示例地址：

itk\ITK\Examples\RegistrationITKv4\ImageRegistration7.cxx

说明：itk二维图像的配准：平移+旋转+缩放

效果图：

运行结果：

52 53.6213 [0.8333298229719548, -0.17450270771316403, -12.806452097490313, -12.724475494918924]
53 53.5935 [0.8332372921962161, -0.17451072912054427, -12.80648932249624, -12.724405572299606]
Optimizer stop condition: RegularStepGradientDescentOptimizerv4: Step too small after 54 iterations. Current step (6.10352e-005) is less than minimum step (0.0001).

Result =
Scale = 0.833237
Angle (radians) = -0.174511
Angle (degrees) = -9.99873
Translation X = -12.8065
Translation Y = -12.7244
Fixed Center X = 111.204
Fixed Center Y = 131.591
Iterations = 55
Metric value = 53.6171

代码整理：

#include "mainwindow.h"

#include <QApplication>

#include "vtkAutoInit.h"
VTK_MODULE_INIT(vtkRenderingOpenGL2)
VTK_MODULE_INIT(vtkRenderingVolumeOpenGL2)
VTK_MODULE_INIT(vtkRenderingFreeType)
VTK_MODULE_INIT(vtkRenderingContextOpenGL2)

#include "itkImageRegistrationMethodv4.h"
#include "itkMeanSquaresImageToImageMetricv4.h"
#include "itkRegularStepGradientDescentOptimizerv4.h"
#include "itkCenteredTransformInitializer.h"

#include "itkSimilarity2DTransform.h"
#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"
#include "itkResampleImageFilter.h"
#include "itkCastImageFilter.h"
#include "itkSubtractImageFilter.h"
#include "itkRescaleIntensityImageFilter.h"
#include "itkIdentityTransform.h"

#include "itkCommand.h"
class CommandIterationUpdate : public itk::Command
{
public:
  using Self = CommandIterationUpdate;
  using Superclass = itk::Command;
  using Pointer = itk::SmartPointer<Self>;
  itkNewMacro(Self);

protected:
  CommandIterationUpdate() = default;

public:
  using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
  using OptimizerPointer = const OptimizerType *;

  void
  Execute(itk::Object * caller, const itk::EventObject & event) override
  {
    Execute((const itk::Object *)caller, event);
  }

  void
  Execute(const itk::Object * object, const itk::EventObject & event) override
  {
    auto optimizer = static_cast<OptimizerPointer>(object);
    if (!itk::IterationEvent().CheckEvent(&event))
    {
      return;
    }
    std::cout << optimizer->GetCurrentIteration() << "   ";
    std::cout << optimizer->GetValue() << "   ";
    std::cout << optimizer->GetCurrentPosition() << std::endl;
  }
};

#include "itkPNGImageIOFactory.h"
int main(int argc, char *argv[])
{
    itk::PNGImageIOFactory::RegisterOneFactory();
    constexpr unsigned int Dimension = 2;
    using PixelType = float;
    using FixedImageType = itk::Image<PixelType, Dimension>;
    using MovingImageType = itk::Image<PixelType, Dimension>;

    using TransformType = itk::Similarity2DTransform<double>;
    using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
    using MetricType = itk::MeanSquaresImageToImageMetricv4<FixedImageType, MovingImageType>;
    using RegistrationType = itk::ImageRegistrationMethodv4<FixedImageType, MovingImageType, TransformType>;

    MetricType::Pointer       metric = MetricType::New();
    OptimizerType::Pointer    optimizer = OptimizerType::New();
    RegistrationType::Pointer registration = RegistrationType::New();
    registration->SetMetric(metric);
    registration->SetOptimizer(optimizer);

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

    using FixedImageReaderType = itk::ImageFileReader<FixedImageType>;
    using MovingImageReaderType = itk::ImageFileReader<MovingImageType>;
    QString baseDir = "D:/learn/itk/ITK/Examples/Data/";
    FixedImageReaderType::Pointer fixedImageReader =
      FixedImageReaderType::New();
    MovingImageReaderType::Pointer movingImageReader =
      MovingImageReaderType::New();
    fixedImageReader->SetFileName((baseDir+"BrainProtonDensitySliceBorder20.png").toStdString());
    movingImageReader->SetFileName((baseDir+"BrainProtonDensitySliceR10X13Y17S12.png").toStdString());
    registration->SetFixedImage(fixedImageReader->GetOutput());
    registration->SetMovingImage(movingImageReader->GetOutput());

    //  In this example, we again use the helper class
    //  \doxygen{CenteredTransformInitializer} to compute a reasonable
    //  value for the initial center of rotation and scaling along with
    //  an initial translation.
    //使用CenteredTransformInitializer计算初始旋转和缩放中心的合理值以及初始平移。
    using TransformInitializerType =
      itk::CenteredTransformInitializer<TransformType,
                                        FixedImageType,
                                        MovingImageType>;

    TransformInitializerType::Pointer initializer = TransformInitializerType::New();
    initializer->SetTransform(transform);
    initializer->SetFixedImage(fixedImageReader->GetOutput());
    initializer->SetMovingImage(movingImageReader->GetOutput());
    initializer->MomentsOn();
    initializer->InitializeTransform();

    // The remaining parameters of the transform are initialized below.
    // 转换的其余参数在下面初始化。
    double initialScale = 1.0;
    double initialAngle = 0.0;
    transform->SetScale(initialScale);
    transform->SetAngle(initialAngle);
    //  Now the initialized transform object will be set to the registration
    //  method, and its initial parameters are used to initialize the
    //  registration process.
    //
    //  Also, by calling the \code{InPlaceOn()} method, this initialized
    //  transform will be the output transform
    //  object or ``grafted'' to the output of the registration process.
    //现在，将初始化的转换对象设置为注册方法，并使用其初始参数初始化注册过程。
    //此外，通过调用InPlaceOn()方法，这个初始化的转换将是输出转换对象或“嫁接”到注册过程的输出。

    registration->SetInitialTransform(transform);
    registration->InPlaceOn();

    //  Keeping in mind that the scale of units in scaling, rotation and
    //  translation are quite different, we take advantage of the scaling
    //  functionality provided by the optimizers. We know that the first element
    //  of the parameters array corresponds to the scale factor, the second
    //  corresponds to the angle, third and fourth are the remaining
    //  translation. We use henceforth small factors in the scales
    //  associated with translations.
    //请记住，缩放、旋转和平移的单位规模是非常不同的，我们利用优化器提供的缩放功能。我们知道参数数组的
    //第一个元素对应比例因子，第二个对应角度，第三和第四个是剩余的平移。今后，我们在与翻译相关的量表中使用小的因素。

    using OptimizerScalesType = OptimizerType::ScalesType;
    OptimizerScalesType optimizerScales(transform->GetNumberOfParameters());
    const double        translationScale = 1.0 / 100.0;
    optimizerScales[0] = 10.0;
    optimizerScales[1] = 1.0;
    optimizerScales[2] = translationScale;
    optimizerScales[3] = translationScale;
    optimizer->SetScales(optimizerScales);

    //  We also set the ordinary parameters of the optimization method. In this
    //  case we are using a
    //  \doxygen{RegularStepGradientDescentOptimizerv4}. Below we define the
    //  optimization parameters, i.e. initial learning rate (step length),
    //  minimal step length and number of iterations. The last two act as
    //  stopping criteria for the optimization.
    //我们还设置了优化方法的普通参数。 在这种情况下，我们使用 {RegularStepGradientDescentOptimizerv4}。
    //下面我们定义优化参数，即初始学习率（步长）、最小步长和迭代次数。 最后两个作为优化的停止标准。
    double steplength = 1.0;
    optimizer->SetLearningRate(steplength);
    optimizer->SetMinimumStepLength(0.0001);
    optimizer->SetNumberOfIterations(200);

    // 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.SetSize(1);
    shrinkFactorsPerLevel[0] = 1;

    RegistrationType::SmoothingSigmasArrayType smoothingSigmasPerLevel;
    smoothingSigmasPerLevel.SetSize(1);
    smoothingSigmasPerLevel[0] = 0;

    registration->SetNumberOfLevels(numberOfLevels);
    registration->SetSmoothingSigmasPerLevel(smoothingSigmasPerLevel);
    registration->SetShrinkFactorsPerLevel(shrinkFactorsPerLevel);

    try
    {
      registration->Update();
      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;
      return EXIT_FAILURE;
    }

    TransformType::ParametersType finalParameters = transform->GetParameters();
    const double finalScale = finalParameters[0];
    const double finalAngle = finalParameters[1];
    const double finalTranslationX = finalParameters[2];
    const double finalTranslationY = finalParameters[3];
    const double rotationCenterX =
      registration->GetOutput()->Get()->GetFixedParameters()[0];
    const double rotationCenterY =
      registration->GetOutput()->Get()->GetFixedParameters()[1];
    const unsigned int numberOfIterations = optimizer->GetCurrentIteration();
    const double bestValue = optimizer->GetValue();
    const double finalAngleInDegrees = finalAngle * 180.0 / itk::Math::pi;

    std::cout << std::endl;
    std::cout << "Result = " << std::endl;
    std::cout << " Scale           = " << finalScale << std::endl;
    std::cout << " Angle (radians) = " << finalAngle << std::endl;
    std::cout << " Angle (degrees) =  " << finalAngleInDegrees << std::endl;
    std::cout << " Translation X   = " << finalTranslationX << std::endl;
    std::cout << " Translation Y   = " << finalTranslationY << std::endl;
    std::cout << " Fixed Center X  = " << rotationCenterX << std::endl;
    std::cout << " Fixed Center Y  = " << rotationCenterY << std::endl;
    std::cout << " Iterations      = " << numberOfIterations << std::endl;
    std::cout << " Metric value    = " << bestValue << std::endl;

    //  The second image is the result of intentionally rotating the first image
    //  by $10$ degrees, scaling by $1/1.2$ and then translating by $(-13,-17)$.
    //  Both images have unit-spacing and are shown in Figure
    //  \ref{fig:FixedMovingImageRegistration7}. The registration takes $53$
    //  iterations and produces:

    //  [0.833237, -0.174511, -12.8065, -12.7244 ]
    //  That are interpreted as
    //  \item Scale factor  =       $0.833237$
    //  \item Angle         =       $-0.174511$   radians
    //  \item Translation   = $( -12.8065, -12.7244 )$ millimeters

    //  These values approximate the misalignment intentionally introduced into
    //  the moving image. Since $10$ degrees is about $0.174532$ radians.
    //
    // Figure \ref{fig:ImageRegistration7Outputs} shows the output of the
    // registration. The right image shows the squared magnitude of pixel
    // differences between the fixed image and the resampled moving image.

    // \includegraphics[height=0.32\textwidth]{ImageRegistration7TraceMetric}
    // \includegraphics[height=0.32\textwidth]{ImageRegistration7TraceAngle}
    // \includegraphics[height=0.32\textwidth]{ImageRegistration7TraceScale}
    // \includegraphics[height=0.32\textwidth]{ImageRegistration7TraceTranslations}
    // \itkcaption[Simularity2DTransform registration plots]{Plots of the
    // Metric, rotation angle, scale factor, and translations during the
    // registration using Similarity2D transform.}

    //  Figure \ref{fig:ImageRegistration7Plots} shows the plots of the main
    //  output parameters of the registration process. The metric values at
    //  every iteration are shown on the left. The rotation angle and scale
    //  factor values are shown in the two center plots while the translation
    //  components of the registration are presented in the plot on the right.
    //
    //  Software Guide : EndLatex

    using ResampleFilterType =
      itk::ResampleImageFilter<MovingImageType, FixedImageType>;
    ResampleFilterType::Pointer resampler = ResampleFilterType::New();
    resampler->SetTransform(transform);
    resampler->SetInput(movingImageReader->GetOutput());
    FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
    resampler->SetSize(fixedImage->GetLargestPossibleRegion().GetSize());
    resampler->SetOutputOrigin(fixedImage->GetOrigin());
    resampler->SetOutputSpacing(fixedImage->GetSpacing());
    resampler->SetOutputDirection(fixedImage->GetDirection());
    resampler->SetDefaultPixelValue(100);

    using OutputPixelType = unsigned char;
    using OutputImageType = itk::Image<OutputPixelType, Dimension>;
    using CastFilterType =
      itk::CastImageFilter<FixedImageType, OutputImageType>;
    using WriterType = itk::ImageFileWriter<OutputImageType>;
    WriterType::Pointer     writer = WriterType::New();
    CastFilterType::Pointer caster = CastFilterType::New();
    writer->SetFileName("./ImageRegistration7Output.png");
    caster->SetInput(resampler->GetOutput());
    writer->SetInput(caster->GetOutput());
    writer->Update();

    using DifferenceFilterType =itk::SubtractImageFilter<FixedImageType, FixedImageType, FixedImageType>;
    DifferenceFilterType::Pointer difference = DifferenceFilterType::New();
    using RescalerType =itk::RescaleIntensityImageFilter<FixedImageType, OutputImageType>;
    RescalerType::Pointer intensityRescaler = RescalerType::New();
    intensityRescaler->SetInput(difference->GetOutput());
    intensityRescaler->SetOutputMinimum(0);
    intensityRescaler->SetOutputMaximum(255);
    difference->SetInput1(fixedImageReader->GetOutput());
    difference->SetInput2(resampler->GetOutput());
    resampler->SetDefaultPixelValue(1);
    WriterType::Pointer writer2 = WriterType::New();
    writer2->SetInput(intensityRescaler->GetOutput());
    // Compute the difference image between the fixed and resampled moving image.
    {
      writer2->SetFileName("./ImageRegistration7DifferenceAfter.png");
      writer2->Update();
    }
    using IdentityTransformType = itk::IdentityTransform<double, Dimension>;
    IdentityTransformType::Pointer identity = IdentityTransformType::New();
    // Compute the difference image between the fixed and moving image before registration.
    {
      resampler->SetTransform(identity);
      writer2->SetFileName("./ImageRegistration7DifferenceBefore.png");
      writer2->Update();
    }
    return EXIT_SUCCESS;
}