Examples/RegistrationITKv4/ImageRegistration5.cxx

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 *
 *  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
 *
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 *  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
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//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySliceBorder20.png}
//    INPUTS:  {BrainProtonDensitySliceRotated10.png}
//    OUTPUTS: {ImageRegistration5Output.png}
//    OUTPUTS: {ImageRegistration5DifferenceAfter.png}
//    OUTPUTS: {ImageRegistration5DifferenceBefore.png}
//    ARGUMENTS:    0.1
//  Software Guide : EndCommandLineArgs

//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySliceBorder20.png}
//    INPUTS:  {BrainProtonDensitySliceR10X13Y17.png}
//    OUTPUTS: {ImageRegistration5Output2.png}
//    OUTPUTS: {ImageRegistration5DifferenceAfter2.png}
//    OUTPUTS: {ImageRegistration5DifferenceBefore2.png}
//    ARGUMENTS:    1.0
//  Software Guide : EndCommandLineArgs


// Software Guide : BeginLatex
//
// This example illustrates the use of the \doxygen{Euler2DTransform}
// for performing rigid registration in $2D$. The example code is for the
// most part identical to that presented in Section
// \ref{sec:IntroductionImageRegistration}.  The main difference is the use
// of the Euler2DTransform here instead of the
// \doxygen{TranslationTransform}.
//
// \index{itk::Euler2DTransform}
//
// Software Guide : EndLatex

#include "itkImageRegistrationMethodv4.h"
#include "itkMeanSquaresImageToImageMetricv4.h"
#include "itkRegularStepGradientDescentOptimizerv4.h"


//  Software Guide : BeginLatex
//
//  In addition to the headers included in previous examples, the
//  following header must also be included.
//
//  \index{itk::Euler2DTransform!header}
//
//  Software Guide : EndLatex

// Software Guide : BeginCodeSnippet
#include "itkEuler2DTransform.h"
// Software Guide : EndCodeSnippet


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

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


//  The following section of code implements a Command observer
//  that will monitor the evolution of the registration process.
//
#include "itkCommand.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  [differenceAfterRegistration] ";
    std::cerr << " [differenceBeforeRegistration] ";
    std::cerr << " [initialStepLength] "<< std::endl;
    return EXIT_FAILURE;
    }

  constexpr unsigned int Dimension = 2;
  using PixelType = float;

  using FixedImageType = itk::Image< PixelType, Dimension >;
  using MovingImageType = itk::Image< PixelType, Dimension >;


  //  Software Guide : BeginLatex
  //
  //  The transform type is instantiated using the code below. The only
  //  template parameter for this class is the representation type of the
  //  space coordinates.
  //
  //  \index{itk::Euler2DTransform!Instantiation}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using TransformType = itk::Euler2DTransform< double >;
  // Software Guide : EndCodeSnippet


  using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
  using MetricType = itk::MeanSquaresImageToImageMetricv4<
                                      FixedImageType,
                                      MovingImageType >;
  using RegistrationType = itk::ImageRegistrationMethodv4<
                                      FixedImageType,
                                      MovingImageType,
                                      TransformType >;

  MetricType::Pointer         metric        = MetricType::New();
  OptimizerType::Pointer      optimizer     = OptimizerType::New();
  RegistrationType::Pointer   registration  = RegistrationType::New();

  registration->SetMetric(        metric        );
  registration->SetOptimizer(     optimizer     );


  //  Software Guide : BeginLatex
  //
  //  In the Hello World! example, we used Fixed/Moving initial transforms
  //  to initialize the registration configuration. That approach was good to
  //  get an intuition of the registration method, specifically when we aim to run
  //  a multistage registration process, from which the output of each stage can
  //  be used to initialize the next registration stage.
  //
  //  To get a better underestanding of the registration process in
  //  such situations, consider an example of 3 stages registration process
  //  that is started using an initial moving transform ($\Gamma_{mi}$).
  //  Multiple stages are handled by linking multiple instantiations of
  //  the \doxygen{ImageRegistrationMethodv4} class.
  //  Inside the registration filter of the first stage, the initial moving
  //  transform is added to an internal composite transform along with an updatable
  //  identity transform ($\Gamma_{u}$). Although the whole composite transform
  //  is used for metric evaluation, only the $\Gamma_{u}$ is set to be updated
  //  by the optimizer at each iteration. The $\Gamma_{u}$ will be considered as
  //  the output transform of the current stage when the optimization process is
  //  converged. This implies that the output of this stage does not include
  //  the initialization parameters, so we need to concatenate the output and the
  //  initialization transform into a composite transform to be considered as the
  //  final transform of the first registration stage.
  //
  //  $ T_{1}(x) = \Gamma_{mi}(\Gamma_{stage_1}(x) ) $
  //
  //  Consider that, as explained in section \ref{sec:FeaturesOfTheRegistrationFramework},
  //  the above transform is a mapping from the vitual domain (i.e. fixed image space, when no
  //  fixed initial transform) to the moving image space.
  //
  //  Then, the result transform of the first stage will be used as the initial moving
  //  transform for the second stage of the registration process, and this approach goes on
  //  until the last stage of the registration process.
  //
  //  At the end of the registration process, the $\Gamma_{mi}$ and the outputs of each stage
  //  can be concatenated into a final composite transform that is considered to be the final
  //  output of the whole registration process.
  //
  //  $I'_{m}(x) = I_{m}(\Gamma_{mi}(\Gamma_{stage_1}(\Gamma_{stage_2}(\Gamma_{stage_3}(x) ) ) ) )$
  //
  //  The above approach is especially useful if individual stages are characterized by
  //  different types of transforms, e.g.  when we run a rigid registration
  //  process that is proceeded by an affine registration which is completed by a BSpline
  //  registration at the end.
  //
  //
  //  In addition to the above method, there is also a direct initialization method in which the
  //  initial transform will be optimized directly. In this way the initial transform will be
  //  modified during the registration process, so it can be used as the final transform when
  //  the registration process is completed. This direct approach is conceptually close to
  //  what was happening in ITKv3 registration.
  //
  //  Using this method is very simple and efficient when we have only one level of
  //  registration, which is the case in this example.
  //  Also, a good application of this initialization method in a multi-stage scenario
  //  is when two consequent stages have the same transform types, or at least the initial
  //  parameters can easily be inferred from the result of the previous stage, such as when a
  //  translation transform is followed by a rigid transform.
  //
  //  The direct initialization approach is shown by the current example in which we try
  //  to initialize the parameters of the optimizable transform ($\Gamma_{u}$) directly.
  //
  //  For this purpose, first, the initial transform object is constructed below.
  //  This transform will be initialized, and its initial parameters will be
  //  used when the registration process starts.
  //
  //  \index{itk::Euler2DTransform!New()}
  //  \index{itk::Euler2DTransform!Pointer}
  //
  //  Software Guide : EndLatex

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


  registration->SetFixedImage(    fixedImageReader->GetOutput()    );
  registration->SetMovingImage(   movingImageReader->GetOutput()   );


  //  Software Guide : BeginLatex
  //
  //  In this example, the input images are taken from readers. The code
  //  below updates the readers in order to ensure that the image parameters
  //  (size, origin and spacing) are valid when used to initialize the
  //  transform.  We intend to use the center of the fixed image as the
  //  rotation center and then use the vector between the fixed image center
  //  and the moving image center as the initial translation to be applied
  //  after the rotation.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  fixedImageReader->Update();
  movingImageReader->Update();
  // Software Guide : EndCodeSnippet

  using SpacingType = FixedImageType::SpacingType;
  using OriginType = FixedImageType::PointType;
  using RegionType = FixedImageType::RegionType;
  using SizeType = FixedImageType::SizeType;

  //  Software Guide : BeginLatex
  //
  //  The center of rotation is computed using the origin, size and spacing of
  //  the fixed image.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();

  const SpacingType fixedSpacing = fixedImage->GetSpacing();
  const OriginType  fixedOrigin  = fixedImage->GetOrigin();
  const RegionType  fixedRegion  = fixedImage->GetLargestPossibleRegion();
  const SizeType    fixedSize    = fixedRegion.GetSize();

  TransformType::InputPointType centerFixed;

  centerFixed[0] = fixedOrigin[0] + fixedSpacing[0] * fixedSize[0] / 2.0;
  centerFixed[1] = fixedOrigin[1] + fixedSpacing[1] * fixedSize[1] / 2.0;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  The center of the moving image is computed in a similar way.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  MovingImageType::Pointer movingImage = movingImageReader->GetOutput();

  const SpacingType movingSpacing = movingImage->GetSpacing();
  const OriginType  movingOrigin  = movingImage->GetOrigin();
  const RegionType  movingRegion  = movingImage->GetLargestPossibleRegion();
  const SizeType    movingSize    = movingRegion.GetSize();

  TransformType::InputPointType centerMoving;

  centerMoving[0] = movingOrigin[0] + movingSpacing[0] * movingSize[0] / 2.0;
  centerMoving[1] = movingOrigin[1] + movingSpacing[1] * movingSize[1] / 2.0;
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //   Then, we initialize the transform by
  //   passing the center of the fixed image as the rotation center with the
  //   \code{SetCenter()} method. Also, the translation is set as the vector
  //   relating the center of the moving image to the center of the fixed
  //   image.  This last vector is passed with the method
  //   \code{SetTranslation()}.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  initialTransform->SetCenter( centerFixed );
  initialTransform->SetTranslation( centerMoving - centerFixed );
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  Let's finally initialize the rotation with a zero angle.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  initialTransform->SetAngle( 0.0 );
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  Now the current parameters of the initial transform will be set
  //  to a registration method, so they can be assigned to the $\Gamma_{u}$ directly.
  //  Note that you should not confuse the following function with the
  //  \code{SetMoving(Fixed)InitialTransform()} methods that were used in Hello World! example.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  registration->SetInitialTransform( initialTransform );
  // Software Guide : EndCodeSnippet

  //  Software Guide : BeginLatex
  //
  //  Keep in mind that the scale of units in rotation and translation is
  //  quite different. For example, here we know that the first element of the
  //  parameters array corresponds to the angle that is measured in radians, while
  //  the other parameters correspond to the translations that are measured in millimeters,
  //  so a naive application of gradient descent optimizer will not produce a smooth
  //  change of parameters, because a similar change of $\delta$
  //  to each parameter will produce a different magnitude of impact on the transform.
  //  As the result, we need ``parameter scales'' to customize the learning rate for
  //  each parameter. We can take advantage of the scaling functionality provided
  //  by the optimizers.
  //
  //  In this example we use small factors in the scales associated with
  //  translations. However, for the transforms with larger parameters
  //  sets, it is not intuitive for a user to  set the
  //  scales. Fortunately, a framework for automated estimation of
  //  parameter scales is provided by ITKv4 that will be discussed
  //  later in the example of section \ref{sec:MultiStageRegistration}.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using OptimizerScalesType = OptimizerType::ScalesType;
  OptimizerScalesType optimizerScales(
    initialTransform->GetNumberOfParameters() );
  const double translationScale = 1.0 / 1000.0;

  optimizerScales[0] = 1.0;
  optimizerScales[1] = translationScale;
  optimizerScales[2] = translationScale;

  optimizer->SetScales( optimizerScales );
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  Next we set the normal parameters of the optimization method. In this
  //  case we are using an \doxygen{RegularStepGradientDescentOptimizerv4}.
  //  Below, we define the optimization parameters like the relaxation factor,
  //  learning rate (initial step length), minimal step length and number of
  //  iterations. These last two act as stopping criteria for the optimization.
  //
  //  \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetRelaxationFactor()}
  //  \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetLearningRate()}
  //  \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetMinimumStepLength()}
  //  \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetNumberOfIterations()}
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  double initialStepLength = 0.1;
  // Software Guide : EndCodeSnippet

  if( argc > 6 )
    {
    initialStepLength = std::stod( argv[6] );
    }

  // Software Guide : BeginCodeSnippet
  optimizer->SetRelaxationFactor( 0.6 );
  optimizer->SetLearningRate( initialStepLength );
  optimizer->SetMinimumStepLength( 0.001 );
  optimizer->SetNumberOfIterations( 200 );
  // Software Guide : EndCodeSnippet


  // Create the Command observer and register it with the optimizer.
  //
  CommandIterationUpdate::Pointer observer = CommandIterationUpdate::New();
  optimizer->AddObserver( itk::IterationEvent(), observer );

  // One level registration process without shrinking and smoothing.
  //
  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 );

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

  const TransformType::ParametersType finalParameters =
                            registration->GetOutput()->Get()->GetParameters();

  const double finalAngle           = finalParameters[0];
  const double finalTranslationX    = finalParameters[1];
  const double finalTranslationY    = finalParameters[2];

  const double rotationCenterX = registration->GetOutput()->Get()->GetCenter()[0];
  const double rotationCenterY = registration->GetOutput()->Get()->GetCenter()[1];

  const unsigned int numberOfIterations = optimizer->GetCurrentIteration();

  const double bestValue = optimizer->GetValue();


  // Print out results
  //
  const double finalAngleInDegrees = finalAngle * 180.0 / itk::Math::pi;

  std::cout << "Result = " << std::endl;
  std::cout << " Angle (radians) = " << finalAngle  << std::endl;
  std::cout << " Angle (degrees) = " << finalAngleInDegrees  << std::endl;
  std::cout << " Translation X   = " << finalTranslationX  << std::endl;
  std::cout << " Translation Y   = " << finalTranslationY  << std::endl;
  std::cout << " Fixed Center X  = " << rotationCenterX  << std::endl;
  std::cout << " Fixed Center Y  = " << rotationCenterY  << 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{BrainProtonDensitySliceRotated10.png}
  //  \end{itemize}
  //
  //  The second image is the result of intentionally rotating the first image
  //  by $10$ degrees around the geometrical center of the image. Both images
  //  have unit-spacing and are shown in Figure
  //  \ref{fig:FixedMovingImageRegistration5}. The registration takes $17$
  //  iterations and produces the results:
  //
  //  \begin{center}
  //  \begin{verbatim}
  //  [0.177612, 0.00681015, 0.00396471]
  //  \end{verbatim}
  //  \end{center}
  //
  //  These results are interpreted as
  //
  //  \begin{itemize}
  //  \item Angle         =                  $0.177612$     radians
  //  \item Translation   = $( 0.00681015, 0.00396471 )$ millimeters
  //  \end{itemize}
  //
  //  As expected, these values match the misalignment intentionally introduced
  //  into the moving image quite well, since $10$ degrees is about $0.174532$
  //  radians.
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceBorder20}
  // \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceRotated10}
  // \itkcaption[Rigid2D Registration input images]{Fixed and moving images
  // are provided as input to the registration method using the CenteredRigid2D
  // transform.}
  // \label{fig:FixedMovingImageRegistration5}
  // \end{figure}
  //
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.32\textwidth]{ImageRegistration5Output}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceBefore}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceAfter}
  // \itkcaption[Rigid2D Registration output images]{Resampled moving image
  // (left). Differences between the fixed and moving images, before (center)
  // and after (right) registration using the Euler2D transform.}
  // \label{fig:ImageRegistration5Outputs}
  // \end{figure}
  //
  // Figure \ref{fig:ImageRegistration5Outputs} shows from left to right the
  // resampled moving image after registration, the difference between the fixed
  // and moving images before registration, and the difference between the fixed
  // and resampled moving image after registration. It can be seen from the
  // last difference image that the rotational component has been solved but
  // that a small centering misalignment persists.
  //
  // \begin{figure}
  // \center
  // \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceMetric1}
  // \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceAngle1}
  // \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceTranslations1}
  // \itkcaption[Rigid2D Registration output plots]{Metric values, rotation
  // angle and translations during registration with the Euler2D
  // transform.}
  // \label{fig:ImageRegistration5Plots}
  // \end{figure}
  //
  //  Figure \ref{fig:ImageRegistration5Plots} shows plots of the main output
  //  parameters produced from the registration process. This includes the
  //  metric values at every iteration, the angle values at every iteration,
  //  and the translation components of the transform as the registration
  //  progresses.
  //
  //  Software Guide : EndLatex


  using ResampleFilterType = itk::ResampleImageFilter<
                            MovingImageType,
                            FixedImageType >;

  //TransformType::ConstPointer finalTransform = TransformType::New();

  //TransformType::ConstPointer finalTransform = registration->GetTransform();

  ResampleFilterType::Pointer resample = ResampleFilterType::New();

  resample->SetTransform( registration->GetTransform() );
  resample->SetInput( movingImageReader->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 >;

  WriterType::Pointer      writer =  WriterType::New();
  CastFilterType::Pointer  caster =  CastFilterType::New();

  writer->SetFileName( argv[3] );

  caster->SetInput( resample->GetOutput() );
  writer->SetInput( caster->GetOutput()   );

  try
    {
    writer->Update();
    }
  catch( itk::ExceptionObject & excp )
    {
    std::cerr << "ExceptionObject while writing the resampled image !" << std::endl;
    std::cerr << excp << std::endl;
    return EXIT_FAILURE;
    }

  using DifferenceImageType = itk::Image< float, Dimension >;

  using DifferenceFilterType = itk::SubtractImageFilter<
                           FixedImageType,
                           FixedImageType,
                           DifferenceImageType >;

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

  using RescalerType = itk::RescaleIntensityImageFilter<
                                  DifferenceImageType,
                                  OutputImageType >;

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

  intensityRescaler->SetOutputMinimum(   0 );
  intensityRescaler->SetOutputMaximum( 255 );

  difference->SetInput1( fixedImageReader->GetOutput() );
  difference->SetInput2( resample->GetOutput() );

  resample->SetDefaultPixelValue( 1 );

  intensityRescaler->SetInput( difference->GetOutput() );

  WriterType::Pointer      writer2 =  WriterType::New();

  writer2->SetInput( intensityRescaler->GetOutput() );


  try
    {
    // Compute the difference image between the
    // fixed and moving image after registration.
    if( argc > 4 )
      {
      writer2->SetFileName( argv[4] );
      writer2->Update();
      }

    // Compute the difference image between the
    // fixed and resampled moving image after registration.
    TransformType::Pointer identityTransform = TransformType::New();
    identityTransform->SetIdentity();
    resample->SetTransform( identityTransform );
    if( argc > 5 )
      {
      writer2->SetFileName( argv[5] );
      writer2->Update();
      }
    }
  catch( itk::ExceptionObject & excp )
    {
    std::cerr << "Error while writing difference images" << std::endl;
    std::cerr << excp << std::endl;
    return EXIT_FAILURE;
    }

  //  Software Guide : BeginLatex
  //
  //  Let's now consider the case in which rotations and translations are
  //  present in the initial registration, as in the following pair
  //  of images:
  //
  //  \begin{itemize}
  //  \item \code{BrainProtonDensitySliceBorder20.png}
  //  \item \code{BrainProtonDensitySliceR10X13Y17.png}
  //  \end{itemize}
  //
  //  The second image is the result of intentionally rotating the first image
  //  by $10$ degrees and then translating it $13mm$ in $X$ and $17mm$ in $Y$.
  //  Both images have unit-spacing and are shown in Figure
  //  \ref{fig:FixedMovingImageRegistration5b}. In order to accelerate
  //  convergence it is convenient to use a larger step length as shown here.
  //
  //  \code{optimizer->SetMaximumStepLength( 1.3 );}
  //
  //  The registration now takes $37$ iterations and produces the following
  //  results:
  //
  //  \begin{center}
  //  \begin{verbatim}
  //  [0.174582, 13.0002, 16.0007]
  //  \end{verbatim}
  //  \end{center}
  //
  //  These parameters are interpreted as
  //
  //  \begin{itemize}
  //  \item Angle         =                     $0.174582$   radians
  //  \item Translation   = $( 13.0002,  16.0007 )$ millimeters
  //  \end{itemize}
  //
  //  These values approximately match the initial misalignment intentionally
  //  introduced into the moving image, since $10$ degrees is about $0.174532$
  //  radians. The horizontal translation is well resolved while the vertical
  //  translation ends up being off by about one millimeter.
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceBorder20}
  // \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceR10X13Y17}
  // \itkcaption[Rigid2D Registration input images]{Fixed and moving images
  // provided as input to the registration method using the CenteredRigid2D
  // transform.}
  // \label{fig:FixedMovingImageRegistration5b}
  // \end{figure}
  //
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.32\textwidth]{ImageRegistration5Output2}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceBefore2}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceAfter2}
  // \itkcaption[Rigid2D Registration output images]{Resampled moving image
  // (left). Differences between the fixed and moving images, before (center)
  // and after (right) registration with the CenteredRigid2D transform.}
  // \label{fig:ImageRegistration5Outputs2}
  // \end{figure}
  //
  // Figure \ref{fig:ImageRegistration5Outputs2} shows the output of the
  // registration. The rightmost image of this figure shows the difference
  // between the fixed image and the resampled moving image after registration.
  //
  // \begin{figure}
  // \center
  // \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceMetric2}
  // \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceAngle2}
  // \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceTranslations2}
  // \itkcaption[Rigid2D Registration output plots]{Metric values, rotation
  // angle and translations during the registration using the Euler2D
  // transform on an image with rotation and translation mis-registration.}
  // \label{fig:ImageRegistration5Plots2}
  // \end{figure}
  //
  //  Figure \ref{fig:ImageRegistration5Plots2} shows plots of the main output
  //  registration parameters when the rotation and translations are combined.
  //  These results include the metric values at every iteration, the angle
  //  values at every iteration, and the translation components of the
  //  registration as the registration converges. It can be seen from the
  //  smoothness of these plots that a larger step length could have been
  //  supported easily by the optimizer. You may want to modify this value in
  //  order to get a better idea of how to tune the parameters.
  //
  //  Software Guide : EndLatex


  return EXIT_SUCCESS;
}