ITK  5.2.0
Insight Toolkit
* Copyright NumFOCUS
* 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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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* See the License for the specific language governing permissions and
* limitations under the License.
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainT1SliceBorder20.png}
// INPUTS: {BrainProtonDensitySliceShifted13x17y.png}
// OUTPUTS: {ImageRegistration4Output.png}
// OUTPUTS: {ImageRegistration4CheckerboardBefore.png}
// OUTPUTS: {ImageRegistration4CheckerboardAfter.png}
// Software Guide : EndCommandLineArgs
// Software Guide : BeginLatex
// In this example, we will solve a simple multi-modality problem using an
// implementation of mutual information. This implementation was published by
// Mattes~\emph{et. al}~\cite{Mattes2003}.
// First, we include the header files of the components used in this example.
// \index{itk::ImageRegistrationMethodv4!Multi-Modality}
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// The following section of code implements a Command observer
// used to monitor the evolution of the registration process.
#include "itkCommand.h"
class CommandIterationUpdate : public itk::Command
using Self = CommandIterationUpdate;
using Superclass = itk::Command;
using Pointer = itk::SmartPointer<Self>;
CommandIterationUpdate() = default;
using OptimizerPointer = const OptimizerType *;
Execute(itk::Object * caller, const itk::EventObject & event) override
Execute((const itk::Object *)caller, event);
Execute(const itk::Object * object, const itk::EventObject & event) override
auto optimizer = static_cast<OptimizerPointer>(object);
if (!itk::IterationEvent().CheckEvent(&event))
std::cout << optimizer->GetCurrentIteration() << " ";
std::cout << optimizer->GetValue() << " ";
std::cout << optimizer->GetCurrentPosition() << std::endl;
main(int argc, char * argv[])
if (argc < 4)
std::cerr << "Missing Parameters " << std::endl;
std::cerr << "Usage: " << argv[0];
std::cerr << " fixedImageFile movingImageFile ";
std::cerr << "outputImagefile [defaultPixelValue]" << std::endl;
std::cerr << "[checkerBoardAfter] [checkerBoardBefore]" << std::endl;
std::cerr << "[numberOfBins] [numberOfSamples]";
std::cerr << "[useExplicitPDFderivatives ] " << std::endl;
constexpr unsigned int Dimension = 2;
using PixelType = float;
using FixedImageType = itk::Image<PixelType, Dimension>;
using MovingImageType = itk::Image<PixelType, Dimension>;
using RegistrationType = itk::
ImageRegistrationMethodv4<FixedImageType, MovingImageType, TransformType>;
// Software Guide : BeginLatex
// In this example the image types and all registration components,
// except the metric, are declared as in Section
// \ref{sec:IntroductionImageRegistration}. The Mattes mutual information
// metric type is instantiated using the image types.
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using MetricType =
// Software Guide : EndCodeSnippet
OptimizerType::Pointer optimizer = OptimizerType::New();
RegistrationType::Pointer registration = RegistrationType::New();
// Software Guide : BeginLatex
// The metric is created using the \code{New()} method and then
// connected to the registration object.
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
MetricType::Pointer metric = MetricType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
// The metric requires the user to specify the number of bins
// used to compute the entropy. In a typical application, 50 histogram bins
// are sufficient. Note however, that the number of bins may have dramatic
// effects on the optimizer's behavior.
// \index{itk::Mattes\-Mutual\-Information\-Image\-To\-Image\-Metricv4!SetNumberOfHistogramBins()}
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
unsigned int numberOfBins = 24;
// Software Guide : EndCodeSnippet
if (argc > 7)
numberOfBins = std::stoi(argv[7]);
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
// To calculate the image gradients, an image gradient calculator based on
// ImageFunction is used instead of image gradient filters. Image gradient
// methods are defined in the superclass \code{ImageToImageMetricv4}.
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
using FixedImageReaderType = itk::ImageFileReader<FixedImageType>;
using MovingImageReaderType = itk::ImageFileReader<MovingImageType>;
FixedImageReaderType::Pointer fixedImageReader =
MovingImageReaderType::Pointer movingImageReader =
// Software Guide : BeginLatex
// Notice that in the ITKv4 registration framework, optimizers always try
// to minimize the cost function, and the metrics always return a parameter
// and derivative result that improves the optimization, so this metric
// computes the negative mutual information.
// The optimization parameters are tuned for this example, so they are not
// exactly the same as the parameters used in Section
// \ref{sec:IntroductionImageRegistration}.
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
// 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 $\{1.0,5.0\}$. 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.
// Whenever the regular step gradient descent optimizer encounters
// change in the direction of movement in the parametric space, it reduces
// the size of the step length. The rate at which the step length is reduced
// is controlled by a relaxation factor. The default value of the factor is
// $0.5$. This value, however may prove to be inadequate for noisy metrics
// since they tend to induce erratic movements on the optimizers and
// therefore result in many directional changes. In those
// conditions, the optimizer will rapidly shrink the step length while it is
// still too far from the location of the extrema in the cost function. In
// this example we set the relaxation factor to a number higher than the
// default in order to prevent the premature shrinkage of the step length.
// \index{itk::Regular\-Step\-Gradient\-Descent\-Optimizer!SetRelaxationFactor()}
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Create the Command observer and register it with the optimizer.
CommandIterationUpdate::Pointer observer = CommandIterationUpdate::New();
optimizer->AddObserver(itk::IterationEvent(), observer);
// One level registration process without shrinking and smoothing.
constexpr unsigned int numberOfLevels = 1;
RegistrationType::ShrinkFactorsArrayType shrinkFactorsPerLevel;
shrinkFactorsPerLevel[0] = 1;
RegistrationType::SmoothingSigmasArrayType smoothingSigmasPerLevel;
smoothingSigmasPerLevel[0] = 0;
// Software Guide : BeginLatex
// Instead of using the whole virtual domain (usually fixed image domain)
// for the registration, we can use a spatial sampled point set by supplying
// an arbitrary point list over which to evaluate the metric. The point list
// is expected to be in the \emph{fixed} image domain, and the points are
// transformed into the \emph{virtual} domain internally as needed. The user
// can define the point set via \code{SetFixedSampledPointSet()}, and the
// point set is used by calling \code{SetUsedFixedSampledPointSet()}.
// Also, instead of dealing with the metric directly, the user may define
// the sampling percentage and sampling strategy for the registration
// framework at each level. In this case, the registration filter manages
// the sampling operation over the fixed image space based on the input
// strategy (REGULAR, RANDOM) and passes the sampled point set to the metric
// internally.
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
RegistrationType::MetricSamplingStrategyEnum samplingStrategy =
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
// The number of spatial samples to be
// used depends on the content of the image. If the images are smooth and do
// not contain many details, the number of spatial samples can usually be as
// low as $1\%$ of the total number of pixels in the fixed image. On the
// other hand, if the images are detailed, it may be necessary to use a much
// higher proportion, such as $20\%$ to $50\%$. Increasing the number of
// samples improves the smoothness of the metric, 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 results in longer computation times per every
// evaluation of the metric.
// One mechanism for bringing the metric to its limit is to disable the
// sampling and use all the pixels present in the FixedImageRegion. This can
// be done with the \code{SetUseSampledPointSet( false )} method.
// You may want to try this
// option only while you are fine tuning all other parameters of your
// registration. We don't use this method in this current example though.
// 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, just as
// illustrated in section~\ref{sec:MonitoringImageRegistration}.
// \index{itk::Mutual\-Information\-Image\-To\-Image\-Metricv4!Trade-offs}
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
double samplingPercentage = 0.20;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
// In ITKv4, a single virtual domain or spatial sample point set is used for
// the all iterations of the registration process. The use of a single
// sample set results in a smooth cost function that can improve the
// functionality of the optimizer.
// The spatial point set is pseudo randomly generated. For
// reproducible results an integer seed should set.
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
std::cout << "Optimizer stop condition: "
<< registration->GetOptimizer()->GetStopConditionDescription()
<< std::endl;
catch (const itk::ExceptionObject & err)
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
TransformType::ParametersType finalParameters =
double TranslationAlongX = finalParameters[0];
double TranslationAlongY = finalParameters[1];
// For stability reasons it may be desirable to round up the values of
// translation
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 << " Stop Condition = "
<< optimizer->GetStopConditionDescription() << std::endl;
// Software Guide : BeginLatex
// Let's execute this example over two of the images provided in
// \code{Examples/Data}:
// \begin{itemize}
// \item \code{BrainT1SliceBorder20.png}
// \item \code{BrainProtonDensitySliceShifted13x17y.png}
// \end{itemize}
// \begin{figure}
// \center
// \includegraphics[width=0.44\textwidth]{BrainT1SliceBorder20}
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceShifted13x17y}
// \itkcaption[Multi-Modality Registration Inputs]{A T1 MRI (fixed image)
// and a proton density MRI (moving image) are provided as input to the
// registration method.} \label{fig:FixedMovingImageRegistration2}
// \end{figure}
// The second image is the result of intentionally translating the image
// \code{Brain\-Proton\-Density\-Slice\-Border20.png} by $(13,17)$
// millimeters. Both images have unit-spacing and are shown in Figure
// \ref{fig:FixedMovingImageRegistration2}. The registration process
// converges after $46$ iterations and produces the following results:
// \begin{verbatim}
// Translation X = 13.0204
// Translation Y = 17.0006
// \end{verbatim}
// These values are a very close match to the true misalignment introduced
// in the moving image.
// Software Guide : EndLatex
using ResampleFilterType =
ResampleFilterType::Pointer resample = ResampleFilterType::New();
FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
PixelType defaultPixelValue = 100;
if (argc > 4)
defaultPixelValue = std::stoi(argv[4]);
using OutputPixelType = unsigned char;
using OutputImageType = itk::Image<OutputPixelType, Dimension>;
using CastFilterType =
WriterType::Pointer writer = WriterType::New();
CastFilterType::Pointer caster = CastFilterType::New();
// Software Guide : BeginLatex
// \begin{figure}
// \center
// \includegraphics[width=0.32\textwidth]{ImageRegistration4Output}
// \includegraphics[width=0.32\textwidth]{ImageRegistration4CheckerboardBefore}
// \includegraphics[width=0.32\textwidth]{ImageRegistration4CheckerboardAfter}
// \itkcaption[MattesMutualInformationImageToImageMetricv4 output
// images]{The mapped moving image (left) and the composition of fixed and
// moving images before (center) and after (right) registration with Mattes
// mutual information.} \label{fig:ImageRegistration4Output} \end{figure}
// The result of resampling the moving image is presented on the left of
// Figure \ref{fig:ImageRegistration4Output}. The center and right parts of
// the figure present a checkerboard composite of the fixed and moving
// images before and after registration respectively.
// Software Guide : EndLatex
// Generate checkerboards before and after registration
using CheckerBoardFilterType = itk::CheckerBoardImageFilter<FixedImageType>;
CheckerBoardFilterType::Pointer checker = CheckerBoardFilterType::New();
// Before registration
TransformType::Pointer identityTransform = TransformType::New();
if (argc > 5)
// After registration
if (argc > 6)
// Software Guide : BeginLatex
// \begin{figure}
// \center
// \includegraphics[width=0.44\textwidth]{ImageRegistration4TraceTranslations}
// \includegraphics[width=0.44\textwidth]{ImageRegistration4TraceTranslations2}
// \includegraphics[width=0.6\textwidth,height=5cm]{ImageRegistration4TraceMetric}
// \itkcaption[MattesMutualInformationImageToImageMetricv4 output
// plots]{Sequence of translations and metric values at each iteration of
// the optimizer.} \label{fig:ImageRegistration4TraceTranslations}
// \end{figure}
// Figure \ref{fig:ImageRegistration4TraceTranslations} (upper-left) shows
// the sequence of translations followed by the optimizer as it searched
// the parameter space. The upper-right figure presents a closer look at
// the convergence basin for the last iterations of the optimizer. The
// bottom of the same figure shows the sequence of metric values computed
// as the optimizer searched the parameter space.
// Software Guide : EndLatex
// Software Guide : BeginLatex
// You must note however that there are a number of non-trivial issues
// involved in the fine tuning of parameters for the optimization. For
// example, the number of bins used in the estimation of Mutual Information
// has a dramatic effect on the performance of the optimizer. In order to
// illustrate this effect, the same example has been executed using a range
// of different values for the number of bins, from $10$ to $30$. If you
// repeat this experiment, you will notice that depending on the number of
// bins used, the optimizer's path may get trapped early on in local minima.
// Figure \ref{fig:ImageRegistration4TraceTranslationsNumberOfBins} shows
// the multiple paths that the optimizer took in the parametric space of the
// transform as a result of different selections on the number of bins used
// by the Mattes Mutual Information metric. Note that many of the paths die
// in local minima instead of reaching the extrema value on the upper right
// corner.
// \begin{figure}
// \center
// \includegraphics[width=0.8\textwidth]{ImageRegistration4TraceTranslationsNumberOfBins}
// \itkcaption[MattesMutualInformationImageToImageMetricv4 number of
// bins]{Sensitivity of the optimization path to the number of Bins used for
// estimating the value of Mutual Information with Mattes et al. approach.}
// \label{fig:ImageRegistration4TraceTranslationsNumberOfBins}
// \end{figure}
// Effects such as the one illustrated here highlight how useless is to
// compare different algorithms based on a non-exhaustive search of their
// parameter setting. It is quite difficult to be able to claim that a
// particular selection of parameters represent the best combination for
// running a particular algorithm. Therefore, when comparing the performance
// of two or more different algorithms, we are faced with the challenge of
// proving that none of the algorithms involved in the comparison are being
// run with a sub-optimal set of parameters.
// Software Guide : EndLatex
// Software Guide : BeginLatex
// The plots in Figures~\ref{fig:ImageRegistration4TraceTranslations}
// and~\ref{fig:ImageRegistration4TraceTranslationsNumberOfBins} were
// generated using Gnuplot\footnote{\url{}}.
// The scripts used for this purpose are available
// in the \code{ITKSoftwareGuide} Git repository under the directory
// ~\code{ITKSoftwareGuide/SoftwareGuide/Art}.
// Data for the plots were taken directly from the output that the
// Command/Observer in this example prints out to the console. The output
// was processed with the UNIX editor
// \code{sed}\footnote{\url{}} in
// order to remove commas and brackets that were confusing for Gnuplot's
// parser. Both the shell script for running \code{sed} and for running
// {Gnuplot} are available in the directory indicated above. You may find
// useful to run them in order to verify the results presented here, and to
// eventually modify them for profiling your own registrations.
// \index{Open Science}
// Open Science is not just an abstract concept. Open Science is something
// to be practiced every day with the simple gesture of sharing information
// with your peers, and by providing all the tools that they need for
// replicating the results that you are reporting. In Open Science, the
// only bad results are those that can not be
// replicated\footnote{\url{}}. Science
// is dead when people blindly trust authorities~\footnote{For example:
// Reviewers of Scientific Journals.} instead of verifying their statements
// by performing their own experiments ~\cite{Popper1971,Popper2002}.
// Software Guide : EndLatex
Casts input pixels to output pixel type.
Definition: itkCastImageFilter.h:104
Combines two images in a checkerboard pattern.
Definition: itkCheckerBoardImageFilter.h:46
itk::SmartPointer< Self >
Data source that reads image data from a single file.
Definition: itkImageFileReader.h:75
Regular Step Gradient descent optimizer.
Definition: itkRegularStepGradientDescentOptimizerv4.h:47
Superclass for callback/observer methods.
Definition: itkCommand.h:45
Writes image data to a single file.
Definition: itkImageFileWriter.h:87
Definition: itkObject.h:43
Translation transformation of a vector space (e.g. space coordinates)
Definition: itkTranslationTransform.h:43
virtual void Execute(Object *caller, const EventObject &event)=0
Resample an image via a coordinate transform.
Definition: itkResampleImageFilter.h:90
Base class for most ITK classes.
Definition: itkObject.h:62
Templated n-dimensional image class.
Definition: itkImage.h:86
Abstraction of the Events used to communicating among filters and with GUIs.
Definition: itkEventObject.h:57
constexpr unsigned int Dimension
Definition: itkGTestTypedefsAndConstructors.h:44
Computes the mutual information between two images to be registered using the method of Mattes et al.
Definition: itkMattesMutualInformationImageToImageMetricv4.h:103