Examples/Statistics/ImageEntropy1.cxx

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// Software Guide : BeginLatex
//
//
// This example shows how to compute the entropy of an image.  More formally
// this should be said : The reduction in uncertainty gained when we measure
// the intensity of \emph{one} randomly selected pixel in this image, given
// that we already know the statistical distribution of the image intensity
// values.
//
// In practice it is almost never possible to know the real statistical
// distribution of intensities and we are forced to estimate it from the
// evaluation of the histogram from one or several images of similar nature.
// We can use the counts in histogram bins in order to compute frequencies and
// then consider those frequencies to be estimations of the probability of a
// new value to belong to the intensity range of that bin.
//
// \index{Entropy!Images}
// \index{Image!Entropy}
// \index{Image!Amount of information}
// \index{Amount of information!Image}
//
// Software Guide : EndLatex
 
// Software Guide : BeginLatex
//
// Since the first stage in estimating the entropy of an image is to compute
// its histogram, we must start by including the headers of the classes that
// will perform such a computation. In this case, we are going to use a scalar
// image as input, therefore we need the
// \subdoxygen{Statistics}{ScalarImageToHistogramGenerator} class, as well as
// the image class.
//
// Software Guide : EndLatex
 
 
// Software Guide : BeginCodeSnippet
#include "itkScalarImageToHistogramGenerator.h"
#include "itkImage.h"
// Software Guide : EndCodeSnippet
 
#include "itkImageFileReader.h"
 
int
main(int argc, char * argv[])
{
 
  if (argc < 3)
  {
    std::cerr << "Missing command line arguments" << std::endl;
    std::cerr << "Usage :  ImageEntropy1  inputImageFileName ";
    std::cerr << "numberOfHistogramBins" << std::endl;
    return EXIT_FAILURE;
  }
 
  // Software Guide : BeginLatex
  //
  // The pixel type and dimension of the image are explicitly declared and
  // then used for instantiating the image type.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using PixelType = unsigned char;
  constexpr unsigned int Dimension = 3;
 
  using ImageType = itk::Image<PixelType, Dimension>;
  // Software Guide : EndCodeSnippet
 
  ImageType::Pointer input;
  try
  {
    input = itk::ReadImage<ImageType>(argv[1]);
  }
  catch (const itk::ExceptionObject & excp)
  {
    std::cerr << "Problem encountered while reading image file : " << argv[1]
              << std::endl;
    std::cerr << excp << std::endl;
    return EXIT_FAILURE;
  }
 
  // Software Guide : BeginLatex
  //
  // The image type is used as template parameter for instantiating the
  // histogram generator.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using HistogramGeneratorType =
    itk::Statistics::ScalarImageToHistogramGenerator<ImageType>;
 
  auto histogramGenerator = HistogramGeneratorType::New();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // The parameters of the desired histogram are defined, including the
  // number of bins and the marginal scale. For convenience in this example,
  // we read the number of bins from the command line arguments. In this way
  // we can easily experiment with different values for the number of bins and
  // see how that choice affects the computation of the entropy.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  const unsigned int numberOfHistogramBins = std::stoi(argv[2]);
 
  histogramGenerator->SetNumberOfBins(numberOfHistogramBins);
  histogramGenerator->SetMarginalScale(10.0);
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We can then connect as input the output image from a reader and trigger
  // the histogram computation by invoking the \code{Compute()} method in the
  // generator.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  histogramGenerator->SetInput(input);
 
  histogramGenerator->Compute();
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // The resulting histogram can be recovered from the generator by using the
  // \code{GetOutput()} method. A histogram class can be declared using the
  // \code{HistogramType} trait from the generator.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using HistogramType = HistogramGeneratorType::HistogramType;
 
  const HistogramType * histogram = histogramGenerator->GetOutput();
  // Software Guide : EndCodeSnippet
 
 
  const unsigned int histogramSize = histogram->Size();
 
  std::cout << "Histogram size " << histogramSize << std::endl;
 
  for (unsigned int bin = 0; bin < histogramSize; ++bin)
  {
    std::cout << "bin = " << bin << " frequency = ";
    std::cout << histogram->GetFrequency(bin, 0) << std::endl;
  }
 
 
  // Software Guide : BeginLatex
  //
  // We proceed now to compute the \emph{estimation} of entropy given the
  // histogram. The first conceptual jump to be done here is to assume that
  // the histogram, which is the simple count of frequency of occurrence for
  // the gray scale values of the image pixels, can be normalized in order to
  // estimate the probability density function \textbf{PDF} of the actual
  // statistical distribution of pixel values.
  //
  //  First we declare an iterator that will visit all the bins in the
  //  histogram. Then we obtain the total number of counts using the
  //  \code{GetTotalFrequency()} method, and we initialize the entropy
  //  variable to zero.
  //
  // Software Guide : EndLatex
 
 
  // Software Guide : BeginCodeSnippet
  HistogramType::ConstIterator       itr = histogram->Begin();
  const HistogramType::ConstIterator end = histogram->End();
 
  const double Sum = histogram->GetTotalFrequency();
 
  double Entropy = 0.0;
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // We start now visiting every bin and estimating the probability of a pixel
  // to have a value in the range of that bin. The base 2 logarithm of that
  // probability is computed, and then weighted by the probability in order to
  // compute the expected amount of information for any given pixel. Note that
  // a minimum value is imposed for the probability in order to avoid
  // computing logarithms of zeros.
  //
  //  Note that the $\log{(2)}$ factor is used to convert the natural
  //  logarithm in to a logarithm of base 2, and makes it possible to report
  //  the entropy in its natural unit: the bit.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  while (itr != end)
  {
    const double probability = itr.GetFrequency() / Sum;
 
    if (probability > 0.99 / Sum)
    {
      Entropy += -probability * std::log(probability) / std::log(2.0);
    }
    ++itr;
  }
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // The result of this sum is considered to be our estimation of the image
  // entropy. Note that the Entropy value will change depending on the number
  // of histogram bins that we use for computing the histogram. This is
  // particularly important when dealing with images whose pixel values have
  // dynamic ranges so large that our number of bins will always underestimate
  // the variability of the data.
  //
  // Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  std::cout << "Image entropy = " << Entropy << " bits " << std::endl;
  // Software Guide : EndCodeSnippet
 
 
  // Software Guide : BeginLatex
  //
  // As an illustration, the application of this program to the image
  //
  // \begin{itemize}
  // \item \code{Examples/Data/BrainProtonDensitySlice.png}
  // \end{itemize}
  //
  // results in the following values of entropy for different values of number
  // of histogram bins.
  //
  // \begin{center}
  // \begin{tabular}{|l|r|r|r|r|r|}
  // \hline
  // Number of Histogram Bins & 16    & 32    & 64    & 128   & 255 \cr
  // \hline
  // Estimated Entropy (bits) & 3.02  & 3.98  & 4.92  & 5.89  & 6.88 \cr
  // \hline
  // \end{tabular}
  // \end{center}
  //
  //
  // This table highlights the importance of carefully considering the
  // characteristics of the histograms used for estimating Information Theory
  // measures such as the entropy.
  //
  // Software Guide : EndLatex
 
 
  return EXIT_SUCCESS;
}