ITK  4.9.0
Insight Segmentation and Registration Toolkit
Examples/RegistrationITKv4/ImageRegistration5.cxx
/*=========================================================================
*
* Copyright Insight Software Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySliceBorder20.png}
// INPUTS: {BrainProtonDensitySliceRotated10.png}
// OUTPUTS: {ImageRegistration5Output.png}
// OUTPUTS: {ImageRegistration5DifferenceAfter.png}
// OUTPUTS: {ImageRegistration5DifferenceBefore.png}
// ARGUMENTS: 0.1
// Software Guide : EndCommandLineArgs
// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySliceBorder20.png}
// INPUTS: {BrainProtonDensitySliceR10X13Y17.png}
// OUTPUTS: {ImageRegistration5Output2.png}
// OUTPUTS: {ImageRegistration5DifferenceAfter2.png}
// OUTPUTS: {ImageRegistration5DifferenceBefore2.png}
// ARGUMENTS: 1.0
// Software Guide : EndCommandLineArgs
// Software Guide : BeginLatex
//
// This example illustrates the use of the \doxygen{CenteredRigid2DTransform}
// for performing rigid registration in $2D$. The example code is for the
// most part identical to that presented in Section
// \ref{sec:IntroductionImageRegistration}. The main difference is the use
// of the CenteredRigid2DTransform here instead of the
// \doxygen{TranslationTransform}.
//
// \index{itk::CenteredRigid2DTransform}
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// In addition to the headers included in previous examples, the
// following header must also be included.
//
// \index{itk::CenteredRigid2DTransform!header}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// The following section of code implements a Command observer
// that will monitor the evolution of the registration process.
//
#include "itkCommand.h"
class CommandIterationUpdate : public itk::Command
{
public:
typedef CommandIterationUpdate Self;
itkNewMacro( Self );
protected:
CommandIterationUpdate() {};
public:
typedef const OptimizerType * OptimizerPointer;
void Execute(itk::Object *caller, const itk::EventObject & event) ITK_OVERRIDE
{
Execute( (const itk::Object *)caller, event);
}
void Execute(const itk::Object * object, const itk::EventObject & event) ITK_OVERRIDE
{
OptimizerPointer 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;
}
};
int 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 [differenceAfterRegistration] ";
std::cerr << " [differenceBeforeRegistration] ";
std::cerr << " [initialStepLength] "<< std::endl;
return EXIT_FAILURE;
}
const unsigned int Dimension = 2;
typedef float PixelType;
typedef itk::Image< PixelType, Dimension > FixedImageType;
typedef itk::Image< PixelType, Dimension > MovingImageType;
// Software Guide : BeginLatex
//
// The transform type is instantiated using the code below. The only
// template parameter for this class is the representation type of the
// space coordinates.
//
// \index{itk::CenteredRigid2DTransform!Instantiation}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
FixedImageType,
MovingImageType > MetricType;
FixedImageType,
MovingImageType,
TransformType > RegistrationType;
MetricType::Pointer metric = MetricType::New();
OptimizerType::Pointer optimizer = OptimizerType::New();
RegistrationType::Pointer registration = RegistrationType::New();
registration->SetMetric( metric );
registration->SetOptimizer( optimizer );
// Software Guide : BeginLatex
//
// In the Hello World! example, we used Fixed/Moving initial transforms
// to initialize the registration configuration. That approach was good to
// get an intuition of the registration method, specifically when we aim to run
// a multistage registration process, from which the output of each stage can
// be used to initialize the next registration stage.
//
// To get a better underestanding of the registration process in
// such situations, consider an example of 3 stages registration process
// that is started using an initial moving transform ($\Gamma_{mi}$).
// Multiple stages are handled by linking multiple instantiations of
// the \doxygen{ImageRegistrationMethodv4} class.
// Inside the registration filter of the first stage, the initial moving
// transform is added to an internal composite transform along with an updatable
// identity transform ($\Gamma_{u}$). Although the whole composite transform
// is used for metric evaluation, only the $\Gamma_{u}$ is set to be updated
// by the optimizer at each iteration. The $\Gamma_{u}$ will be considered as
// the output transform of the current stage when the optimization process is
// converged. This implies that the output of this stage does not include
// the initialization parameters, so we need to concatenate the output and the
// initialization transform into a composite transform to be considered as the
// final transform of the first registration stage.
//
// $ T_{1}(x) = \Gamma_{mi}(\Gamma_{stage_1}(x) ) $
//
// Consider that, as explained in section \ref{sec:FeaturesOfTheRegistrationFramework},
// the above transform is a mapping from the vitual domain (i.e. fixed image space, when no
// fixed initial transform) to the moving image space.
//
// Then, the result transform of the first stage will be used as the initial moving
// transform for the second stage of the registration process, and this approach goes on
// until the last stage of the registration process.
//
// At the end of the registration process, the $\Gamma_{mi}$ and the outputs of each stage
// can be concatenated into a final composite transform that is considered to be the final
// output of the whole registration process.
//
// $I'_{m}(x) = I_{m}(\Gamma_{mi}(\Gamma_{stage_1}(\Gamma_{stage_2}(\Gamma_{stage_3}(x) ) ) ) )$
//
// The above approach is especially useful if individual stages are characterized by
// different types of transforms, e.g. when we run a rigid registration
// process that is proceeded by an affine registration which is completed by a BSpline
// registration at the end.
//
//
// In addition to the above method, there is also a direct initialization method in which the
// initial transform will be optimized directly. In this way the initial transform will be
// modified during the registration process, so it can be used as the final transform when
// the registration process is completed. This direct approach is conceptually close to
// what was happening in ITKv3 registration.
//
// Using this method is very simple and efficient when we have only one level of
// registration, which is the case in this example.
// Also, a good application of this initialization method in a multi-stage scenario
// is when two consequent stages have the same transform types, or at least the initial
// parameters can easily be inferred from the result of the previous stage, such as when a
// translation transform is followed by a rigid transform.
//
// The direct initialization approach is shown by the current example in which we try
// to initialize the parameters of the optimizable transform ($\Gamma_{u}$) directly.
//
// For this purpose, first, the initial transform object is constructed below.
// This transform will be initialized, and its initial parameters will be
// used when the registration process starts.
//
// \index{itk::CenteredRigid2DTransform!New()}
// \index{itk::CenteredRigid2DTransform!Pointer}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
TransformType::Pointer initialTransform = TransformType::New();
// Software Guide : EndCodeSnippet
typedef itk::ImageFileReader< FixedImageType > FixedImageReaderType;
typedef itk::ImageFileReader< MovingImageType > MovingImageReaderType;
FixedImageReaderType::Pointer fixedImageReader = FixedImageReaderType::New();
MovingImageReaderType::Pointer movingImageReader = MovingImageReaderType::New();
fixedImageReader->SetFileName( argv[1] );
movingImageReader->SetFileName( argv[2] );
registration->SetFixedImage( fixedImageReader->GetOutput() );
registration->SetMovingImage( movingImageReader->GetOutput() );
// Software Guide : BeginLatex
//
// In this example, the input images are taken from readers. The code
// below updates the readers in order to ensure that the image parameters
// (size, origin and spacing) are valid when used to initialize the
// transform. We intend to use the center of the fixed image as the
// rotation center and then use the vector between the fixed image center
// and the moving image center as the initial translation to be applied
// after the rotation.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
fixedImageReader->Update();
movingImageReader->Update();
// Software Guide : EndCodeSnippet
typedef FixedImageType::SpacingType SpacingType;
typedef FixedImageType::PointType OriginType;
typedef FixedImageType::RegionType RegionType;
typedef FixedImageType::SizeType SizeType;
// Software Guide : BeginLatex
//
// The center of rotation is computed using the origin, size and spacing of
// the fixed image.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
const SpacingType fixedSpacing = fixedImage->GetSpacing();
const OriginType fixedOrigin = fixedImage->GetOrigin();
const RegionType fixedRegion = fixedImage->GetLargestPossibleRegion();
const SizeType fixedSize = fixedRegion.GetSize();
TransformType::InputPointType centerFixed;
centerFixed[0] = fixedOrigin[0] + fixedSpacing[0] * fixedSize[0] / 2.0;
centerFixed[1] = fixedOrigin[1] + fixedSpacing[1] * fixedSize[1] / 2.0;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The center of the moving image is computed in a similar way.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
MovingImageType::Pointer movingImage = movingImageReader->GetOutput();
const SpacingType movingSpacing = movingImage->GetSpacing();
const OriginType movingOrigin = movingImage->GetOrigin();
const RegionType movingRegion = movingImage->GetLargestPossibleRegion();
const SizeType movingSize = movingRegion.GetSize();
TransformType::InputPointType centerMoving;
centerMoving[0] = movingOrigin[0] + movingSpacing[0] * movingSize[0] / 2.0;
centerMoving[1] = movingOrigin[1] + movingSpacing[1] * movingSize[1] / 2.0;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Then, we initialize the transform by
// passing the center of the fixed image as the rotation center with the
// \code{SetCenter()} method. Also, the translation is set as the vector
// relating the center of the moving image to the center of the fixed
// image. This last vector is passed with the method
// \code{SetTranslation()}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
initialTransform->SetCenter( centerFixed );
initialTransform->SetTranslation( centerMoving - centerFixed );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Let's finally initialize the rotation with a zero angle.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
initialTransform->SetAngle( 0.0 );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Now the current parameters of the initial transform will be set
// to a registration method, so they can be assigned to the $\Gamma_{u}$ directly.
// Note that you should not confuse the following function with the
// \code{SetMoving(Fixed)InitialTransform()} methods that were used in Hello World! example.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
registration->SetInitialTransform( initialTransform );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Keep in mind that the scale of units in rotation and translation is
// quite different. For example, here we know that the first element of the
// parameters array corresponds to the angle that is measured in radians, while
// the other parameters correspond to the translations and the center point
// coordinates that are measured in millimeters,
// so a naive application of gradient descent optimizer will not produce a smooth
// change of parameters, because a similar change of $\delta$
// to each parameter will produce a different magnitude of impact on the transform.
// As the result, we need ``parameter scales'' to customize the learning rate for
// each parameter. We can take advantage of the scaling functionality provided
// by the optimizers.
//
// In this example we use small factors in the scales associated with
// translations and the coordinates of the rotation center.
// However, for the transforms with larger parameters sets, it is not intuitive for a user to
// set the scales. Fortunately, a framework for automated estimation of
// parameter scales is provided by ITKv4 that will be discussed later in the example of
// section \ref{sec:MultiStageRegistration}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef OptimizerType::ScalesType OptimizerScalesType;
OptimizerScalesType optimizerScales(
initialTransform->GetNumberOfParameters() );
const double translationScale = 1.0 / 1000.0;
optimizerScales[0] = 1.0;
optimizerScales[1] = translationScale;
optimizerScales[2] = translationScale;
optimizerScales[3] = translationScale;
optimizerScales[4] = translationScale;
optimizer->SetScales( optimizerScales );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Next we set the normal parameters of the optimization method. In this
// case we are using an \doxygen{RegularStepGradientDescentOptimizerv4}.
// Below, we define the optimization parameters like the relaxation factor,
// learning rate (initial step length), minimal step length and number of
// iterations. These last two act as stopping criteria for the optimization.
//
// \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetRelaxationFactor()}
// \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetLearningRate()}
// \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetMinimumStepLength()}
// \index{Regular\-Step\-Gradient\-Descent\-Optimizer!SetNumberOfIterations()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
double initialStepLength = 0.1;
// Software Guide : EndCodeSnippet
if( argc > 6 )
{
initialStepLength = atof( argv[6] );
}
// Software Guide : BeginCodeSnippet
optimizer->SetRelaxationFactor( 0.6 );
optimizer->SetLearningRate( initialStepLength );
optimizer->SetMinimumStepLength( 0.001 );
optimizer->SetNumberOfIterations( 200 );
// 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.
//
const 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( itk::ExceptionObject & err )
{
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
return EXIT_FAILURE;
}
const TransformType::ParametersType finalParameters =
registration->GetOutput()->Get()->GetParameters();
const double finalAngle = finalParameters[0];
const double finalRotationCenterX = finalParameters[1];
const double finalRotationCenterY = finalParameters[2];
const double finalTranslationX = finalParameters[3];
const double finalTranslationY = finalParameters[4];
const unsigned int numberOfIterations = optimizer->GetCurrentIteration();
const double bestValue = optimizer->GetValue();
// Print out results
//
const double finalAngleInDegrees = finalAngle * 180.0 / vnl_math::pi;
std::cout << "Result = " << std::endl;
std::cout << " Angle (radians) = " << finalAngle << std::endl;
std::cout << " Angle (degrees) = " << finalAngleInDegrees << std::endl;
std::cout << " Center X = " << finalRotationCenterX << std::endl;
std::cout << " Center Y = " << finalRotationCenterY << std::endl;
std::cout << " Translation X = " << finalTranslationX << std::endl;
std::cout << " Translation Y = " << finalTranslationY << std::endl;
std::cout << " Iterations = " << numberOfIterations << std::endl;
std::cout << " Metric value = " << bestValue << std::endl;
// Software Guide : BeginLatex
//
// Let's execute this example over two of the images provided in
// \code{Examples/Data}:
//
// \begin{itemize}
// \item \code{BrainProtonDensitySliceBorder20.png}
// \item \code{BrainProtonDensitySliceRotated10.png}
// \end{itemize}
//
// The second image is the result of intentionally rotating the first image
// by $10$ degrees around the geometrical center of the image. Both images
// have unit-spacing and are shown in Figure
// \ref{fig:FixedMovingImageRegistration5}. The registration takes $20$
// iterations and produces the results:
//
// \begin{center}
// \begin{verbatim}
// [0.17762, 110.489, 128.487, 0.00925022, 0.00140223]
// \end{verbatim}
// \end{center}
//
// These results are interpreted as
//
// \begin{itemize}
// \item Angle = $0.17762$ radians
// \item Center = $( 110.489 , 128.487 )$ millimeters
// \item Translation = $( 0.00925022, 0.00140223 )$ millimeters
// \end{itemize}
//
// As expected, these values match the misalignment intentionally introduced
// into the moving image quite well, since $10$ degrees is about $0.174532$
// radians.
//
// \begin{figure}
// \center
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceBorder20}
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceRotated10}
// \itkcaption[Rigid2D Registration input images]{Fixed and moving images
// are provided as input to the registration method using the CenteredRigid2D
// transform.}
// \label{fig:FixedMovingImageRegistration5}
// \end{figure}
//
//
// \begin{figure}
// \center
// \includegraphics[width=0.32\textwidth]{ImageRegistration5Output}
// \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceBefore}
// \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceAfter}
// \itkcaption[Rigid2D Registration output images]{Resampled moving image
// (left). Differences between the fixed and moving images, before (center)
// and after (right) registration using the CenteredRigid2D transform.}
// \label{fig:ImageRegistration5Outputs}
// \end{figure}
//
// Figure \ref{fig:ImageRegistration5Outputs} shows from left to right the
// resampled moving image after registration, the difference between the fixed
// and moving images before registration, and the difference between the fixed
// and resampled moving image after registration. It can be seen from the
// last difference image that the rotational component has been solved but
// that a small centering misalignment persists.
//
// \begin{figure}
// \center
// \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceMetric1}
// \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceAngle1}
// \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceTranslations1}
// \itkcaption[Rigid2D Registration output plots]{Metric values, rotation
// angle and translations during registration with the CenteredRigid2D
// transform.}
// \label{fig:ImageRegistration5Plots}
// \end{figure}
//
// Figure \ref{fig:ImageRegistration5Plots} shows plots of the main output
// parameters produced from the registration process. This includes the
// metric values at every iteration, the angle values at every iteration,
// and the translation components of the transform as the registration
// progresses.
//
// Software Guide : EndLatex
MovingImageType,
FixedImageType > ResampleFilterType;
//TransformType::ConstPointer finalTransform = TransformType::New();
//TransformType::ConstPointer finalTransform = registration->GetTransform();
ResampleFilterType::Pointer resample = ResampleFilterType::New();
resample->SetTransform( registration->GetTransform() );
resample->SetInput( movingImageReader->GetOutput() );
resample->SetSize( fixedImage->GetLargestPossibleRegion().GetSize() );
resample->SetOutputOrigin( fixedImage->GetOrigin() );
resample->SetOutputSpacing( fixedImage->GetSpacing() );
resample->SetOutputDirection( fixedImage->GetDirection() );
resample->SetDefaultPixelValue( 100 );
typedef unsigned char OutputPixelType;
FixedImageType,
OutputImageType > CastFilterType;
WriterType::Pointer writer = WriterType::New();
CastFilterType::Pointer caster = CastFilterType::New();
writer->SetFileName( argv[3] );
caster->SetInput( resample->GetOutput() );
writer->SetInput( caster->GetOutput() );
try
{
writer->Update();
}
catch( itk::ExceptionObject & excp )
{
std::cerr << "ExceptionObject while writing the resampled image !" << std::endl;
std::cerr << excp << std::endl;
return EXIT_FAILURE;
}
typedef itk::Image< float, Dimension > DifferenceImageType;
FixedImageType,
FixedImageType,
DifferenceImageType > DifferenceFilterType;
DifferenceFilterType::Pointer difference = DifferenceFilterType::New();
DifferenceImageType,
OutputImageType > RescalerType;
RescalerType::Pointer intensityRescaler = RescalerType::New();
intensityRescaler->SetOutputMinimum( 0 );
intensityRescaler->SetOutputMaximum( 255 );
difference->SetInput1( fixedImageReader->GetOutput() );
difference->SetInput2( resample->GetOutput() );
resample->SetDefaultPixelValue( 1 );
intensityRescaler->SetInput( difference->GetOutput() );
WriterType::Pointer writer2 = WriterType::New();
writer2->SetInput( intensityRescaler->GetOutput() );
try
{
// Compute the difference image between the
// fixed and moving image after registration.
if( argc > 4 )
{
writer2->SetFileName( argv[4] );
writer2->Update();
}
// Compute the difference image between the
// fixed and resampled moving image after registration.
TransformType::Pointer identityTransform = TransformType::New();
identityTransform->SetIdentity();
resample->SetTransform( identityTransform );
if( argc > 5 )
{
writer2->SetFileName( argv[5] );
writer2->Update();
}
}
catch( itk::ExceptionObject & excp )
{
std::cerr << "Error while writing difference images" << std::endl;
std::cerr << excp << std::endl;
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// Let's now consider the case in which rotations and translations are
// present in the initial registration, as in the following pair
// of images:
//
// \begin{itemize}
// \item \code{BrainProtonDensitySliceBorder20.png}
// \item \code{BrainProtonDensitySliceR10X13Y17.png}
// \end{itemize}
//
// The second image is the result of intentionally rotating the first image
// by $10$ degrees and then translating it $13mm$ in $X$ and $17mm$ in $Y$.
// Both images have unit-spacing and are shown in Figure
// \ref{fig:FixedMovingImageRegistration5b}. In order to accelerate
// convergence it is convenient to use a larger step length as shown here.
//
// \code{optimizer->SetMaximumStepLength( 1.3 );}
//
// The registration now takes $35$ iterations and produces the following
// results:
//
// \begin{center}
// \begin{verbatim}
// [0.174552, 110.041, 128.917, 12.9339, 15.9149]
// \end{verbatim}
// \end{center}
//
// These parameters are interpreted as
//
// \begin{itemize}
// \item Angle = $0.17452$ radians
// \item Center = $( 110.041 , 128.917 )$ millimeters
// \item Translation = $( 12.9339 , 15.9149 )$ millimeters
// \end{itemize}
//
// These values approximately match the initial misalignment intentionally
// introduced into the moving image, since $10$ degrees is about $0.174532$
// radians. The horizontal translation is well resolved while the vertical
// translation ends up being off by about one millimeter.
//
// \begin{figure}
// \center
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceBorder20}
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceR10X13Y17}
// \itkcaption[Rigid2D Registration input images]{Fixed and moving images
// provided as input to the registration method using the CenteredRigid2D
// transform.}
// \label{fig:FixedMovingImageRegistration5b}
// \end{figure}
//
//
// \begin{figure}
// \center
// \includegraphics[width=0.32\textwidth]{ImageRegistration5Output2}
// \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceBefore2}
// \includegraphics[width=0.32\textwidth]{ImageRegistration5DifferenceAfter2}
// \itkcaption[Rigid2D Registration output images]{Resampled moving image
// (left). Differences between the fixed and moving images, before (center)
// and after (right) registration with the CenteredRigid2D transform.}
// \label{fig:ImageRegistration5Outputs2}
// \end{figure}
//
// Figure \ref{fig:ImageRegistration5Outputs2} shows the output of the
// registration. The rightmost image of this figure shows the difference
// between the fixed image and the resampled moving image after registration.
//
// \begin{figure}
// \center
// \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceMetric2}
// \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceAngle2}
// \includegraphics[height=0.32\textwidth]{ImageRegistration5TraceTranslations2}
// \itkcaption[Rigid2D Registration output plots]{Metric values, rotation
// angle and translations during the registration using the CenteredRigid2D
// transform on an image with rotation and translation mis-registration.}
// \label{fig:ImageRegistration5Plots2}
// \end{figure}
//
// Figure \ref{fig:ImageRegistration5Plots2} shows plots of the main output
// registration parameters when the rotation and translations are combined.
// These results include the metric values at every iteration, the angle
// values at every iteration, and the translation components of the
// registration as the registration converges. It can be seen from the
// smoothness of these plots that a larger step length could have been
// supported easily by the optimizer. You may want to modify this value in
// order to get a better idea of how to tune the parameters.
//
// Software Guide : EndLatex
return EXIT_SUCCESS;
}