ITK  5.2.0
Insight Toolkit
Examples/Segmentation/FastMarchingImageFilter.cxx
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*
* Copyright NumFOCUS
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
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// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {FastMarchingImageFilterOutput5.png}
// ARGUMENTS: 81 114 1.0 -0.5 3.0 100 100
// OUTPUTS: {FastMarchingFilterOutput1.png}
// OUTPUTS: {FastMarchingFilterOutput2.png}
// OUTPUTS: {FastMarchingFilterOutput3.png}
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {FastMarchingImageFilterOutput6.png}
// ARGUMENTS: 99 114 1.0 -0.5 3.0 100 100
// OUTPUTS: {FastMarchingFilterOutput1.png}
// OUTPUTS: {FastMarchingFilterOutput2.png}
// OUTPUTS: {FastMarchingFilterOutput3.png}
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {FastMarchingImageFilterOutput7.png}
// ARGUMENTS: 56 92 1.0 -0.3 2.0 200 100
// OUTPUTS: {FastMarchingFilterOutput1.png}
// OUTPUTS: {FastMarchingFilterOutput2.png}
// OUTPUTS: {FastMarchingFilterOutput3.png}
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {FastMarchingImageFilterOutput8.png}
// ARGUMENTS: 40 90 0.5 -0.3 2.0 200 100
// OUTPUTS: {FastMarchingFilterOutput1.png}
// OUTPUTS: {FastMarchingFilterOutput2.png}
// OUTPUTS: {FastMarchingFilterOutput3.png}
// Software Guide : EndCommandLineArgs
// Software Guide : BeginLatex
//
// When the differential equation governing the level set evolution has
// a very simple form, a fast evolution algorithm called fast marching
// can be used.
//
// The following example illustrates the use of the
// \doxygen{FastMarchingImageFilter}. This filter implements a fast marching
// solution to a simple level set evolution problem. In this example, the
// speed term used in the differential equation is expected to be provided by
// the user in the form of an image. This image is typically computed as a
// function of the gradient magnitude. Several mappings are popular in the
// literature, for example, the negative exponential $exp(-x)$ and the
// reciprocal $1/(1+x)$. In the current example we decided to use a Sigmoid
// function since it offers a good number of control parameters that can be
// customized to shape a nice speed image.
//
// The mapping should be done in such a way that the propagation speed of the
// front will be very low close to high image gradients while it will move
// rather fast in low gradient areas. This arrangement will make the contour
// propagate until it reaches the edges of anatomical structures in the image
// and then slow down in front of those edges. The output of the
// FastMarchingImageFilter is a \emph{time-crossing map} that
// indicates, for each pixel, how much time it would take for the front to
// arrive at the pixel location.
//
// \begin{figure} \center
// \includegraphics[width=\textwidth]{FastMarchingCollaborationDiagram1}
// \itkcaption[FastMarchingImageFilter collaboration diagram]{Collaboration
// diagram of the FastMarchingImageFilter applied to a segmentation task.}
// \label{fig:FastMarchingCollaborationDiagram}
// \end{figure}
//
// The application of a threshold in the output image is then equivalent to
// taking a snapshot of the contour at a particular time during its evolution.
// It is expected that the contour will take a longer time to cross over
// the edges of a particular anatomical structure. This should result in large
// changes on the time-crossing map values close to the structure edges.
// Segmentation is performed with this filter by locating a time range in
// which the contour was contained for a long time in a region of the image
// space.
//
// Figure~\ref{fig:FastMarchingCollaborationDiagram} shows the major
// components involved in the application of the FastMarchingImageFilter to a
// segmentation task. It involves an initial stage of smoothing using the
// \doxygen{CurvatureAnisotropicDiffusionImageFilter}. The smoothed image is
// passed as the input to the
// \doxygen{GradientMagnitudeRecursiveGaussianImageFilter} and then to the
// \doxygen{SigmoidImageFilter}. Finally, the output of the
// FastMarchingImageFilter is passed to a
// \doxygen{BinaryThresholdImageFilter} in order to produce a binary mask
// representing the segmented object.
//
// The code in the following example illustrates the typical setup of a
// pipeline for performing segmentation with fast marching. First, the input
// image is smoothed using an edge-preserving filter. Then the magnitude of
// its gradient is computed and passed to a sigmoid filter. The result of the
// sigmoid filter is the image potential that will be used to affect the speed
// term of the differential equation.
//
// Let's start by including the following headers. First we include the header
// of the CurvatureAnisotropicDiffusionImageFilter that will be used
// for removing noise from the input image.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The headers of the GradientMagnitudeRecursiveGaussianImageFilter and
// SigmoidImageFilter are included below. Together, these two filters will
// produce the image potential for regulating the speed term in the
// differential equation describing the evolution of the level set.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Of course, we will need the \doxygen{Image} class and the
// FastMarchingImageFilter class. Hence we include their headers.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The time-crossing map resulting from the FastMarchingImageFilter
// will be thresholded using the BinaryThresholdImageFilter. We
// include its header here.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Reading and writing images will be done with the \doxygen{ImageFileReader}
// and \doxygen{ImageFileWriter}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// The \doxygen{RescaleIntensityImageFilter} is used to renormailize the
// output of filters before sending them to files.
//
static void
PrintCommandLineUsage(const int argc, const char * const argv[])
{
std::cerr << "Missing Parameters " << std::endl;
std::cerr << "Usage: " << argv[0];
std::cerr << " inputImage outputImage seedX seedY";
std::cerr << " Sigma SigmoidAlpha SigmoidBeta TimeThreshold StoppingValue";
std::cerr
<< " smoothingOutputImage gradientMagnitudeOutputImage sigmoidOutputImage"
<< std::endl;
for (int qq = 0; qq < argc; ++qq)
{
std::cout << "argv[" << qq << "] = " << argv[qq] << std::endl;
}
}
int
main(int argc, char * argv[])
{
if (argc != 13)
{
PrintCommandLineUsage(argc, argv);
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// We now define the image type using a pixel type and a particular
// 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
// Software Guide : BeginLatex
//
// The output image, on the other hand, is declared to be binary.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using OutputPixelType = unsigned char;
using OutputImageType = itk::Image<OutputPixelType, Dimension>;
// 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
using ThresholdingFilterType =
ThresholdingFilterType::Pointer thresholder = ThresholdingFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The upper threshold passed to the BinaryThresholdImageFilter
// will define the time snapshot that we are taking from the time-crossing
// map. In an ideal application the user should be able to select this
// threshold interactively using visual feedback. Here, since it is a
// minimal example, the value is taken from the command line arguments.
//
// Software Guide : EndLatex
const InternalPixelType timeThreshold = std::stod(argv[8]);
// Software Guide : BeginCodeSnippet
thresholder->SetLowerThreshold(0.0);
thresholder->SetUpperThreshold(timeThreshold);
thresholder->SetOutsideValue(0);
thresholder->SetInsideValue(255);
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// We instantiate reader and writer types in the following lines.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
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 =
// Software Guide : BeginLatex
//
// The CurvatureAnisotropicDiffusionImageFilter type is
// instantiated using the internal image type.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using SmoothingFilterType =
InternalImageType>;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Then, the filter is created 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
using GradientFilterType =
InternalImageType>;
using SigmoidFilterType =
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The corresponding filter objects are instantiated with the
// \code{New()} method.
//
// 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.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using FastMarchingFilterType =
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Then, 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
//
// The filters are now connected in a pipeline shown in
// Figure~\ref{fig:FastMarchingCollaborationDiagram} using the following
// lines.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
smoothing->SetInput(reader->GetOutput());
gradientMagnitude->SetInput(smoothing->GetOutput());
sigmoid->SetInput(gradientMagnitude->GetOutput());
fastMarching->SetInput(sigmoid->GetOutput());
thresholder->SetInput(fastMarching->GetOutput());
writer->SetInput(thresholder->GetOutput());
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The CurvatureAnisotropicDiffusionImageFilter class 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 = std::stod(argv[5]);
// Software Guide : BeginCodeSnippet
gradientMagnitude->SetSigma(sigma);
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The SigmoidImageFilter class requires two parameters to define the
// linear transformation to be applied to the sigmoid argument. These
// parameters are passed using the \code{SetAlpha()} and \code{SetBeta()}
// methods. In the context of this example, the parameters are used to
// intensify the differences between regions of low and high values in the
// speed image. In an ideal case, the speed value should be $1.0$ in the
// homogeneous regions of anatomical structures and the value should decay
// rapidly to $0.0$ around the edges of structures. The heuristic for
// finding the values is the following: From the gradient magnitude image,
// let's call $K1$ the minimum value along the contour of the anatomical
// structure to be segmented. Then, let's call $K2$ an average value of the
// gradient magnitude in the middle of the structure. These two values
// indicate the dynamic range that we want to map to the interval $[0:1]$
// in the speed image. We want the sigmoid to map $K1$ to $0.0$ and $K2$
// to $1.0$. Given that $K1$ is expected to be higher than $K2$ and we want
// to map those values to $0.0$ and $1.0$ respectively, we want to select a
// negative value for alpha so that the sigmoid function will also do an
// inverse intensity mapping. This mapping will produce a speed image such
// that the level set will march rapidly on the homogeneous region and will
// definitely stop on the contour. The suggested value for beta is
// $(K1+K2)/2$ while the suggested value for alpha is $(K2-K1)/6$, which
// must be a negative number. In our simple example the values are
// provided by the user from the command line arguments. The user can
// estimate these values by observing the gradient magnitude image.
//
// Software Guide : EndLatex
const double alpha = std::stod(argv[6]);
const double beta = std::stod(argv[7]);
// 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 contour will expand. The user can actually pass not only
// one seed point but a set of them. A good set of seed points increases
// the chances of segmenting a complex object without missing parts. The
// use of multiple seeds also helps to reduce the amount of time needed by
// the front to visit a whole object and hence reduces the risk of leaks
// on the edges of regions visited earlier. For example, when segmenting
// an elongated object, it is undesirable to place a single seed at one
// extreme of the object since the front will need a long time to
// propagate to the other end of the object. Placing several seeds along
// the axis of the object will probably be the best strategy to ensure
// that the entire object is captured early in the expansion of the
// front. One of the important properties of level sets is their natural
// ability to fuse several fronts implicitly without any extra
// bookkeeping. The use of multiple seeds takes good advantage of this
// property.
//
// \index{itk::FastMarchingImageFilter!Multiple seeds}
//
// The seeds are passed 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
using NodeContainer = FastMarchingFilterType::NodeContainer;
using NodeType = FastMarchingFilterType::NodeType;
NodeContainer::Pointer seeds = NodeContainer::New();
// Software Guide : EndCodeSnippet
seedPosition[0] = std::stoi(argv[3]);
seedPosition[1] = std::stoi(argv[4]);
// Software Guide : BeginLatex
//
// Nodes are created as stack variables and initialized with a value and an
// \doxygen{Index} position.
//
// \index{itk::FastMarchingImageFilter!Seed initialization}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
NodeType node;
constexpr double seedValue = 0.0;
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
// the \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
// Here we configure all the writers required to see the intermediate
// outputs of the pipeline. This is added here to provide
// the necessary images for generating the ITKSoftwareGuide.
// These intermediate outputs are normally 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.
//
try
{
CastFilterType::Pointer caster1 = CastFilterType::New();
WriterType::Pointer writer1 = WriterType::New();
caster1->SetInput(smoothing->GetOutput());
writer1->SetInput(caster1->GetOutput());
writer1->SetFileName(argv[10]);
caster1->SetOutputMinimum(0);
caster1->SetOutputMaximum(255);
writer1->Update();
}
catch (const itk::ExceptionObject & err)
{
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
return EXIT_FAILURE;
}
try
{
CastFilterType::Pointer caster2 = CastFilterType::New();
WriterType::Pointer writer2 = WriterType::New();
caster2->SetInput(gradientMagnitude->GetOutput());
writer2->SetInput(caster2->GetOutput());
writer2->SetFileName(argv[11]);
caster2->SetOutputMinimum(0);
caster2->SetOutputMaximum(255);
writer2->Update();
}
catch (const itk::ExceptionObject & err)
{
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
return EXIT_FAILURE;
}
try
{
CastFilterType::Pointer caster3 = CastFilterType::New();
WriterType::Pointer writer3 = WriterType::New();
caster3->SetInput(sigmoid->GetOutput());
writer3->SetInput(caster3->GetOutput());
writer3->SetFileName(argv[12]);
caster3->SetOutputMinimum(0);
caster3->SetOutputMaximum(255);
writer3->Update();
}
catch (const itk::ExceptionObject & err)
{
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
return EXIT_FAILURE;
}
// 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()} method. 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()} method of this filter has been
// called directly or indirectly.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
fastMarching->SetOutputSize(
reader->GetOutput()->GetBufferedRegion().GetSize());
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Since the front representing the contour will propagate continuously
// over time, it is desirable to stop the process once a certain time has
// been reached. This allows us to save computation time under the
// assumption that the region of interest has already been computed. The
// value for stopping the process is defined with the method
// \code{SetStoppingValue()}. In principle, the stopping value should be a
// little bit higher than the threshold value.
//
// \index{itk::FastMarchingImageFilter!SetStoppingValue()}
//
// Software Guide : EndLatex
const double stoppingTime = std::stod(argv[9]);
// Software Guide : BeginCodeSnippet
fastMarching->SetStoppingValue(stoppingTime);
// 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 (const itk::ExceptionObject & excep)
{
std::cerr << "Exception caught !" << std::endl;
std::cerr << excep << std::endl;
return EXIT_FAILURE;
}
// Software Guide : EndCodeSnippet
try
{
CastFilterType::Pointer caster4 = CastFilterType::New();
WriterType::Pointer writer4 = WriterType::New();
caster4->SetInput(fastMarching->GetOutput());
writer4->SetInput(caster4->GetOutput());
writer4->SetFileName("FastMarchingFilterOutput4.png");
caster4->SetOutputMinimum(0);
caster4->SetOutputMaximum(255);
writer4->Update();
}
catch (const itk::ExceptionObject & err)
{
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
return EXIT_FAILURE;
}
// The following writer type is used to save the output of the
// time-crossing map in a file with appropiate 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 \code{fastmarching} filter.
//
using InternalWriterType = itk::ImageFileWriter<InternalImageType>;
InternalWriterType::Pointer mapWriter = InternalWriterType::New();
mapWriter->SetInput(fastMarching->GetOutput());
mapWriter->SetFileName("FastMarchingFilterOutput4.mha");
mapWriter->Update();
InternalWriterType::Pointer speedWriter = InternalWriterType::New();
speedWriter->SetInput(sigmoid->GetOutput());
speedWriter->SetFileName("FastMarchingFilterOutput3.mha");
speedWriter->Update();
InternalWriterType::Pointer gradientWriter = InternalWriterType::New();
gradientWriter->SetInput(gradientMagnitude->GetOutput());
gradientWriter->SetFileName("FastMarchingFilterOutput2.mha");
gradientWriter->Update();
// clang-format off
// Software Guide : BeginLatex
//
// Now let's run this example using the input 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. The following
// table presents the parameters used for some structures.
//
// \begin{table}
// \begin{center}
// \begin{tabular}{|l|c|c|c|c|c|c|p{2cm}|}
// \hline
// Structure & Seed Index & $\sigma$ & $\alpha$ & $\beta$ & Threshold & Output Image from left \\ \hline
// Left Ventricle & $(81,114)$ & 1.0 & -0.5 & 3.0 & 100 & First \\ \hline
// Right Ventricle & $(99,114)$ & 1.0 & -0.5 & 3.0 & 100 & Second \\ \hline
// White matter & $(56, 92)$ & 1.0 & -0.3 & 2.0 & 200 & Third \\ \hline
// Gray matter & $(40, 90)$ & 0.5 & -0.3 & 2.0 & 200 & Fourth \\ \hline
// \end{tabular}
// \end{center}
// \itkcaption[FastMarching segmentation example parameters]{Parameters used
// for segmenting some brain structures shown in
// Figure~\ref{fig:FastMarchingImageFilterOutput2} using the filter
// FastMarchingImageFilter. All of them used a stopping value of
// 100.\label{tab:FastMarchingImageFilterOutput2}}
// \end{table}
//
// Figure~\ref{fig:FastMarchingImageFilterOutput} presents the intermediate
// outputs of the pipeline illustrated in
// Figure~\ref{fig:FastMarchingCollaborationDiagram}. 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 speed image for the
// FastMarchingImageFilter.
//
// \begin{figure} \center
// \includegraphics[height=0.40\textheight]{BrainProtonDensitySlice}
// \includegraphics[height=0.40\textheight]{FastMarchingFilterOutput1}
// \includegraphics[height=0.40\textheight]{FastMarchingFilterOutput2}
// \includegraphics[height=0.40\textheight]{FastMarchingFilterOutput3}
// \itkcaption[FastMarchingImageFilter intermediate output]{Images generated by
// the segmentation process based on the FastMarchingImageFilter. 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:FastMarchingImageFilterOutput}
// \end{figure}
//
// Notice that the gray matter is not being completely segmented. This
// illustrates the vulnerability of the level set methods when the
// anatomical structures to be segmented do not occupy extended regions of
// the image. This is especially true when the width of the structure is
// comparable to the size of the attenuation bands generated by the
// gradient filter. A possible workaround for this limitation is to use
// multiple seeds distributed along the elongated object. However, note
// that white matter versus gray matter segmentation is not a trivial task,
// and may require a more elaborate approach than the one used in this
// basic example.
//
// \begin{figure} \center
// \includegraphics[width=0.24\textwidth]{FastMarchingImageFilterOutput5}
// \includegraphics[width=0.24\textwidth]{FastMarchingImageFilterOutput6}
// \includegraphics[width=0.24\textwidth]{FastMarchingImageFilterOutput7}
// \includegraphics[width=0.24\textwidth]{FastMarchingImageFilterOutput8}
// \itkcaption[FastMarchingImageFilter segmentations]{Images generated by the
// segmentation process based on the FastMarchingImageFilter. 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:FastMarchingImageFilterOutput2}
// \end{figure}
//
// Software Guide : EndLatex
// clang-format on
return EXIT_SUCCESS;
}
itkSigmoidImageFilter.h
itk::BinaryThresholdImageFilter
Binarize an input image by thresholding.
Definition: itkBinaryThresholdImageFilter.h:139
itkImageFileReader.h
itk::SigmoidImageFilter
Computes the sigmoid function pixel-wise.
Definition: itkSigmoidImageFilter.h:150
itkFastMarchingImageFilter.h
itk::ImageFileReader
Data source that reads image data from a single file.
Definition: itkImageFileReader.h:75
itk::GTest::TypedefsAndConstructors::Dimension2::IndexType
ImageBaseType::IndexType IndexType
Definition: itkGTestTypedefsAndConstructors.h:50
itk::CurvatureAnisotropicDiffusionImageFilter
This filter performs anisotropic diffusion on a scalar itk::Image using the modified curvature diffus...
Definition: itkCurvatureAnisotropicDiffusionImageFilter.h:58
itkCurvatureAnisotropicDiffusionImageFilter.h
itk::ImageFileWriter
Writes image data to a single file.
Definition: itkImageFileWriter.h:87
itk::FastMarchingImageFilter
Solve an Eikonal equation using Fast Marching.
Definition: itkFastMarchingImageFilter.h:136
itk::GradientMagnitudeRecursiveGaussianImageFilter
Computes the Magnitude of the Gradient of an image by convolution with the first derivative of a Gaus...
Definition: itkGradientMagnitudeRecursiveGaussianImageFilter.h:50
itkRescaleIntensityImageFilter.h
itkImageFileWriter.h
itk::RescaleIntensityImageFilter
Applies a linear transformation to the intensity levels of the input Image.
Definition: itkRescaleIntensityImageFilter.h:154
itkBinaryThresholdImageFilter.h
itk::Image
Templated n-dimensional image class.
Definition: itkImage.h:86
itk::GTest::TypedefsAndConstructors::Dimension2::Dimension
constexpr unsigned int Dimension
Definition: itkGTestTypedefsAndConstructors.h:44
itkGradientMagnitudeRecursiveGaussianImageFilter.h