Examples/Segmentation/GeodesicActiveContourImageFilter.cxx

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//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput5.png}
//    ARGUMENTS:    81 114 5 1.0  -0.5  3.0   2
//  Software Guide : EndCommandLineArgs
//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput6.png}
//    ARGUMENTS:    99 114 5 1.0  -0.5  3.0  2
//  Software Guide : EndCommandLineArgs
 //  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput7.png}
//    ARGUMENTS:    56 92 5.0 1.0 -0.3 2.0 10.0
//  Software Guide : EndCommandLineArgs
//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput8.png}
//    ARGUMENTS:    40 90 5 0.5  -0.3  2.0 10
//  Software Guide : EndCommandLineArgs
//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput1.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput2.png}
//    OUTPUTS: {GeodesicActiveContourImageFilterOutput3.png}
//    ARGUMENTS:    56 92 5 1.0  -0.3  2.0 10
//  Software Guide : EndCommandLineArgs

// Software Guide : BeginLatex
//
// The use of the \doxygen{GeodesicActiveContourLevelSetImageFilter} is
// illustrated in the following example. The implementation of this filter in
// ITK is based on the paper by Caselles \cite{Caselles1997}.  This
// implementation extends the functionality of the
// \doxygen{ShapeDetectionLevelSetImageFilter} by the addition of a third
// advection term which attracts the level set to the object boundaries.
//
// GeodesicActiveContourLevelSetImageFilter expects two inputs.  The first is
// an initial level set in the form of an \doxygen{Image}. The second input
// is a feature image. For this algorithm, the feature image is an edge
// potential image that basically follows the same rules used for the
// ShapeDetectionLevelSetImageFilter discussed in
// Section~\ref{sec:ShapeDetectionLevelSetFilter}.  The configuration of this
// example is quite similar to the example on the use of the
// ShapeDetectionLevelSetImageFilter. We omit most of the redundant
// description. A look at the code will reveal the great degree of similarity
// between both examples.
//
// \begin{figure} \center
// \includegraphics[width=\textwidth]{GeodesicActiveContoursCollaborationDiagram1}
// \itkcaption[GeodesicActiveContourLevelSetImageFilter collaboration
// diagram]{Collaboration diagram for the GeodesicActiveContourLevelSetImageFilter
// applied to a segmentation task.}
// \label{fig:GeodesicActiveContoursCollaborationDiagram}
// \end{figure}
//
// Figure~\ref{fig:GeodesicActiveContoursCollaborationDiagram} shows the major
// components involved in the application of the
// GeodesicActiveContourLevelSetImageFilter to a segmentation task.
// This pipeline is quite similar to the one used by the
// ShapeDetectionLevelSetImageFilter in
// section~\ref{sec:ShapeDetectionLevelSetFilter}.
//
// The pipeline involves a first stage of smoothing using the\newline
// \doxygen{CurvatureAnisotropicDiffusionImageFilter}. The smoothed image is
// passed as the input to the
// \doxygen{GradientMagnitudeRecursiveGaussianImageFilter} and then to the
// \doxygen{SigmoidImageFilter} in order to produce the edge potential image.
// A set of user-provided seeds is passed to a
// \doxygen{FastMarchingImageFilter} in order to compute the distance map. A
// constant value is subtracted from this map in order to obtain a level set
// in which the \emph{zero set} represents the initial contour. This level
// set is also passed as input to the
// GeodesicActiveContourLevelSetImageFilter.
//
// Finally, the level set generated by the
// GeodesicActiveContourLevelSetImageFilter is passed to a
// \doxygen{BinaryThresholdImageFilter} in order to produce a binary mask
// representing the segmented object.
//
// Let's start by including the headers of the main filters involved in the
// preprocessing.
//
// Software Guide : EndLatex


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


#include "itkCurvatureAnisotropicDiffusionImageFilter.h"
#include "itkGradientMagnitudeRecursiveGaussianImageFilter.h"
#include "itkSigmoidImageFilter.h"
#include "itkFastMarchingImageFilter.h"
#include "itkRescaleIntensityImageFilter.h"
#include "itkBinaryThresholdImageFilter.h"
#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"


int main( int argc, char *argv[] )
{
  if ( argc < 10 )
    {
    std::cerr << "Missing Parameters " << std::endl;
    std::cerr << "Usage: " << argv[0];
    std::cerr << " inputImage  outputImage";
    std::cerr << " seedX seedY InitialDistance";
    std::cerr << " Sigma SigmoidAlpha SigmoidBeta";
    std::cerr << " PropagationScaling"  << std::endl;
    return EXIT_SUCCESS;
    }


  //  Software Guide : BeginLatex
  //
  //  We now define the image type using a particular pixel type and
  //  dimension. In this case the \code{float} type is used for the pixels
  //  due to the requirements of the smoothing filter.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using InternalPixelType = float;
  constexpr unsigned int Dimension = 2;
  using InternalImageType = itk::Image< InternalPixelType, Dimension >;
  // Software Guide : EndCodeSnippet


  //  The following lines instantiate the thresholding filter that will
  //  process the final level set at the output of the
  //  GeodesicActiveContourLevelSetImageFilter.
  //
  using OutputPixelType = unsigned char;
  using OutputImageType = itk::Image< OutputPixelType, Dimension >;
  using ThresholdingFilterType = itk::BinaryThresholdImageFilter<
                        InternalImageType,
                        OutputImageType    >;

  ThresholdingFilterType::Pointer thresholder = ThresholdingFilterType::New();

  thresholder->SetLowerThreshold( -1000.0 );
  thresholder->SetUpperThreshold(     0.0 );

  thresholder->SetOutsideValue(  0  );
  thresholder->SetInsideValue(  255 );


  // We instantiate reader and writer types in the following lines.
  //
  using ReaderType = itk::ImageFileReader< InternalImageType >;
  using WriterType = itk::ImageFileWriter<  OutputImageType  >;

  ReaderType::Pointer reader = ReaderType::New();
  WriterType::Pointer writer = WriterType::New();

  reader->SetFileName( argv[1] );
  writer->SetFileName( argv[2] );


  //  The RescaleIntensityImageFilter type is declared below. This filter will
  //  renormalize image before sending them to writers.
  //
  using CastFilterType = itk::RescaleIntensityImageFilter<
                               InternalImageType,
                               OutputImageType >;


  //  The \doxygen{CurvatureAnisotropicDiffusionImageFilter} type is
  //  instantiated using the internal image type.
  //
  using SmoothingFilterType = itk::CurvatureAnisotropicDiffusionImageFilter<
                               InternalImageType,
                               InternalImageType >;

  SmoothingFilterType::Pointer smoothing = SmoothingFilterType::New();


  //  The types of the
  //  GradientMagnitudeRecursiveGaussianImageFilter and
  //  SigmoidImageFilter are instantiated using the internal image
  //  type.
  //
  using GradientFilterType = itk::GradientMagnitudeRecursiveGaussianImageFilter<
                               InternalImageType,
                               InternalImageType >;
  using SigmoidFilterType = itk::SigmoidImageFilter<
                               InternalImageType,
                               InternalImageType >;

  GradientFilterType::Pointer  gradientMagnitude = GradientFilterType::New();

  SigmoidFilterType::Pointer sigmoid = SigmoidFilterType::New();


  //  The minimum and maximum values of the SigmoidImageFilter output
  //  are defined with the methods \code{SetOutputMinimum()} and
  //  \code{SetOutputMaximum()}. In our case, we want these two values to be
  //  $0.0$ and $1.0$ respectively in order to get a nice speed image to feed
  //  the \code{FastMarchingImageFilter}. Additional details on the user of the
  //  \doxygen{SigmoidImageFilter} are presented in
  //  section~\ref{sec:IntensityNonLinearMapping}.

  sigmoid->SetOutputMinimum(  0.0  );
  sigmoid->SetOutputMaximum(  1.0  );


  //  We declare now the type of the FastMarchingImageFilter that
  //  will be used to generate the initial level set in the form of a distance
  //  map.
  //
  using FastMarchingFilterType = itk::FastMarchingImageFilter<
                              InternalImageType,
                              InternalImageType >;


  //  Next we construct one filter of this class using the \code{New()}
  //  method.
  //
  FastMarchingFilterType::Pointer  fastMarching = FastMarchingFilterType::New();

  //  Software Guide : BeginLatex
  //
  //  In the following lines we instantiate the type of the
  //  GeodesicActiveContourLevelSetImageFilter and create an object of this
  //  type using the \code{New()} method.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  using GeodesicActiveContourFilterType =
    itk::GeodesicActiveContourLevelSetImageFilter< InternalImageType,
                                                   InternalImageType >;
  GeodesicActiveContourFilterType::Pointer geodesicActiveContour =
                                     GeodesicActiveContourFilterType::New();
  // Software Guide : EndCodeSnippet


  //  Software Guide : BeginLatex
  //
  //  For the GeodesicActiveContourLevelSetImageFilter, scaling parameters
  //  are used to trade off between the propagation (inflation), the
  //  curvature (smoothing) and the advection terms. These parameters are set
  //  using methods \code{SetPropagationScaling()},
  //  \code{SetCurvatureScaling()} and \code{SetAdvectionScaling()}. In this
  //  example, we will set the curvature and advection scales to one and let
  //  the propagation scale be a command-line argument.
  //
  //  \index{itk::Geodesic\-Active\-Contour\-LevelSet\-Image\-Filter!SetPropagationScaling()}
  //  \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetPropagationScaling()}
  //  \index{itk::Geodesic\-Active\-Contour\-LevelSet\-Image\-Filter!SetCurvatureScaling()}
  //  \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetCurvatureScaling()}
  //  \index{itk::Geodesic\-Active\-Contour\-LevelSet\-Image\-Filter!SetAdvectionScaling()}
  //  \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetAdvectionScaling()}
  //
  //  Software Guide : EndLatex

  const double propagationScaling = std::stod( argv[9] );

  //  Software Guide : BeginCodeSnippet
  geodesicActiveContour->SetPropagationScaling( propagationScaling );
  geodesicActiveContour->SetCurvatureScaling( 1.0 );
  geodesicActiveContour->SetAdvectionScaling( 1.0 );
  //  Software Guide : EndCodeSnippet

  //  Once activiated the level set evolution will stop if the convergence
  //  criteria or if the maximum number of iterations is reached.  The
  //  convergence criteria is defined in terms of the root mean squared (RMS)
  //  change in the level set function. The evolution is said to have
  //  converged if the RMS change is below a user specified threshold.  In a
  //  real application is desirable to couple the evolution of the zero set
  //  to a visualization module allowing the user to follow the evolution of
  //  the zero set. With this feedback, the user may decide when to stop the
  //  algorithm before the zero set leaks through the regions of low gradient
  //  in the contour of the anatomical structure to be segmented.

  geodesicActiveContour->SetMaximumRMSError( 0.02 );
  geodesicActiveContour->SetNumberOfIterations( 800 );


  //  Software Guide : BeginLatex
  //
  //  The filters are now connected in a pipeline indicated in
  //  Figure~\ref{fig:GeodesicActiveContoursCollaborationDiagram} using the
  //  following lines:
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  smoothing->SetInput( reader->GetOutput() );
  gradientMagnitude->SetInput( smoothing->GetOutput() );
  sigmoid->SetInput( gradientMagnitude->GetOutput() );

  geodesicActiveContour->SetInput(  fastMarching->GetOutput() );
  geodesicActiveContour->SetFeatureImage( sigmoid->GetOutput() );

  thresholder->SetInput( geodesicActiveContour->GetOutput() );
  writer->SetInput( thresholder->GetOutput() );
  // Software Guide : EndCodeSnippet


  //  The CurvatureAnisotropicDiffusionImageFilter requires a couple of
  //  parameter to be defined. The following are typical values for $2D$
  //  images. However they may have to be adjusted depending on the amount of
  //  noise present in the input image. This filter has been discussed in
  //  section~\ref{sec:GradientAnisotropicDiffusionImageFilter}.

  smoothing->SetTimeStep( 0.125 );
  smoothing->SetNumberOfIterations(  5 );
  smoothing->SetConductanceParameter( 9.0 );


  //  The GradientMagnitudeRecursiveGaussianImageFilter performs the
  //  equivalent of a convolution with a Gaussian kernel, followed by a
  //  derivative operator. The sigma of this Gaussian can be used to control
  //  the range of influence of the image edges. This filter has been discussed
  //  in Section~\ref{sec:GradientMagnitudeRecursiveGaussianImageFilter}.

  const double sigma = std::stod( argv[6] );
  gradientMagnitude->SetSigma(  sigma  );


  //  The SigmoidImageFilter requires two parameters that define the linear
  //  transformation to be applied to the sigmoid argument. This parameters
  //  have been discussed in Sections~\ref{sec:IntensityNonLinearMapping} and
  //  \ref{sec:FastMarchingImageFilter}.

  const double alpha =  std::stod( argv[7] );
  const double beta  =  std::stod( argv[8] );

  sigmoid->SetAlpha( alpha );
  sigmoid->SetBeta(  beta  );


  //  The FastMarchingImageFilter requires the user to provide a seed
  //  point from which the level set will be generated. The user can actually
  //  pass not only one seed point but a set of them. Note the the
  //  FastMarchingImageFilter is used here only as a helper in the
  //  determination of an initial level set. We could have used the
  //  \doxygen{DanielssonDistanceMapImageFilter} in the same way.
  //
  //  The seeds are passed stored in a container. The type of this
  //  container is defined as \code{NodeContainer} among the
  //  FastMarchingImageFilter traits.
  //
  using NodeContainer = FastMarchingFilterType::NodeContainer;
  using NodeType = FastMarchingFilterType::NodeType;

  NodeContainer::Pointer seeds = NodeContainer::New();

  InternalImageType::IndexType  seedPosition;

  seedPosition[0] = std::stoi( argv[3] );
  seedPosition[1] = std::stoi( argv[4] );


  //  Nodes are created as stack variables and initialized with a value and an
  //  \doxygen{Index} position. Note that here we assign the value of minus the
  //  user-provided distance to the unique node of the seeds passed to the
  //  FastMarchingImageFilter. In this way, the value will increment
  //  as the front is propagated, until it reaches the zero value corresponding
  //  to the contour. After this, the front will continue propagating until it
  //  fills up the entire image. The initial distance is taken here from the
  //  command line arguments. The rule of thumb for the user is to select this
  //  value as the distance from the seed points at which she want the initial
  //  contour to be.
  const double initialDistance = std::stod( argv[5] );

  NodeType node;

  const double seedValue = - initialDistance;

  node.SetValue( seedValue );
  node.SetIndex( seedPosition );


  //  The list of nodes is initialized and then every node is inserted using
  //  the \code{InsertElement()}.

  seeds->Initialize();
  seeds->InsertElement( 0, node );


  //  The set of seed nodes is passed now to the
  //  FastMarchingImageFilter with the method
  //  \code{SetTrialPoints()}.
  //
  fastMarching->SetTrialPoints(  seeds  );


  //  Since the FastMarchingImageFilter is used here just as a
  //  Distance Map generator. It does not require a speed image as input.
  //  Instead the constant value $1.0$ is passed using the
  //  \code{SetSpeedConstant()} method.
  //
  fastMarching->SetSpeedConstant( 1.0 );


  //  Here we configure all the writers required to see the intermediate
  //  outputs of the pipeline. This is added here only for
  //  pedagogical/debugging purposes. These intermediate output are normaly not
  //  required. Only the output of the final thresholding filter should be
  //  relevant.  Observing intermediate output is helpful in the process of
  //  fine tuning the parameters of filters in the pipeline.
  //
  CastFilterType::Pointer caster1 = CastFilterType::New();
  CastFilterType::Pointer caster2 = CastFilterType::New();
  CastFilterType::Pointer caster3 = CastFilterType::New();
  CastFilterType::Pointer caster4 = CastFilterType::New();

  WriterType::Pointer writer1 = WriterType::New();
  WriterType::Pointer writer2 = WriterType::New();
  WriterType::Pointer writer3 = WriterType::New();
  WriterType::Pointer writer4 = WriterType::New();

  caster1->SetInput( smoothing->GetOutput() );
  writer1->SetInput( caster1->GetOutput() );
  writer1->SetFileName("GeodesicActiveContourImageFilterOutput1.png");
  caster1->SetOutputMinimum(   0 );
  caster1->SetOutputMaximum( 255 );
  writer1->Update();

  caster2->SetInput( gradientMagnitude->GetOutput() );
  writer2->SetInput( caster2->GetOutput() );
  writer2->SetFileName("GeodesicActiveContourImageFilterOutput2.png");
  caster2->SetOutputMinimum(   0 );
  caster2->SetOutputMaximum( 255 );
  writer2->Update();

  caster3->SetInput( sigmoid->GetOutput() );
  writer3->SetInput( caster3->GetOutput() );
  writer3->SetFileName("GeodesicActiveContourImageFilterOutput3.png");
  caster3->SetOutputMinimum(   0 );
  caster3->SetOutputMaximum( 255 );
  writer3->Update();

  caster4->SetInput( fastMarching->GetOutput() );
  writer4->SetInput( caster4->GetOutput() );
  writer4->SetFileName("GeodesicActiveContourImageFilterOutput4.png");
  caster4->SetOutputMinimum(   0 );
  caster4->SetOutputMaximum( 255 );


  //  The FastMarchingImageFilter requires the user to specify the
  //  size of the image to be produced as output. This is done using the
  //  \code{SetOutputSize()}. Note that the size is obtained here from the
  //  output image of the smoothing filter. The size of this image is valid
  //  only after the \code{Update()} methods of this filter has been called
  //  directly or indirectly.
  //
  fastMarching->SetOutputSize(
           reader->GetOutput()->GetBufferedRegion().GetSize() );


  //  Software Guide : BeginLatex
  //
  //  The invocation of the \code{Update()} method on the writer triggers the
  //  execution of the pipeline.  As usual, the call is placed in a
  //  \code{try/catch} block should any errors occur or exceptions be thrown.
  //
  //  Software Guide : EndLatex

  // Software Guide : BeginCodeSnippet
  try
    {
    writer->Update();
    }
  catch( itk::ExceptionObject & excep )
    {
    std::cerr << "Exception caught !" << std::endl;
    std::cerr << excep << std::endl;
    return EXIT_FAILURE;
    }
  // Software Guide : EndCodeSnippet

  // Print out some useful information
  std::cout << std::endl;
  std::cout << "Max. no. iterations: " << geodesicActiveContour->GetNumberOfIterations() << std::endl;
  std::cout << "Max. RMS error: " << geodesicActiveContour->GetMaximumRMSError() << std::endl;
  std::cout << std::endl;
  std::cout << "No. elpased iterations: " << geodesicActiveContour->GetElapsedIterations() << std::endl;
  std::cout << "RMS change: " << geodesicActiveContour->GetRMSChange() << std::endl;

  writer4->Update();


  // The following writer type is used to save the output of the time-crossing
  // map in a file with apropiate pixel representation. The advantage of saving
  // this image in native format is that it can be used with a viewer to help
  // determine an appropriate threshold to be used on the output of the
  // fastmarching filter.
  //
  using InternalWriterType = itk::ImageFileWriter< InternalImageType >;

  InternalWriterType::Pointer mapWriter = InternalWriterType::New();
  mapWriter->SetInput( fastMarching->GetOutput() );
  mapWriter->SetFileName("GeodesicActiveContourImageFilterOutput4.mha");
  mapWriter->Update();

  InternalWriterType::Pointer speedWriter = InternalWriterType::New();
  speedWriter->SetInput( sigmoid->GetOutput() );
  speedWriter->SetFileName("GeodesicActiveContourImageFilterOutput3.mha");
  speedWriter->Update();

  InternalWriterType::Pointer gradientWriter = InternalWriterType::New();
  gradientWriter->SetInput( gradientMagnitude->GetOutput() );
  gradientWriter->SetFileName("GeodesicActiveContourImageFilterOutput2.mha");
  gradientWriter->Update();


  //  Software Guide : BeginLatex
  //
  //  Let's now run this example using as input the image
  //  \code{BrainProtonDensitySlice.png} provided in the directory
  //  \code{Examples/Data}. We can easily segment the major anatomical
  //  structures by providing seeds in the appropriate locations.
  //  Table~\ref{tab:GeodesicActiveContourImageFilterOutput2} presents the
  //  parameters used for some structures.
  //
  //  \begin{table}
  //  \begin{center}
  //  \begin{tabular}{|l|c|c|c|c|c|c|c|c|}
  //  \hline
  //  Structure    & Seed Index &  Distance   &   $\sigma$  &
  //  $\alpha$     &  $\beta$   & Propag. & Output Image \\  \hline
  //  Left Ventricle  & $(81,114)$ & 5.0 & 1.0 & -0.5 & 3.0  &  2.0 & First   \\  \hline
  //  Right Ventricle & $(99,114)$ & 5.0 & 1.0 & -0.5 & 3.0  &  2.0 & Second  \\  \hline
  //  White matter    & $(56, 92)$ & 5.0 & 1.0 & -0.3 & 2.0  & 10.0 & Third   \\  \hline
  //  Gray matter     & $(40, 90)$ & 5.0 & 0.5 & -0.3 & 2.0  & 10.0 & Fourth  \\  \hline
  //  \end{tabular}
  //  \end{center}
  //  \itkcaption[GeodesicActiveContour segmentation example parameters]{Parameters used
  //  for segmenting some brain structures shown in
  //  Figure~\ref{fig:GeodesicActiveContourImageFilterOutput2} using the filter
  //  GeodesicActiveContourLevelSetImageFilter.
  //  \label{tab:GeodesicActiveContourImageFilterOutput2}}
  //  \end{table}
  //
  //  Figure~\ref{fig:GeodesicActiveContourImageFilterOutput} presents the
  //  intermediate outputs of the pipeline illustrated in
  //  Figure~\ref{fig:GeodesicActiveContoursCollaborationDiagram}. They are
  //  from left to right: the output of the anisotropic diffusion filter, the
  //  gradient magnitude of the smoothed image and the sigmoid of the gradient
  //  magnitude which is finally used as the edge potential for the
  //  GeodesicActiveContourLevelSetImageFilter.
  //
  // \begin{figure} \center
  // \includegraphics[height=0.40\textheight]{BrainProtonDensitySlice}
  // \includegraphics[height=0.40\textheight]{GeodesicActiveContourImageFilterOutput1}
  // \includegraphics[height=0.40\textheight]{GeodesicActiveContourImageFilterOutput2}
  // \includegraphics[height=0.40\textheight]{GeodesicActiveContourImageFilterOutput3}
  // \itkcaption[GeodesicActiveContourLevelSetImageFilter intermediate
  // output]{Images generated by the segmentation process based on the
  // GeodesicActiveContourLevelSetImageFilter. From left to right and top to
  // bottom: input image to be segmented, image smoothed with an
  // edge-preserving smoothing filter, gradient magnitude of the smoothed
  // image, sigmoid of the gradient magnitude. This last image, the sigmoid, is
  // used to compute the speed term for the front propagation.}
  // \label{fig:GeodesicActiveContourImageFilterOutput} \end{figure}
  //
  //  Segmentations of the main brain structures are presented in
  //  Figure~\ref{fig:GeodesicActiveContourImageFilterOutput2}. The results
  //  are quite similar to those obtained with the
  //  ShapeDetectionLevelSetImageFilter in
  //  Section~\ref{sec:ShapeDetectionLevelSetFilter}.
  //
  //  Note that a relatively larger propagation scaling value was required to
  //  segment the white matter. This is due to two factors: the lower
  //  contrast at the border of the white matter and the complex shape of the
  //  structure. Unfortunately the optimal value of these scaling parameters
  //  can only be determined by experimentation. In a real application we
  //  could imagine an interactive mechanism by which a user supervises the
  //  contour evolution and adjusts these parameters accordingly.
  //
  // \begin{figure} \center
  // \includegraphics[width=0.24\textwidth]{GeodesicActiveContourImageFilterOutput5}
  // \includegraphics[width=0.24\textwidth]{GeodesicActiveContourImageFilterOutput6}
  // \includegraphics[width=0.24\textwidth]{GeodesicActiveContourImageFilterOutput7}
  // \includegraphics[width=0.24\textwidth]{GeodesicActiveContourImageFilterOutput8}
  // \itkcaption[GeodesicActiveContourImageFilter segmentations]{Images generated by the
  // segmentation process based on the GeodesicActiveContourImageFilter. From left to
  // right: segmentation of the left ventricle, segmentation of the right
  // ventricle, segmentation of the white matter, attempt of segmentation of
  // the gray matter.}
  // \label{fig:GeodesicActiveContourImageFilterOutput2}
  // \end{figure}
  //
  //  Software Guide : EndLatex

  return EXIT_SUCCESS;
}