Examples/RegistrationITKv4/ImageRegistration4.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
 *
 *         http://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
 
//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainT1SliceBorder20.png}
//    INPUTS:  {BrainProtonDensitySliceShifted13x17y.png}
//    OUTPUTS: {ImageRegistration4Output.png}
//    ARGUMENTS:    100
//    OUTPUTS: {ImageRegistration4CheckerboardBefore.png}
//    OUTPUTS: {ImageRegistration4CheckerboardAfter.png}
//    ARGUMENTS:    24
//  Software Guide : EndCommandLineArgs
 
// Software Guide : BeginLatex
//
// In this example, we will solve a simple multi-modality problem using an
// implementation of mutual information. This implementation was published by
// Mattes~\emph{et. al}~\cite{Mattes2003}.
//
// First, we include the header files of the components used in this example.
//
// \index{itk::ImageRegistrationMethodv4!Multi-Modality}
//
// Software Guide : EndLatex
 
 
// Software Guide : BeginCodeSnippet
#include "itkImageRegistrationMethodv4.h"
#include "itkTranslationTransform.h"
#include "itkMattesMutualInformationImageToImageMetricv4.h"
#include "itkRegularStepGradientDescentOptimizerv4.h"
// Software Guide : EndCodeSnippet
 
 
#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"
 
#include "itkResampleImageFilter.h"
#include "itkCastImageFilter.h"
#include "itkCheckerBoardImageFilter.h"
#include "itkMersenneTwisterRandomVariateGenerator.h"
 
 
//  The following section of code implements a Command observer
//  used to 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 [defaultPixelValue]" << std::endl;
    std::cerr << "[checkerBoardAfter] [checkerBoardBefore]" << std::endl;
    std::cerr << "[numberOfBins] [numberOfSamples]";
    std::cerr << "[useExplicitPDFderivatives ] " << 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>;
 
  using TransformType = itk::TranslationTransform<double, Dimension>;
  using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
  using RegistrationType = itk::
    ImageRegistrationMethodv4<FixedImageType, MovingImageType, TransformType>;
 
  //  Software Guide : BeginLatex
  //
  //  In this example the image types and all registration components,
  //  except the metric, are declared as in Section
  //  \ref{sec:IntroductionImageRegistration}. The Mattes mutual information
  //  metric type is instantiated using the image types.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using MetricType =
    itk::MattesMutualInformationImageToImageMetricv4<FixedImageType,
                                                     MovingImageType>;
  // Software Guide : EndCodeSnippet
 
  OptimizerType::Pointer    optimizer = OptimizerType::New();
  RegistrationType::Pointer registration = RegistrationType::New();
 
  registration->SetOptimizer(optimizer);
 
 
  //  Software Guide : BeginLatex
  //
  //  The metric is created using the \code{New()} method and then
  //  connected to the registration object.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  MetricType::Pointer metric = MetricType::New();
  registration->SetMetric(metric);
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  The metric requires the user to specify the number of bins
  //  used to compute the entropy. In a typical application, 50 histogram bins
  //  are sufficient. Note however, that the number of bins may have dramatic
  //  effects on the optimizer's behavior.
  //
  //  \index{itk::Mattes\-Mutual\-Information\-Image\-To\-Image\-Metricv4!SetNumberOfHistogramBins()}
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  unsigned int numberOfBins = 24;
  // Software Guide : EndCodeSnippet
 
  if (argc > 7)
  {
    numberOfBins = std::stoi(argv[7]);
  }
 
 
  // Software Guide : BeginCodeSnippet
  metric->SetNumberOfHistogramBins(numberOfBins);
  // Software Guide : EndCodeSnippet
 
  //  Software Guide : BeginLatex
  //
  //  To calculate the image gradients, an image gradient calculator based on
  //  ImageFunction is used instead of image gradient filters. Image gradient
  //  methods are defined in the superclass \code{ImageToImageMetricv4}.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  metric->SetUseMovingImageGradientFilter(false);
  metric->SetUseFixedImageGradientFilter(false);
  // 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
  //
  //  Notice that in the ITKv4 registration framework, optimizers always try
  //  to minimize the cost function, and the metrics always return a parameter
  //  and derivative result that improves the optimization, so this metric
  //  computes the negative mutual information.
  //  The optimization parameters are tuned for this example, so they are not
  //  exactly the same as the parameters used in Section
  //  \ref{sec:IntroductionImageRegistration}.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  optimizer->SetLearningRate(8.00);
  optimizer->SetMinimumStepLength(0.001);
  optimizer->SetNumberOfIterations(200);
  optimizer->ReturnBestParametersAndValueOn();
  // Software Guide : EndCodeSnippet
 
  // Software Guide : BeginLatex
  //
  // Note that large values of the learning rate will make the optimizer
  // unstable. Small values, on the other hand, may result in the optimizer
  // needing too many iterations in order to walk to the extrema of the cost
  // function. The easy way of fine tuning this parameter is to start with
  // small values, probably in the range of $\{1.0,5.0\}$. Once the other
  // registration parameters have been tuned for producing convergence, you
  // may want to revisit the learning rate and start increasing its value
  // until you observe that the optimization becomes unstable.  The ideal
  // value for this parameter is the one that results in a minimum number of
  // iterations while still keeping a stable path on the parametric space of
  // the optimization. Keep in mind that this parameter is a multiplicative
  // factor applied on the gradient of the metric. Therefore, its effect on
  // the optimizer step length is proportional to the metric values
  // themselves. Metrics with large values will require you to use smaller
  // values for the learning rate in order to maintain a similar optimizer
  // behavior.
  //
  // Whenever the regular step gradient descent optimizer encounters
  // change in the direction of movement in the parametric space, it reduces
  // the size of the step length. The rate at which the step length is reduced
  // is controlled by a relaxation factor. The default value of the factor is
  // $0.5$. This value, however may prove to be inadequate for noisy metrics
  // since they tend to induce erratic movements on the optimizers and
  // therefore result in many directional changes. In those
  // conditions, the optimizer will rapidly shrink the step length while it is
  // still too far from the location of the extrema in the cost function. In
  // this example we set the relaxation factor to a number higher than the
  // default in order to prevent the premature shrinkage of the step length.
  //
  // \index{itk::Regular\-Step\-Gradient\-Descent\-Optimizer!SetRelaxationFactor()}
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  optimizer->SetRelaxationFactor(0.8);
  // 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);
 
  // Software Guide : BeginLatex
  //
  // Instead of using the whole virtual domain (usually fixed image domain)
  // for the registration, we can use a spatial sampled point set by supplying
  // an arbitrary point list over which to evaluate the metric. The point list
  // is expected to be in the \emph{fixed} image domain, and the points are
  // transformed into the \emph{virtual} domain internally as needed. The user
  // can define the point set via \code{SetFixedSampledPointSet()}, and the
  // point set is used by calling \code{SetUsedFixedSampledPointSet()}.
  //
  // Also, instead of dealing with the metric directly, the user may define
  // the sampling percentage and sampling strategy for the registration
  // framework at each level. In this case, the registration filter manages
  // the sampling operation over the fixed image space based on the input
  // strategy (REGULAR, RANDOM) and passes the sampled point set to the metric
  // internally.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  RegistrationType::MetricSamplingStrategyEnum samplingStrategy =
    RegistrationType::MetricSamplingStrategyEnum::RANDOM;
  // Software Guide : EndCodeSnippet
 
  // Software Guide : BeginLatex
  //
  // The number of spatial samples to be
  // used depends on the content of the image. If the images are smooth and do
  // not contain many details, the number of spatial samples can usually be as
  // low as $1\%$ of the total number of pixels in the fixed image. On the
  // other hand, if the images are detailed, it may be necessary to use a much
  // higher proportion, such as $20\%$ to $50\%$. Increasing the number of
  // samples improves the smoothness of the metric, and therefore helps when
  // this metric is used in conjunction with optimizers that rely of the
  // continuity of the metric values. The trade-off, of course, is that a
  // larger number of samples results in longer computation times per every
  // evaluation of the metric.
  //
  // One mechanism for bringing the metric to its limit is to disable the
  // sampling and use all the pixels present in the FixedImageRegion. This can
  // be done with the \code{SetUseSampledPointSet( false )} method.
  // You may want to try this
  // option only while you are fine tuning all other parameters of your
  // registration. We don't use this method in this current example though.
  //
  // It has been demonstrated empirically that the number of samples is not a
  // critical parameter for the registration process. When you start fine
  // tuning your own registration process, you should start using high values
  // of number of samples, for example in the range of $20\%$ to $50\%$ of the
  // number of pixels in the fixed image. Once you have succeeded to register
  // your images you can then reduce the number of samples progressively until
  // you find a good compromise on the time it takes to compute one evaluation
  // of the metric. Note that it is not useful to have very fast evaluations
  // of the metric if the noise in their values results in more iterations
  // being required by the optimizer to converge. You must then study the
  // behavior of the metric values as the iterations progress, just as
  // illustrated in section~\ref{sec:MonitoringImageRegistration}.
  //
  // \index{itk::Mutual\-Information\-Image\-To\-Image\-Metricv4!Trade-offs}
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  double samplingPercentage = 0.20;
  // Software Guide : EndCodeSnippet
 
  // Software Guide : BeginLatex
  //
  // In ITKv4, a single virtual domain or spatial sample point set is used for
  // the all iterations of the registration process. The use of a single
  // sample set results in a smooth cost function that can improve the
  // functionality of the optimizer.
  //
  // The spatial point set is pseudo randomly generated. For
  // reproducible results an integer seed should set.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  registration->SetMetricSamplingStrategy(samplingStrategy);
  registration->SetMetricSamplingPercentage(samplingPercentage);
 
  registration->MetricSamplingReinitializeSeed(121213);
  // Software Guide : EndCodeSnippet
 
  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;
  }
 
  TransformType::ParametersType finalParameters =
    registration->GetOutput()->Get()->GetParameters();
 
  double TranslationAlongX = finalParameters[0];
  double TranslationAlongY = finalParameters[1];
 
  // For stability reasons it may be desirable to round up the values of
  // translation
  //
  unsigned int numberOfIterations = optimizer->GetCurrentIteration();
 
  double bestValue = optimizer->GetValue();
 
 
  // Print out results
  //
  std::cout << std::endl;
  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;
  std::cout << " Stop Condition  = "
            << optimizer->GetStopConditionDescription() << std::endl;
 
  //  Software Guide : BeginLatex
  //
  //  Let's execute this example over two of the images provided in
  //  \code{Examples/Data}:
  //
  //  \begin{itemize}
  //  \item \code{BrainT1SliceBorder20.png}
  //  \item \code{BrainProtonDensitySliceShifted13x17y.png}
  //  \end{itemize}
  //
  //  \begin{figure}
  //  \center
  //  \includegraphics[width=0.44\textwidth]{BrainT1SliceBorder20}
  //  \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceShifted13x17y}
  //  \itkcaption[Multi-Modality Registration Inputs]{A T1 MRI (fixed image)
  //  and a proton density MRI (moving image) are provided as input to the
  //  registration method.} \label{fig:FixedMovingImageRegistration2}
  //  \end{figure}
  //
  //  The second image is the result of intentionally translating the image
  //  \code{Brain\-Proton\-Density\-Slice\-Border20.png} by $(13,17)$
  //  millimeters. Both images have unit-spacing and are shown in Figure
  //  \ref{fig:FixedMovingImageRegistration2}. The registration process
  //  converges after $46$ iterations and produces the following results:
  //
  //  \begin{verbatim}
  //  Translation X = 13.0204
  //  Translation Y = 17.0006
  //  \end{verbatim}
  //
  //  These values are a very close match to the true misalignment introduced
  //  in the moving image.
  //
  //  Software Guide : EndLatex
 
  using ResampleFilterType =
    itk::ResampleImageFilter<MovingImageType, FixedImageType>;
 
  ResampleFilterType::Pointer resample = ResampleFilterType::New();
 
  resample->SetTransform(registration->GetTransform());
  resample->SetInput(movingImageReader->GetOutput());
 
  FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
 
  PixelType defaultPixelValue = 100;
 
  if (argc > 4)
  {
    defaultPixelValue = std::stoi(argv[4]);
  }
 
  resample->SetSize(fixedImage->GetLargestPossibleRegion().GetSize());
  resample->SetOutputOrigin(fixedImage->GetOrigin());
  resample->SetOutputSpacing(fixedImage->GetSpacing());
  resample->SetOutputDirection(fixedImage->GetDirection());
  resample->SetDefaultPixelValue(defaultPixelValue);
 
 
  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());
  writer->Update();
 
 
  //  Software Guide : BeginLatex
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.32\textwidth]{ImageRegistration4Output}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration4CheckerboardBefore}
  // \includegraphics[width=0.32\textwidth]{ImageRegistration4CheckerboardAfter}
  // \itkcaption[MattesMutualInformationImageToImageMetricv4 output
  // images]{The mapped moving image (left) and the composition of fixed and
  // moving images before (center) and after (right) registration with Mattes
  // mutual information.} \label{fig:ImageRegistration4Output} \end{figure}
  //
  //  The result of resampling the moving image is presented on the left of
  //  Figure \ref{fig:ImageRegistration4Output}. The center and right parts of
  //  the figure present a checkerboard composite of the fixed and moving
  //  images before and after registration respectively.
  //
  //  Software Guide : EndLatex
 
 
  //
  // Generate checkerboards before and after registration
  //
  using CheckerBoardFilterType = itk::CheckerBoardImageFilter<FixedImageType>;
 
  CheckerBoardFilterType::Pointer checker = CheckerBoardFilterType::New();
 
  checker->SetInput1(fixedImage);
  checker->SetInput2(resample->GetOutput());
 
  caster->SetInput(checker->GetOutput());
  writer->SetInput(caster->GetOutput());
 
  resample->SetDefaultPixelValue(0);
 
  // Before registration
  TransformType::Pointer identityTransform = TransformType::New();
  identityTransform->SetIdentity();
  resample->SetTransform(identityTransform);
 
  if (argc > 5)
  {
    writer->SetFileName(argv[5]);
    writer->Update();
  }
 
 
  // After registration
  resample->SetTransform(registration->GetTransform());
  if (argc > 6)
  {
    writer->SetFileName(argv[6]);
    writer->Update();
  }
 
 
  //  Software Guide : BeginLatex
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.44\textwidth]{ImageRegistration4TraceTranslations}
  // \includegraphics[width=0.44\textwidth]{ImageRegistration4TraceTranslations2}
  // \includegraphics[width=0.6\textwidth,height=5cm]{ImageRegistration4TraceMetric}
  // \itkcaption[MattesMutualInformationImageToImageMetricv4 output
  // plots]{Sequence of translations and metric values at each iteration of
  // the optimizer.} \label{fig:ImageRegistration4TraceTranslations}
  // \end{figure}
  //
  //  Figure \ref{fig:ImageRegistration4TraceTranslations} (upper-left) shows
  //  the sequence of translations followed by the optimizer as it searched
  //  the parameter space. The upper-right figure presents a closer look at
  //  the convergence basin for the last iterations of the optimizer. The
  //  bottom of the same figure shows the sequence of metric values computed
  //  as the optimizer searched the parameter space.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginLatex
  //
  // You must note however that there are a number of non-trivial issues
  // involved in the fine tuning of parameters for the optimization. For
  // example, the number of bins used in the estimation of Mutual Information
  // has a dramatic effect on the performance of the optimizer. In order to
  // illustrate this effect, the same example has been executed using a range
  // of different values for the number of bins, from $10$ to $30$. If you
  // repeat this experiment, you will notice that depending on the number of
  // bins used, the optimizer's path may get trapped early on in local minima.
  // Figure \ref{fig:ImageRegistration4TraceTranslationsNumberOfBins} shows
  // the multiple paths that the optimizer took in the parametric space of the
  // transform as a result of different selections on the number of bins used
  // by the Mattes Mutual Information metric. Note that many of the paths die
  // in local minima instead of reaching the extrema value on the upper right
  // corner.
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.8\textwidth]{ImageRegistration4TraceTranslationsNumberOfBins}
  // \itkcaption[MattesMutualInformationImageToImageMetricv4 number of
  // bins]{Sensitivity of the optimization path to the number of Bins used for
  // estimating the value of Mutual Information with Mattes et al. approach.}
  // \label{fig:ImageRegistration4TraceTranslationsNumberOfBins}
  // \end{figure}
  //
  //
  // Effects such as the one illustrated here highlight how useless is to
  // compare different algorithms based on a non-exhaustive search of their
  // parameter setting. It is quite difficult to be able to claim that a
  // particular selection of parameters represent the best combination for
  // running a particular algorithm. Therefore, when comparing the performance
  // of two or more different algorithms, we are faced with the challenge of
  // proving that none of the algorithms involved in the comparison are being
  // run with a sub-optimal set of parameters.
  //
  // Software Guide : EndLatex
 
 
  // Software Guide : BeginLatex
  //
  //  The plots in Figures~\ref{fig:ImageRegistration4TraceTranslations}
  //  and~\ref{fig:ImageRegistration4TraceTranslationsNumberOfBins} were
  //  generated using Gnuplot\footnote{\url{http://www.gnuplot.info/}}.
  //  The scripts used for this purpose are available
  //  in the \code{ITKSoftwareGuide} Git repository under the directory
  //
  //  ~\code{ITKSoftwareGuide/SoftwareGuide/Art}.
  //
  //  Data for the plots were taken directly from the output that the
  //  Command/Observer in this example prints out to the console. The output
  //  was processed with the UNIX editor
  //  \code{sed}\footnote{\url{http://www.gnu.org/software/sed/sed.html}} in
  //  order to remove commas and brackets that were confusing for Gnuplot's
  //  parser. Both the shell script for running \code{sed} and for running
  //  {Gnuplot} are available in the directory indicated above. You may find
  //  useful to run them in order to verify the results presented here, and to
  //  eventually modify them for profiling your own registrations.
  //
  //  \index{Open Science}
  //
  //  Open Science is not just an abstract concept. Open Science is something
  //  to be practiced every day with the simple gesture of sharing information
  //  with your peers, and by providing all the tools that they need for
  //  replicating the results that you are reporting. In Open Science, the
  //  only bad results are those that can not be
  //  replicated\footnote{\url{http://science.creativecommons.org/}}. Science
  //  is dead when people blindly trust authorities~\footnote{For example:
  //  Reviewers of Scientific Journals.} instead of verifying their statements
  //  by performing their own experiments ~\cite{Popper1971,Popper2002}.
  //
  // Software Guide : EndLatex
 
 
  return EXIT_SUCCESS;
}