << "ExceptionObject caught !" << std::endl;
    std::cerr << err << std::endl;
    return EXIT_FAILURE;
  }
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  In a real life application, you may attempt to recover from the error by
  //  taking more effective actions in the catch block. Here we are simply
  //  printing out a message and then terminating the execution of the
  //  program.
  //
  //
  //  The result of the registration process is obtained using the
  //  \code{GetTransform()} method that returns a constant pointer to the
  //  output transform.
  //
  //  \index{itk::ImageRegistrationMethodv4!GetTransform()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  TransformType::ConstPointer transform = registration->GetTransform();
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  In the case of the \doxygen{TranslationTransform}, there is a
  //  straightforward interpretation of the parameters.  Each element of the
  //  array corresponds to a translation along one spatial dimension.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  TransformType::ParametersType finalParameters = transform->GetParameters();
  const double                  TranslationAlongX = finalParameters[0];
  const double                  TranslationAlongY = finalParameters[1];
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The optimizer can be queried for the actual number of iterations
  //  performed to reach convergence.  The \code{GetCurrentIteration()}
  //  method returns this value. A large number of iterations may be an
  //  indication that the learning rate has been set too small, which
  //  is undesirable since it results in long computational times.
  //
  //  \index{itk::Gradient\-Descent\-Optimizerv4\-Template!GetCurrentIteration()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  const unsigned int numberOfIterations = optimizer->GetCurrentIteration();
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  The value of the image metric corresponding to the last set of
  //  parameters can be obtained with the \code{GetValue()} method of the
  //  optimizer.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  const double bestValue = optimizer->GetValue();
  // Software Guide : EndCodeSnippet


  // Print out results
  //
  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;


  //  Software Guide : BeginLatex
  //
  //  Let's execute this example over two of the images provided in
  //  \code{Examples/Data}:
  //
  //  \begin{itemize}
  //  \item \code{BrainProtonDensitySliceBorder20.png}
  //  \item \code{BrainProtonDensitySliceShifted13x17y.png}
  //  \end{itemize}
  //
  //  The second image is the result of intentionally translating the first
  //  image by $(13,17)$ millimeters. Both images have unit-spacing and
  //  are shown in Figure \ref{fig:FixedMovingImageRegistration1}. The
  //  registration takes 20 iterations and the resulting transform parameters
  //  are:
  //
  //  \begin{verbatim}
  //  Translation X = 13.0012
  //  Translation Y = 16.9999
  //  \end{verbatim}
  //
  //  As expected, these values match quite well the misalignment that we
  //  intentionally introduced in the moving image.
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceBorder20}
  // \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceShifted13x17y}
  // \itkcaption[Fixed and Moving images in registration framework]{Fixed and
  // Moving image provided as input to the registration method.}
  // \label{fig:FixedMovingImageRegistration1}
  // \end{figure}
  //
  //
  //  Software Guide : EndLatex


  //  Software Guide : BeginLatex
  //
  //  It is common, as the last step of a registration task, to use the
  //  resulting transform to map the moving image into the fixed image space.
  //
  //  Before the mapping process, notice that we have not used the direct
  //  initialization of the output transform in this example, so the
  //  parameters of the moving initial transform are not reflected in the
  //  output parameters of the registration filter. Hence, a composite
  //  transform is needed to concatenate both initial and output transforms
  //  together.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using CompositeTransformType = itk::CompositeTransform<double, Dimension>;
  CompositeTransformType::Pointer outputCompositeTransform =
    CompositeTransformType::New();
  outputCompositeTransform->AddTransform(movingInitialTransform);
  outputCompositeTransform->AddTransform(
    registration->GetModifiableTransform());
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  Now the mapping process is easily done with the
  //  \doxygen{ResampleImageFilter}. Please refer to
  //  Section~\ref{sec:ResampleImageFilter} for details on the use of this
  //  filter.  First, a ResampleImageFilter type is instantiated using the
  //  image types. It is convenient to use the fixed image type as the output
  //  type since it is likely that the transformed moving image will be
  //  compared with the fixed image.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using ResampleFilterType =
    itk::ResampleImageFilter<MovingImageType, FixedImageType>;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  A resampling filter is created and the moving image is connected as
  //  its input.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  ResampleFilterType::Pointer resampler = ResampleFilterType::New();
  resampler->SetInput(movingImageReader->GetOutput());
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The created output composite transform is also passed as input to the
  //  resampling filter.
  //
  //  \index{itk::ImageRegistrationMethod!Resampling image}
  //  \index{itk::ImageRegistrationMethod!Pipeline}
  //  \index{itk::ImageRegistrationMethod!DataObjectDecorator}
  //  \index{itk::ImageRegistrationMethod!GetOutput()}
  //  \index{itk::DataObjectDecorator!Use in Registration}
  //  \index{itk::DataObjectDecorator!Get()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  resampler->SetTransform(outputCompositeTransform);
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  As described in Section \ref{sec:ResampleImageFilter}, the
  //  ResampleImageFilter requires additional parameters to be specified, in
  //  particular, the spacing, origin and size of the output image. The
  //  default pixel value is also set to a distinct gray level in order to
  //  highlight the regions that are mapped outside of the moving image.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
  resampler->SetSize(fixedImage->GetLargestPossibleRegion().GetSize());
  resampler->SetOutputOrigin(fixedImage->GetOrigin());
  resampler->SetOutputSpacing(fixedImage->GetSpacing());
  resampler->SetOutputDirection(fixedImage->GetDirection());
  resampler->SetDefaultPixelValue(100);
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.32\textwidth]{ImageRegistration1Output}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration1DifferenceBefore}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration1DifferenceAfter}
  // \itkcaption[HelloWorld registration output images]{Mapped moving image
  // and its difference with the fixed image before and after registration}
  // \label{fig:ImageRegistration1Output}
  // \end{figure}
  //
  //  Software Guide : EndLatex


  //  Software Guide : BeginLatex
  //
  //  The output of the filter is passed to a writer that will store the
  //  image in a file. An \doxygen{CastImageFilter} is used to convert the
  //  pixel type of the resampled image to the final type used by the
  //  writer. The cast and writer filters are instantiated below.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using OutputPixelType = unsigned char;

  using OutputImageType = itk::Image<OutputPixelType, Dimension>;

  using CastFilterType =
    itk::CastImageFilter<FixedImageType, OutputImageType>;

  using WriterType = itk::ImageFileWriter<OutputImageType>;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The filters are created by invoking their \code{New()}
  //  method.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  WriterType::Pointer     writer = WriterType::New();
  CastFilterType::Pointer caster = CastFilterType::New();
  // Software Guide : EndCodeSnippet


  writer->SetFileName(argv[3]);


  //  Software Guide : BeginLatex
  //
  //  The filters are connected together and the \code{Update()} method of the
  //  writer is invoked in order to trigger the execution of the pipeline.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  caster->SetInput(resampler->GetOutput());
  writer->SetInput(caster->GetOutput());
  writer->Update();
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=\textwidth]{ImageRegistration1Pipeline}
  // \itkcaption[Pipeline structure of the registration example]{Pipeline
  // structure of the registration example.}
  // \label{fig:ImageRegistration1Pipeline}
  // \end{figure}
  //
  //
  //  Software Guide : EndLatex


  //  Software Guide : BeginLatex
  //
  //  The fixed image and the transformed moving image can easily be compared
  //  using the \doxygen{SubtractImageFilter}. This pixel-wise filter computes
  //  the difference between homologous pixels of its two input images.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using DifferenceFilterType =
    itk::SubtractImageFilter<FixedImageType, FixedImageType, FixedImageType>;

  DifferenceFilterType::Pointer difference = DifferenceFilterType::New();

  difference->SetInput1(fixedImageReader->GetOutput());
  difference->SetInput2(resampler->GetOutput());
  // Software Guide : EndCodeSnippet


  // Software Guide : BeginLatex
  //
  //  Note that the use of subtraction as a method for comparing the images is
  //  appropriate here because we chose to represent the images using a pixel
  //  type \code{float}. A different filter would have been used if the pixel
  //  type of the images were any of the \code{unsigned} integer types.
  //
  // Software Guide : EndLatex


  //  Software Guide : BeginLatex
  //
  //  Since the differences between the two images may correspond to very low
  //  values of intensity, we rescale those intensities with a
  //  \doxygen{RescaleIntensityImageFilter} in order to make them more
  //  visible. This rescaling will also make it possible to visualize the
  //  negative values even if we save the difference image in a file format
  //  that only supports unsigned pixel values\footnote{This is the case of
  //  PNG, BMP, JPEG and TIFF among other common file formats.}.  We also
  //  reduce the \code{DefaultPixelValue} to ``1'' in order to prevent that
  //  value from absorbing the dynamic range of the differences between the
  //  two images.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using RescalerType =
    itk::RescaleIntensityImageFilter<FixedImageType, OutputImageType>;

  RescalerType::Pointer intensityRescaler = RescalerType::New();

  intensityRescaler->SetInput(difference->GetOutput());
  intensityRescaler->SetOutputMinimum(0);
  intensityRescaler->SetOutputMaximum(255);

  resampler->SetDefaultPixelValue(1);
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  Its output can be passed to another writer.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  WriterType::Pointer writer2 = WriterType::New();
  writer2->SetInput(intensityRescaler->GetOutput());
  // Software Guide : EndCodeSnippet


  if (argc > 4)
  {
    writer2->SetFileName(argv[4]);
    writer2->Update();
  }


  //  Software Guide : BeginLatex
  //
  //  For the purpose of comparison, the difference between the fixed image
  //  and the moving image before registration can also be computed by simply
  //  setting the transform to an identity transform. Note that the resampling
  //  is still necessary because the moving image does not necessarily have
  //  the same spacing, origin and number of pixels as the fixed image.
  //  Therefore a pixel-by-pixel operation cannot in general be performed. The
  //  resampling process with an identity transform will ensure that we have a
  //  representation of the moving image in the grid of the fixed image.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  resampler->SetTransform(identityTransform);
  // Software Guide : EndCodeSnippet


  if (argc > 5)
  {
    writer2->SetFileName(argv[5]);
    writer2->Update();
  }


  //  Software Guide : BeginLatex
  //
  //  The complete pipeline structure of the current example is presented in
  //  Figure~\ref{fig:ImageRegistration1Pipeline}.  The components of the
  //  registration method are depicted as well.  Figure
  //  \ref{fig:ImageRegistration1Output} (left) shows the result of resampling
  //  the moving image in order to map it onto the fixed image space. The top
  //  and right borders of the image appear in the gray level selected with
  //  the \code{SetDefaultPixelValue()} in the ResampleImageFilter. The center
  //  image shows the difference between the fixed image and the original
  //  moving image (i.e. the difference before the registration is
  //  performed). The right image shows the difference between the fixed image
  //  and the transformed moving image (i.e. after the registration has
  //  been performed).  Both difference images have been rescaled in intensity
  //  in order to highlight those pixels where differences exist.  Note that
  //  the final registration is still off by a fraction of a pixel, which
  //  causes bands around edges of anatomical structures to appear in the
  //  difference image. A perfect registration would have produced a null
  //  difference image.
  //
  //  Software Guide : EndLatex


  //  Software Guide : BeginLatex
  //
  // \begin{figure}
  // \center
  // \includegraphics[height=0.44\textwidth]{ImageRegistration1TraceTranslations}
  // \includegraphics[height=0.44\textwidth]{ImageRegistration1TraceMetric}
  // \itkcaption[Trace of translations and metrics during registration]{The
  // sequence of translations and metric values at each iteration of the
  // optimizer.} \label{fig:ImageRegistration1Trace} \end{figure}
  //
  //  It is always useful to keep in mind that registration is essentially an
  //  optimization problem. Figure \ref{fig:ImageRegistration1Trace} helps to
  //  reinforce this notion by showing the trace of translations and values of
  //  the image metric at each iteration of the optimizer. It can be seen from
  //  the top figure that the step length is reduced progressively as the
  //  optimizer gets closer to the metric extrema. The bottom plot clearly
  //  shows how the metric value decreases as the optimization advances. The
  //  log plot helps to highlight the normal oscillations of the optimizer
  //  around the extrema value.
  //
  //  In this section, we used a very simple example to introduce the basic
  //  components of a registration process in ITKv4. However, studying this
  //  example alone is not enough to start using the
  //  \doxygen{ImageRegistrationMethodv4}. In order to choose the best
  //  registration practice for a specific application, knowledge of other
  //  registration method instantiations and their capabilities are required.
  //  For example, direct initialization of the output optimizable transform
  //  is shown in section~\ref{sec:RigidRegistrationIn2D}. This method can
  //  simplify the registration process in many cases. Also, multi-resolution
  //  and multistage registration approaches are illustrated in
  //  sections~\ref{sec:MultiResolutionRegistration} and
  //  ~\ref{sec:MultiStageRegistration}.
  //  These examples illustrate the flexibility in the usage of ITKv4
  //  registration method framework that can help to provide faster and more
  //  reliable registration processes.
  //
  //  Software Guide : EndLatex


  return EXIT_SUCCESS;
}