Examples/Statistics/ImageMutualInformation1.cxx

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// Software Guide : BeginLatex
//
// This example illustrates how to compute the Mutual Information between two
// images using classes from the Statistics framework. Note that you could
// also use for this purpose the ImageMetrics designed for the image
// registration framework.
//
// For example, you could use:
//
// \begin{itemize}
// \item \doxygen{MutualInformationImageToImageMetric}
// \item \doxygen{MattesMutualInformationImageToImageMetric}
// \item \doxygen{MutualInformationHistogramImageToImageMetric}
// \item \doxygen{MutualInformationImageToImageMetric}
// \item \doxygen{NormalizedMutualInformationHistogramImageToImageMetric}
// \item \doxygen{KullbackLeiblerCompareHistogramImageToImageMetric}
// \end{itemize}
//
// Mutual Information as computed in this example, and as commonly used in the
// context of image registration provides a measure of how much uncertainty on
// the value of a pixel in one image is reduced by measuring the homologous
// pixel in the other image. Note that Mutual Information as used here does
// not measure the amount of information that one image provides on the other
// image; this would require us to take into account the spatial
// structures in the images as well as the semantics of the image context in
// terms of an observer.
//
// This implies that there is still an enormous unexploited potential on the
// use of the Mutual Information concept in the domain of medical images,
// among the most interesting of which is the semantic description of
// image in terms of anatomical structures.
//
// \index{Mutual Information!Statistics}
// \index{Statistics!Mutual Information}
// \index{Joint Entropy!Statistics}
// \index{Statistics!Joint Entropy}
// \index{Joint Histogram!Statistics}
// \index{Statistics!Joint Histogram}
//
// Software Guide : EndLatex
 
 
// Software Guide : BeginLatex
//
// In this particular example we make use of classes from the Statistics
// framework in order to compute the measure of Mutual Information between two
// images. We assume that both images have the same number of pixels along
// every dimension and that they have the same origin and spacing. Therefore
// the pixels from one image are perfectly aligned with those of the other
// image.
//
// We must start by including the header files of the image, histogram
// filter, reader and Join image filter. We will read both images and use
// the Join image filter in order to compose an image of two components using
// the information of each one of the input images in one component. This is
// the natural way of using the Statistics framework in ITK given that the
// fundamental statistical classes are expecting to receive multi-valued
// measures.
//
// Software Guide : EndLatex
 
// Software Guide : BeginCodeSnippet
#include "itkImage.h"
#include "itkImageFileReader.h"
#include "itkJoinImageFilter.h"
#include "itkImageToHistogramFilter.h"
// Software Guide : EndCodeSnippet
 
 
int
main(int argc, char * argv[])
{
 
  if (argc < 3)
  {
    std::cerr << "Missing command line arguments" << std::endl;
    std::cerr << "Usage :  ImageMutualInformation1  inputImage1 inputImage2 "
              << std::endl;
    return EXIT_FAILURE;
  }
 
 
  // Software Guide : BeginLatex
  //
  // We define the pixel type and dimension of the images to be read.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using PixelComponentType = unsigned char;
  constexpr unsigned int Dimension = 2;
 
  using ImageType = itk::Image<PixelComponentType, Dimension>;
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // Using the image type we proceed to instantiate the readers for both input
  // images. Then, we take their filenames from the command line arguments.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using ReaderType = itk::ImageFileReader<ImageType>;
 
  auto reader1 = ReaderType::New();
  auto reader2 = ReaderType::New();
 
  reader1->SetFileName(argv[1]);
  reader2->SetFileName(argv[2]);
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // Using the \doxygen{JoinImageFilter} we use the two input images and put
  // them together in an image of two components.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using JoinFilterType = itk::JoinImageFilter<ImageType, ImageType>;
 
  auto joinFilter = JoinFilterType::New();
 
  joinFilter->SetInput1(reader1->GetOutput());
  joinFilter->SetInput2(reader2->GetOutput());
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // At this point we trigger the execution of the pipeline by invoking the
  // \code{Update()} method on the Join filter. We must put the call inside a
  // try/catch block because the Update() call may potentially result in
  // exceptions being thrown.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  try
  {
    joinFilter->Update();
  }
  catch (const itk::ExceptionObject & excp)
  {
    std::cerr << excp << std::endl;
    return EXIT_FAILURE;
  }
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We now prepare the types to be used for the computation of the joint
  // histogram. For this purpose, we take the type of the image resulting from
  // the JoinImageFilter and use it as template argument of the
  // \doxygen{ImageToHistogramFilter}. We then construct one by invoking the
  // \code{New()} method.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using VectorImageType = JoinFilterType::OutputImageType;
 
  using HistogramFilterType =
    itk::Statistics::ImageToHistogramFilter<VectorImageType>;
 
  auto histogramFilter = HistogramFilterType::New();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We pass the multiple-component image as input to the histogram filter,
  // and setup the marginal scale value that will define the precision to be
  // used for classifying values into the histogram bins.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  histogramFilter->SetInput(joinFilter->GetOutput());
 
  histogramFilter->SetMarginalScale(10.0);
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We must now define the number of bins to use for each one of the
  // components in the joint image. For this purpose we take the
  // \code{HistogramSizeType} from the traits of the histogram filter type.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using HistogramSizeType = HistogramFilterType::HistogramSizeType;
 
  HistogramSizeType size(2);
 
  size[0] = 255; // number of bins for the first  channel
  size[1] = 255; // number of bins for the second channel
 
  histogramFilter->SetHistogramSize(size);
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // Finally, we must specify the upper and lower bounds for the histogram
  // using the \code{SetHistogramBinMinimum()} and
  // \code{SetHistogramBinMaximum()} methods. The \code{Update()} method is
  // then called in order to trigger the computation of the histogram.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using HistogramMeasurementVectorType =
    HistogramFilterType::HistogramMeasurementVectorType;
 
  HistogramMeasurementVectorType binMinimum(3);
  HistogramMeasurementVectorType binMaximum(3);
 
  binMinimum[0] = -0.5;
  binMinimum[1] = -0.5;
  binMinimum[2] = -0.5;
 
  binMaximum[0] = 255.5;
  binMaximum[1] = 255.5;
  binMaximum[2] = 255.5;
 
  histogramFilter->SetHistogramBinMinimum(binMinimum);
  histogramFilter->SetHistogramBinMaximum(binMaximum);
 
  histogramFilter->Update();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // The histogram can be recovered from the filter by creating a variable
  // with the histogram type taken from the filter traits.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using HistogramType = HistogramFilterType::HistogramType;
 
  const HistogramType * histogram = histogramFilter->GetOutput();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We now walk over all the bins of the joint histogram and compute their
  // contribution to the value of the joint entropy. For this purpose we use
  // histogram iterators, and the \code{Begin()} and \code{End()} methods.
  // Since the values returned from the histogram are measuring frequency we
  // must convert them to an estimation of probability by dividing them over
  // the total sum of frequencies returned by the \code{GetTotalFrequency()}
  // method.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  HistogramType::ConstIterator itr = histogram->Begin();
  HistogramType::ConstIterator end = histogram->End();
 
  const double Sum = histogram->GetTotalFrequency();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We initialize to zero the variable to use for accumulating the value of
  // the joint entropy, and then use the iterator for visiting all the bins of
  // the joint histogram. For every bin we compute their contribution to the
  // reduction of uncertainty. Note that in order to avoid logarithmic
  // operations on zero values, we skip over those bins that have less than
  // one count. The entropy contribution must be computed using logarithms in
  // base two in order to express entropy in \textbf{bits}.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  double JointEntropy = 0.0;
 
  while (itr != end)
  {
    const double count = itr.GetFrequency();
    if (count > 0.0)
    {
      const double probability = count / Sum;
      JointEntropy += -probability * std::log(probability) / std::log(2.0);
    }
    ++itr;
  }
  // Software Guide : EndCodeSnippet
 
  std::cout << "Joint Entropy      = " << JointEntropy << " bits "
            << std::endl;
 
 
  // Software Guide : BeginLatex
  //
  // Now that we have the value of the joint entropy we can proceed to
  // estimate the values of the entropies for each image independently. This
  // can be done by simply changing the number of bins and then recomputing
  // the histogram.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  size[0] = 255; // number of bins for the first  channel
  size[1] = 1;   // number of bins for the second channel
 
  histogramFilter->SetHistogramSize(size);
  histogramFilter->Update();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We initialize to zero another variable in order to start accumulating the
  // entropy contributions from every bin.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  itr = histogram->Begin();
  end = histogram->End();
 
  double Entropy1 = 0.0;
 
  while (itr != end)
  {
    const double count = itr.GetFrequency();
    if (count > 0.0)
    {
      const double probability = count / Sum;
      Entropy1 += -probability * std::log(probability) / std::log(2.0);
    }
    ++itr;
  }
  // Software Guide : EndCodeSnippet
 
  std::cout << "Image1 Entropy   = " << Entropy1 << " bits " << std::endl;
 
 
  // Software Guide : BeginLatex
  //
  // The same process is used for computing the entropy of the other
  // component, simply by swapping the number of bins in the histogram.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  size[0] = 1;   // number of bins for the first channel
  size[1] = 255; // number of bins for the second channel
 
  histogramFilter->SetHistogramSize(size);
  histogramFilter->Update();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // The entropy is computed in a similar manner, just by visiting all the
  // bins on the histogram and accumulating their entropy contributions.
  //
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  itr = histogram->Begin();
  end = histogram->End();
 
  double Entropy2 = 0.0;
 
  while (itr != end)
  {
    const double count = itr.GetFrequency();
    if (count > 0.0)
    {
      const double probability = count / Sum;
      Entropy2 += -probability * std::log(probability) / std::log(2.0);
    }
    ++itr;
  }
  // Software Guide : EndCodeSnippet
 
  std::cout << "Image2 Entropy   = " << Entropy2 << " bits " << std::endl;
 
 
  // Software Guide : BeginLatex
  //
  // At this point we can compute any of the popular measures of Mutual
  // Information. For example
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  double MutualInformation = Entropy1 + Entropy2 - JointEntropy;
  // Software Guide : EndCodeSnippet
 
  std::cout << "Mutual Information = " << MutualInformation << " bits "
            << std::endl;
 
 
  // Software Guide : BeginLatex
  //
  // or Normalized Mutual Information, where the value of Mutual Information
  // is divided by the mean entropy of the input images.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  double NormalizedMutualInformation1 =
    2.0 * MutualInformation / (Entropy1 + Entropy2);
  // Software Guide : EndCodeSnippet
 
  std::cout << "Normalized Mutual Information 1 = "
            << NormalizedMutualInformation1 << std::endl;
 
 
  // Software Guide : BeginLatex
  //
  // A second form of Normalized Mutual Information has been defined as the
  // mean entropy of the two images divided by their joint entropy.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  double NormalizedMutualInformation2 = (Entropy1 + Entropy2) / JointEntropy;
  // Software Guide : EndCodeSnippet
 
 
  std::cout << "Normalized Mutual Information 2 = "
            << NormalizedMutualInformation2 << std::endl;
 
 
  // Software Guide : BeginLatex
  //
  // You probably will find very interesting how the value of Mutual
  // Information is strongly dependent on the number of bins over which the
  // histogram is defined.
  //
  // Software Guide : EndLatex
 
 
  return EXIT_SUCCESS;
}