ITK  4.13.0
Insight Segmentation and Registration Toolkit
Examples/Segmentation/ShapeDetectionLevelSetFilter.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.
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// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput5.png}
// ARGUMENTS: 81 114 5 1.0 -0.5 3.0 .05 1
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput6.png}
// ARGUMENTS: 99 114 5 1.0 -0.5 3.0 .05 1
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput7.png}
// ARGUMENTS: 56 92 5 1.0 -0.3 2.0 .05 1
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput8.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput1.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput2.png}
// OUTPUTS: {ShapeDetectionLevelSetFilterOutput3.png}
// ARGUMENTS: 40 90 5 0.5 -0.3 2.0 .05 1
// Software Guide : EndCommandLineArgs
// Software Guide : BeginLatex
//
// The use of the \doxygen{ShapeDetectionLevelSetImageFilter} is illustrated
// in the following example. The implementation of this filter in ITK is
// based on the paper by Malladi et al \cite{Malladi1995}. In this
// implementation, the governing differential equation has an additional
// curvature-based term. This term acts as a smoothing term where areas of
// high curvature, assumed to be due to noise, are smoothed out. Scaling
// parameters are used to control the tradeoff between the expansion term and
// the smoothing term. One consequence of this additional curvature term is
// that the fast marching algorithm is no longer applicable, because the
// contour is no longer guaranteed to always be expanding. Instead, the level
// set function is updated iteratively.
//
// The ShapeDetectionLevelSetImageFilter expects two inputs,
// the first being an initial Level Set in the form of an
// \doxygen{Image}, and the second being a feature image. For this algorithm,
// the feature image is an edge potential image that basically
// follows the same rules applicable to the speed image used for the
// FastMarchingImageFilter discussed in
// Section~\ref{sec:FastMarchingImageFilter}.
//
// In this example we use an FastMarchingImageFilter to produce the initial
// level set as the distance function to a set of user-provided seeds. The
// FastMarchingImageFilter is run with a constant speed value which enables
// us to employ this filter as a distance map calculator.
//
// \begin{figure} \center
// \includegraphics[width=\textwidth]{ShapeDetectionCollaborationDiagram1}
// \itkcaption[ShapeDetectionLevelSetImageFilter collaboration diagram]{Collaboration
// diagram for the ShapeDetectionLevelSetImageFilter applied to a segmentation task.}
// \label{fig:ShapeDetectionCollaborationDiagram}
// \end{figure}
//
// Figure~\ref{fig:ShapeDetectionCollaborationDiagram} shows the major
// components involved in the application of the
// ShapeDetectionLevelSetImageFilter to a segmentation task. The first stage
// involves smoothing using the
// \doxygen{CurvatureAnisotropicDiffusionImageFilter}. The smoothed image is
// passed as the input for 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 an 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 ShapeDetectionLevelSetImageFilter.
//
// Finally, the level set at the output of the
// ShapeDetectionLevelSetImageFilter is passed to an
// 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
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The edge potential map is generated using these filters as in the previous
// example.
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// We will need the Image class, the FastMarchingImageFilter class and the
// ShapeDetectionLevelSetImageFilter class. Hence we include their headers
// here.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The level set resulting from the ShapeDetectionLevelSetImageFilter will
// be thresholded at the zero level in order to get a binary image
// representing the segmented object. The BinaryThresholdImageFilter is used
// for this purpose.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Reading and writing images will be done with the \doxygen{ImageFileReader}
// and \doxygen{ImageFileWriter}.
// The RescaleIntensityImageFilter is used to renormailize the output
// of filters before sending them to files.
int main( int argc, char *argv[] )
{
if( argc < 11 )
{
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 << " curvatureScaling propagationScaling" << std::endl;
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// We now define the image type using a particular pixel type and a
// 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
typedef float InternalPixelType;
const unsigned int Dimension = 2;
typedef itk::Image< InternalPixelType, Dimension > InternalImageType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The output image, on the other hand, is declared to be binary.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef unsigned char OutputPixelType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The type of the BinaryThresholdImageFilter filter is instantiated below
// using the internal image type and the output image type.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
ThresholdingFilterType;
ThresholdingFilterType::Pointer thresholder = ThresholdingFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The upper threshold of the BinaryThresholdImageFilter is set
// to $0.0$ in order to display the zero set of the resulting level
// set. The lower threshold is set to a large negative number in order to
// ensure that the interior of the segmented object will appear
// inside the binary region.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
thresholder->SetLowerThreshold( -1000.0 );
thresholder->SetUpperThreshold( 0.0 );
thresholder->SetOutsideValue( 0 );
thresholder->SetInsideValue( 255 );
// Software Guide : EndCodeSnippet
// We instantiate reader and writer types in the following lines.
//
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.
//
CastFilterType;
// Software Guide : BeginLatex
//
// The CurvatureAnisotropicDiffusionImageFilter type is instantiated using
// the internal image type.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
InternalImageType,
InternalImageType > SmoothingFilterType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The filter is instantiated by invoking the \code{New()} method and
// assigning the result to a \doxygen{SmartPointer}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
SmoothingFilterType::Pointer smoothing = SmoothingFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The types of the GradientMagnitudeRecursiveGaussianImageFilter and
// SigmoidImageFilter are instantiated using the internal
// image type.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
InternalImageType,
InternalImageType > GradientFilterType;
InternalImageType,
InternalImageType > SigmoidFilterType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The corresponding filter objects are created with the method
// \code{New()}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
GradientFilterType::Pointer gradientMagnitude = GradientFilterType::New();
SigmoidFilterType::Pointer sigmoid = SigmoidFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// 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
// to the FastMarchingImageFilter. Additional details on the use of the
// SigmoidImageFilter are presented in
// Section~\ref{sec:IntensityNonLinearMapping}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
sigmoid->SetOutputMinimum( 0.0 );
sigmoid->SetOutputMaximum( 1.0 );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// We now declare the type of the FastMarchingImageFilter that
// will be used to generate the initial level set in the form of a distance
// map.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
FastMarchingFilterType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Next we construct one filter of this class using the \code{New()}
// method.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
FastMarchingFilterType::Pointer fastMarching
= FastMarchingFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// In the following lines we instantiate the type of the
// ShapeDetectionLevelSetImageFilter and create an object of this type
// using the \code{New()} method.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::ShapeDetectionLevelSetImageFilter< InternalImageType,
InternalImageType > ShapeDetectionFilterType;
ShapeDetectionFilterType::Pointer
shapeDetection = ShapeDetectionFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The filters are now connected in a pipeline indicated in
// Figure~\ref{fig:ShapeDetectionCollaborationDiagram} with the following
// code.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
smoothing->SetInput( reader->GetOutput() );
gradientMagnitude->SetInput( smoothing->GetOutput() );
sigmoid->SetInput( gradientMagnitude->GetOutput() );
shapeDetection->SetInput( fastMarching->GetOutput() );
shapeDetection->SetFeatureImage( sigmoid->GetOutput() );
thresholder->SetInput( shapeDetection->GetOutput() );
writer->SetInput( thresholder->GetOutput() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The CurvatureAnisotropicDiffusionImageFilter requires a couple
// of parameters 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}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
smoothing->SetTimeStep( 0.125 );
smoothing->SetNumberOfIterations( 5 );
smoothing->SetConductanceParameter( 9.0 );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// 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}.
//
// \index{itk::Gradient\-Magnitude\-Recursive\-Gaussian\-Image\-Filter!SetSigma()}
//
// Software Guide : EndLatex
const double sigma = atof( argv[6] );
// Software Guide : BeginCodeSnippet
gradientMagnitude->SetSigma( sigma );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The SigmoidImageFilter requires two parameters that define the linear
// transformation to be applied to the sigmoid argument. These parameters
// have been discussed in Sections~\ref{sec:IntensityNonLinearMapping} and
// \ref{sec:FastMarchingImageFilter}.
//
// Software Guide : EndLatex
const double alpha = atof( argv[7] );
const double beta = atof( argv[8] );
// Software Guide : BeginCodeSnippet
sigmoid->SetAlpha( alpha );
sigmoid->SetBeta( beta );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// 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
// 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.
//
// \index{itk::FastMarchingImageFilter!Multiple seeds}
//
// The seeds are stored in a container. The type of this
// container is defined as \code{NodeContainer} among the
// FastMarchingImageFilter traits.
//
// \index{itk::FastMarchingImageFilter!Nodes}
// \index{itk::FastMarchingImageFilter!NodeContainer}
// \index{itk::FastMarchingImageFilter!NodeType}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef FastMarchingFilterType::NodeContainer NodeContainer;
typedef FastMarchingFilterType::NodeType NodeType;
NodeContainer::Pointer seeds = NodeContainer::New();
// Software Guide : EndCodeSnippet
seedPosition[0] = atoi( argv[3] );
seedPosition[1] = atoi( argv[4] );
// Software Guide : BeginLatex
//
// Nodes are created as stack variables and initialized with a value and
// an \doxygen{Index} position. Note that we assign the negative of the
// value of 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 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
// the initial contour should be.
//
// \index{itk::FastMarchingImageFilter!Seed initialization}
//
// Software Guide : EndLatex
const double initialDistance = atof( argv[5] );
// Software Guide : BeginCodeSnippet
NodeType node;
const double seedValue = - initialDistance;
node.SetValue( seedValue );
node.SetIndex( seedPosition );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The list of nodes is initialized and then every node is inserted using
// \code{InsertElement()}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
seeds->Initialize();
seeds->InsertElement( 0, node );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The set of seed nodes is now passed to the FastMarchingImageFilter with
// the method \code{SetTrialPoints()}.
//
// \index{itk::FastMarchingImageFilter!SetTrialPoints()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
fastMarching->SetTrialPoints( seeds );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Since the FastMarchingImageFilter is used here only 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.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
fastMarching->SetSpeedConstant( 1.0 );
// Software Guide : EndCodeSnippet
// 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("ShapeDetectionLevelSetFilterOutput1.png");
caster1->SetOutputMinimum( 0 );
caster1->SetOutputMaximum( 255 );
writer1->Update();
caster2->SetInput( gradientMagnitude->GetOutput() );
writer2->SetInput( caster2->GetOutput() );
writer2->SetFileName("ShapeDetectionLevelSetFilterOutput2.png");
caster2->SetOutputMinimum( 0 );
caster2->SetOutputMaximum( 255 );
writer2->Update();
caster3->SetInput( sigmoid->GetOutput() );
writer3->SetInput( caster3->GetOutput() );
writer3->SetFileName("ShapeDetectionLevelSetFilterOutput3.png");
caster3->SetOutputMinimum( 0 );
caster3->SetOutputMaximum( 255 );
writer3->Update();
caster4->SetInput( fastMarching->GetOutput() );
writer4->SetInput( caster4->GetOutput() );
writer4->SetFileName("ShapeDetectionLevelSetFilterOutput4.png");
caster4->SetOutputMinimum( 0 );
caster4->SetOutputMaximum( 255 );
// Software Guide : BeginLatex
//
// 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 have been called
// directly or indirectly.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
fastMarching->SetOutputSize(
reader->GetOutput()->GetBufferedRegion().GetSize() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// ShapeDetectionLevelSetImageFilter provides two parameters to control
// the competition between the propagation or expansion term and the
// curvature smoothing term. The methods \code{SetPropagationScaling()}
// and \code{SetCurvatureScaling()} defines the relative weighting between
// the two terms. In this example, we will set the propagation scaling to
// one and let the curvature scaling be an input argument. The larger the
// the curvature scaling parameter the smoother the resulting
// segmentation. However, the curvature scaling parameter should not be
// set too large, as it will draw the contour away from the shape
// boundaries.
//
// \index{itk::Shape\-Detection\-LevelSet\-Image\-Filter!SetPropagationScaling()}
// \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetPropagationScaling()}
// \index{itk::Shape\-Detection\-Level\-Set\-Image\-Filter!SetCurvatureScaling()}
// \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetCurvatureScaling()}
//
// Software Guide : EndLatex
const double curvatureScaling = atof( argv[ 9 ] );
const double propagationScaling = atof( argv[ 10 ] );
// Software Guide : BeginCodeSnippet
shapeDetection->SetPropagationScaling( propagationScaling );
shapeDetection->SetCurvatureScaling( curvatureScaling );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Once activated, the level set evolution will stop if the convergence
// criteria or the maximum number of iterations is reached. The
// convergence criteria are 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, it 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.
//
// \index{itk::Shape\-Detection\-Level\-Set\-Image\-Filter!SetMaximumRMSError()}
// \index{itk::Shape\-Detection\-Level\-Set\-Image\-Filter!SetNumberOfIterations()}
// \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetMaximumRMSError()}
// \index{itk::Segmentation\-Level\-Set\-Image\-Filter!SetNumberOfIterations()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
shapeDetection->SetMaximumRMSError( 0.02 );
shapeDetection->SetNumberOfIterations( 800 );
// Software Guide : EndCodeSnippet
// 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: " << shapeDetection->GetNumberOfIterations() << std::endl;
std::cout << "Max. RMS error: " << shapeDetection->GetMaximumRMSError() << std::endl;
std::cout << std::endl;
std::cout << "No. elpased iterations: " << shapeDetection->GetElapsedIterations() << std::endl;
std::cout << "RMS change: " << shapeDetection->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.
//
typedef itk::ImageFileWriter< InternalImageType > InternalWriterType;
InternalWriterType::Pointer mapWriter = InternalWriterType::New();
mapWriter->SetInput( fastMarching->GetOutput() );
mapWriter->SetFileName("ShapeDetectionLevelSetFilterOutput4.mha");
mapWriter->Update();
InternalWriterType::Pointer speedWriter = InternalWriterType::New();
speedWriter->SetInput( sigmoid->GetOutput() );
speedWriter->SetFileName("ShapeDetectionLevelSetFilterOutput3.mha");
speedWriter->Update();
InternalWriterType::Pointer gradientWriter = InternalWriterType::New();
gradientWriter->SetInput( gradientMagnitude->GetOutput() );
gradientWriter->SetFileName("ShapeDetectionLevelSetFilterOutput2.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:ShapeDetectionLevelSetFilterOutput} presents the
// parameters used for some structures. For all of the examples illustrated
// in this table, the propagation scaling was set to $1.0$, and the
// curvature scaling set to 0.05.
//
// \begin{table}
// \begin{center}
// \begin{tabular}{|l|c|c|c|c|c|c|}
// \hline
// Structure & Seed Index & Distance & $\sigma$ & $\alpha$ & $\beta$ & Output Image \\ \hline
// Left Ventricle & $(81,114)$ & 5.0 & 1.0 & -0.5 & 3.0 & First in Figure \ref{fig:ShapeDetectionLevelSetFilterOutput2} \\ \hline
// Right Ventricle & $(99,114)$ & 5.0 & 1.0 & -0.5 & 3.0 & Second in Figure \ref{fig:ShapeDetectionLevelSetFilterOutput2} \\ \hline
// White matter & $(56, 92)$ & 5.0 & 1.0 & -0.3 & 2.0 & Third in Figure \ref{fig:ShapeDetectionLevelSetFilterOutput2} \\ \hline
// Gray matter & $(40, 90)$ & 5.0 & 0.5 & -0.3 & 2.0 & Fourth in Figure \ref{fig:ShapeDetectionLevelSetFilterOutput2} \\ \hline
// \end{tabular}
// \end{center}
// \itkcaption[ShapeDetection example parameters]{Parameters used for
// segmenting some brain structures shown in
// Figure~\ref{fig:ShapeDetectionLevelSetFilterOutput} using the filter
// ShapeDetectionLevelSetFilter. All of them used a propagation
// scaling of $1.0$ and curvature scaling of
// $0.05$.\label{tab:ShapeDetectionLevelSetFilterOutput}}
// \end{table}
//
// Figure~\ref{fig:ShapeDetectionLevelSetFilterOutput} presents the
// intermediate outputs of the pipeline illustrated in
// Figure~\ref{fig:ShapeDetectionCollaborationDiagram}. 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
// ShapeDetectionLevelSetImageFilter.
//
// Notice that in Figure~\ref{fig:ShapeDetectionLevelSetFilterOutput2} the
// segmented shapes are rounder than in
// Figure~\ref{fig:FastMarchingImageFilterOutput2} due to the effects of the
// curvature term in the driving equation. As with the previous example,
// segmentation of the gray matter is still problematic.
//
// \begin{figure} \center
// \includegraphics[height=0.40\textheight]{BrainProtonDensitySlice}
// \includegraphics[height=0.40\textheight]{ShapeDetectionLevelSetFilterOutput1}
// \includegraphics[height=0.40\textheight]{ShapeDetectionLevelSetFilterOutput2}
// \includegraphics[height=0.40\textheight]{ShapeDetectionLevelSetFilterOutput3}
// \itkcaption[ShapeDetectionLevelSetImageFilter intermediate output]{Images generated by
// the segmentation process based on the ShapeDetectionLevelSetImageFilter. 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:ShapeDetectionLevelSetFilterOutput}
// \end{figure}
//
// A larger number of iterations is reguired for segmenting large
// structures since it takes longer for the front to propagate and cover
// the structure. This drawback can be easily mitigated by setting many
// seed points in the initialization of the
// FastMarchingImageFilter. This will generate an initial level
// set much closer in shape to the object to be segmented and hence
// require fewer iterations to fill and reach the edges of the anatomical
// structure.
//
// \begin{figure} \center
// \includegraphics[width=0.24\textwidth]{ShapeDetectionLevelSetFilterOutput5}
// \includegraphics[width=0.24\textwidth]{ShapeDetectionLevelSetFilterOutput6}
// \includegraphics[width=0.24\textwidth]{ShapeDetectionLevelSetFilterOutput7}
// \includegraphics[width=0.24\textwidth]{ShapeDetectionLevelSetFilterOutput8}
// \itkcaption[ShapeDetectionLevelSetImageFilter segmentations]{Images generated by the
// segmentation process based on the ShapeDetectionLevelSetImageFilter. 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:ShapeDetectionLevelSetFilterOutput2}
// \end{figure}
//
// Software Guide : EndLatex
return EXIT_SUCCESS;
}