Mutual Information

Synopsis

Global registration by maximizing the mutual information and using a translation only transform.

Results

fixed.png

fixed.png

moving.png

moving.png

output.png

output.png

Output:

Optimizer stop condition: GradientDescentOptimizer: Maximum number of iterations (200) exceeded.

Result =
Translation X = -5.58344
Translation Y = -0.129678
Iterations    = 200
Metric value  = -0.00067634
Numb. Samples = 100

Code

C++

#include "itkImageRegistrationMethod.h"
#include "itkTranslationTransform.h"
#include "itkMutualInformationImageToImageMetric.h"
#include "itkGradientDescentOptimizer.h"
#include "itkNormalizeImageFilter.h"
#include "itkDiscreteGaussianImageFilter.h"
#include "itkResampleImageFilter.h"
#include "itkCastImageFilter.h"
#include "itkCheckerBoardImageFilter.h"
#include "itkEllipseSpatialObject.h"
#include "itkSpatialObjectToImageFilter.h"
#include "itkImageFileWriter.h"

constexpr unsigned int Dimension = 2;
using PixelType = unsigned char;

using ImageType = itk::Image<PixelType, Dimension>;

static void
CreateEllipseImage(ImageType::Pointer image);
static void
CreateCircleImage(ImageType::Pointer image);

int
main(int itkNotUsed(argc), char * itkNotUsed(argv)[])
{
  // Generate synthetic fixed and moving images
  ImageType::Pointer fixedImage = ImageType::New();
  CreateCircleImage(fixedImage);
  ImageType::Pointer movingImage = ImageType::New();
  CreateEllipseImage(movingImage);

  // Write the two synthetic inputs
  using WriterType = itk::ImageFileWriter<ImageType>;

  WriterType::Pointer fixedWriter = WriterType::New();
  fixedWriter->SetFileName("fixed.png");
  fixedWriter->SetInput(fixedImage);
  fixedWriter->Update();

  WriterType::Pointer movingWriter = WriterType::New();
  movingWriter->SetFileName("moving.png");
  movingWriter->SetInput(movingImage);
  movingWriter->Update();

  // We use floats internally
  using InternalImageType = itk::Image<float, 2>;

  // Normalize the images
  using NormalizeFilterType = itk::NormalizeImageFilter<ImageType, InternalImageType>;

  NormalizeFilterType::Pointer fixedNormalizer = NormalizeFilterType::New();
  NormalizeFilterType::Pointer movingNormalizer = NormalizeFilterType::New();

  fixedNormalizer->SetInput(fixedImage);
  movingNormalizer->SetInput(movingImage);

  // Smooth the normalized images
  using GaussianFilterType = itk::DiscreteGaussianImageFilter<InternalImageType, InternalImageType>;

  GaussianFilterType::Pointer fixedSmoother = GaussianFilterType::New();
  GaussianFilterType::Pointer movingSmoother = GaussianFilterType::New();

  fixedSmoother->SetVariance(2.0);
  movingSmoother->SetVariance(2.0);

  fixedSmoother->SetInput(fixedNormalizer->GetOutput());
  movingSmoother->SetInput(movingNormalizer->GetOutput());

  using TransformType = itk::TranslationTransform<double, Dimension>;
  using OptimizerType = itk::GradientDescentOptimizer;
  using InterpolatorType = itk::LinearInterpolateImageFunction<InternalImageType, double>;
  using RegistrationType = itk::ImageRegistrationMethod<InternalImageType, InternalImageType>;
  using MetricType = itk::MutualInformationImageToImageMetric<InternalImageType, InternalImageType>;

  TransformType::Pointer    transform = TransformType::New();
  OptimizerType::Pointer    optimizer = OptimizerType::New();
  InterpolatorType::Pointer interpolator = InterpolatorType::New();
  RegistrationType::Pointer registration = RegistrationType::New();

  registration->SetOptimizer(optimizer);
  registration->SetTransform(transform);
  registration->SetInterpolator(interpolator);

  MetricType::Pointer metric = MetricType::New();
  registration->SetMetric(metric);

  //  The metric requires a number of parameters to be selected, including
  //  the standard deviation of the Gaussian kernel for the fixed image
  //  density estimate, the standard deviation of the kernel for the moving
  //  image density and the number of samples use to compute the densities
  //  and entropy values. Details on the concepts behind the computation of
  //  the metric can be found in Section
  //  \ref{sec:MutualInformationMetric}.  Experience has
  //  shown that a kernel standard deviation of $0.4$ works well for images
  //  which have been normalized to a mean of zero and unit variance.  We
  //  will follow this empirical rule in this example.

  metric->SetFixedImageStandardDeviation(0.4);
  metric->SetMovingImageStandardDeviation(0.4);

  registration->SetFixedImage(fixedSmoother->GetOutput());
  registration->SetMovingImage(movingSmoother->GetOutput());

  fixedNormalizer->Update();
  ImageType::RegionType fixedImageRegion = fixedNormalizer->GetOutput()->GetBufferedRegion();
  registration->SetFixedImageRegion(fixedImageRegion);

  using ParametersType = RegistrationType::ParametersType;
  ParametersType initialParameters(transform->GetNumberOfParameters());

  initialParameters[0] = 0.0; // Initial offset along X
  initialParameters[1] = 0.0; // Initial offset along Y

  registration->SetInitialTransformParameters(initialParameters);

  //  Software Guide : BeginLatex
  //
  //  We should now define the number of spatial samples to be considered in
  //  the metric computation. Note that we were forced to postpone this setting
  //  until we had done the preprocessing of the images because the number of
  //  samples is usually defined as a fraction of the total number of pixels in
  //  the fixed image.
  //
  //  The number of spatial samples can usually be as low as $1\%$ of the total
  //  number of pixels in the fixed image. Increasing the number of samples
  //  improves the smoothness of the metric from one iteration to another and
  //  therefore helps when this metric is used in conjunction with optimizers
  //  that rely of the continuity of the metric values. The trade-off, of
  //  course, is that a larger number of samples result in longer computation
  //  times per every evaluation of the metric.
  //
  //  It has been demonstrated empirically that the number of samples is not a
  //  critical parameter for the registration process. When you start fine
  //  tuning your own registration process, you should start using high values
  //  of number of samples, for example in the range of $20\%$ to $50\%$ of the
  //  number of pixels in the fixed image. Once you have succeeded to register
  //  your images you can then reduce the number of samples progressively until
  //  you find a good compromise on the time it takes to compute one evaluation
  //  of the Metric. Note that it is not useful to have very fast evaluations
  //  of the Metric if the noise in their values results in more iterations
  //  being required by the optimizer to converge. You must then study the
  //  behavior of the metric values as the iterations progress.

  const unsigned int numberOfPixels = fixedImageRegion.GetNumberOfPixels();

  const auto numberOfSamples = static_cast<unsigned int>(numberOfPixels * 0.01);

  metric->SetNumberOfSpatialSamples(numberOfSamples);

  //  Since larger values of mutual information indicate better matches than
  //  smaller values, we need to maximize the cost function in this example.
  //  By default the GradientDescentOptimizer class is set to minimize the
  //  value of the cost-function. It is therefore necessary to modify its
  //  default behavior by invoking the \code{MaximizeOn()} method.
  //  Additionally, we need to define the optimizer's step size using the
  //  \code{SetLearningRate()} method.

  optimizer->SetLearningRate(15.0);
  optimizer->SetNumberOfIterations(200);
  optimizer->MaximizeOn(); // We want to maximize mutual information (the default of the optimizer is to minimize)

  // Note that large values of the learning rate will make the optimizer
  // unstable. Small values, on the other hand, may result in the optimizer
  // needing too many iterations in order to walk to the extrema of the cost
  // function. The easy way of fine tuning this parameter is to start with
  // small values, probably in the range of $\{5.0,10.0\}$. Once the other
  // registration parameters have been tuned for producing convergence, you
  // may want to revisit the learning rate and start increasing its value until
  // you observe that the optimization becomes unstable.  The ideal value for
  // this parameter is the one that results in a minimum number of iterations
  // while still keeping a stable path on the parametric space of the
  // optimization. Keep in mind that this parameter is a multiplicative factor
  // applied on the gradient of the Metric. Therefore, its effect on the
  // optimizer step length is proportional to the Metric values themselves.
  // Metrics with large values will require you to use smaller values for the
  // learning rate in order to maintain a similar optimizer behavior.

  try
  {
    registration->Update();
    std::cout << "Optimizer stop condition: " << registration->GetOptimizer()->GetStopConditionDescription()
              << std::endl;
  }
  catch (itk::ExceptionObject & err)
  {
    std::cout << "ExceptionObject caught !" << std::endl;
    std::cout << err << std::endl;
    return EXIT_FAILURE;
  }

  ParametersType finalParameters = registration->GetLastTransformParameters();

  double TranslationAlongX = finalParameters[0];
  double TranslationAlongY = finalParameters[1];

  unsigned int numberOfIterations = optimizer->GetCurrentIteration();

  double bestValue = optimizer->GetValue();


  // Print out results
  std::cout << std::endl;
  std::cout << "Result = " << std::endl;
  std::cout << " Translation X = " << TranslationAlongX << std::endl;
  std::cout << " Translation Y = " << TranslationAlongY << std::endl;
  std::cout << " Iterations    = " << numberOfIterations << std::endl;
  std::cout << " Metric value  = " << bestValue << std::endl;
  std::cout << " Numb. Samples = " << numberOfSamples << std::endl;

  using ResampleFilterType = itk::ResampleImageFilter<ImageType, ImageType>;

  TransformType::Pointer finalTransform = TransformType::New();

  finalTransform->SetParameters(finalParameters);
  finalTransform->SetFixedParameters(transform->GetFixedParameters());

  ResampleFilterType::Pointer resample = ResampleFilterType::New();

  resample->SetTransform(finalTransform);
  resample->SetInput(movingImage);

  resample->SetSize(fixedImage->GetLargestPossibleRegion().GetSize());
  resample->SetOutputOrigin(fixedImage->GetOrigin());
  resample->SetOutputSpacing(fixedImage->GetSpacing());
  resample->SetOutputDirection(fixedImage->GetDirection());
  resample->SetDefaultPixelValue(100);

  WriterType::Pointer writer = WriterType::New();
  writer->SetFileName("output.png");
  writer->SetInput(resample->GetOutput());
  writer->Update();

  return EXIT_SUCCESS;
}


void
CreateEllipseImage(ImageType::Pointer image)
{
  using EllipseType = itk::EllipseSpatialObject<Dimension>;

  using SpatialObjectToImageFilterType = itk::SpatialObjectToImageFilter<EllipseType, ImageType>;

  SpatialObjectToImageFilterType::Pointer imageFilter = SpatialObjectToImageFilterType::New();

  ImageType::SizeType size;
  size[0] = 100;
  size[1] = 100;

  imageFilter->SetSize(size);

  ImageType::SpacingType spacing;
  spacing.Fill(1);
  imageFilter->SetSpacing(spacing);

  EllipseType::Pointer   ellipse = EllipseType::New();
  EllipseType::ArrayType radiusArray;
  radiusArray[0] = 10;
  radiusArray[1] = 20;
  ellipse->SetRadiusInObjectSpace(radiusArray);

  using TransformType = EllipseType::TransformType;
  TransformType::Pointer transform = TransformType::New();
  transform->SetIdentity();

  TransformType::OutputVectorType translation;
  translation[0] = 65;
  translation[1] = 45;
  transform->Translate(translation, false);

  ellipse->SetObjectToParentTransform(transform);

  imageFilter->SetInput(ellipse);

  ellipse->SetDefaultInsideValue(255);
  ellipse->SetDefaultOutsideValue(0);
  imageFilter->SetUseObjectValue(true);
  imageFilter->SetOutsideValue(0);

  imageFilter->Update();

  image->Graft(imageFilter->GetOutput());
}

void
CreateCircleImage(ImageType::Pointer image)
{
  using EllipseType = itk::EllipseSpatialObject<Dimension>;

  using SpatialObjectToImageFilterType = itk::SpatialObjectToImageFilter<EllipseType, ImageType>;

  SpatialObjectToImageFilterType::Pointer imageFilter = SpatialObjectToImageFilterType::New();

  ImageType::SizeType size;
  size[0] = 100;
  size[1] = 100;

  imageFilter->SetSize(size);

  ImageType::SpacingType spacing;
  spacing.Fill(1);
  imageFilter->SetSpacing(spacing);

  EllipseType::Pointer   ellipse = EllipseType::New();
  EllipseType::ArrayType radiusArray;
  radiusArray[0] = 10;
  radiusArray[1] = 10;
  ellipse->SetRadiusInObjectSpace(radiusArray);

  using TransformType = EllipseType::TransformType;
  TransformType::Pointer transform = TransformType::New();
  transform->SetIdentity();

  TransformType::OutputVectorType translation;
  translation[0] = 50;
  translation[1] = 50;
  transform->Translate(translation, false);

  ellipse->SetObjectToParentTransform(transform);

  imageFilter->SetInput(ellipse);

  ellipse->SetDefaultInsideValue(255);
  ellipse->SetDefaultOutsideValue(0);
  imageFilter->SetUseObjectValue(true);
  imageFilter->SetOutsideValue(0);

  imageFilter->Update();

  image->Graft(imageFilter->GetOutput());
}

Classes demonstrated