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ImageRegistration1.cxx
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ImageRegistration1.cxx
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/*=========================================================================
*
* 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: {BrainProtonDensitySliceShifted13x17y.png}
// OUTPUTS: {ImageRegistration1Output.png}
// OUTPUTS: {ImageRegistration1DifferenceAfter.png}
// OUTPUTS: {ImageRegistration1DifferenceBefore.png}
// Software Guide : EndCommandLineArgs
// Software Guide : BeginLatex
//
// This example illustrates the use of the image registration framework in
// Insight. It should be read as a ``Hello World'' for ITK registration.
// Instead of means to an end, this example should be read as a basic
// introduction to the elements typically involved when solving a problem
// of image registration.
//
// \index{itk::Image!Instantiation}
// \index{itk::Image!Header}
//
// A registration method requires the following set of components: two input
// images, a transform, a metric, an interpolator and an optimizer. Some of
// these components are parameterized by the image type for which the
// registration is intended. The following header files provide declarations
// of common types used for these components.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
#include "itkImageRegistrationMethod.h"
#include "itkTranslationTransform.h"
#include "itkMeanSquaresImageToImageMetric.h"
#include "itkRegularStepGradientDescentOptimizer.h"
// Software Guide : EndCodeSnippet
#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"
#include "itkResampleImageFilter.h"
#include "itkCastImageFilter.h"
#include "itkRescaleIntensityImageFilter.h"
#include "itkSubtractImageFilter.h"
class CommandIterationUpdate : public itk::Command
{
public:
typedef CommandIterationUpdate Self;
typedef itk::Command Superclass;
typedef itk::SmartPointer<Self> Pointer;
itkNewMacro( Self );
protected:
CommandIterationUpdate() {};
public:
typedef itk::RegularStepGradientDescentOptimizer OptimizerType;
typedef const OptimizerType* OptimizerPointer;
void Execute(itk::Object *caller, const itk::EventObject & event)
{
Execute( (const itk::Object *)caller, event);
}
void Execute(const itk::Object * object, const itk::EventObject & event)
{
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 [differenceImageAfter]";
std::cerr << "[differenceImageBefore]" << std::endl;
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// The types of each one of the components in the registration methods should
// be instantiated first. We start by selecting the image
// dimension and the types to be used for representing image pixels.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
const unsigned int Dimension = 2;
typedef float PixelType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The types of the input images are instantiated by the following lines.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::Image< PixelType, Dimension > FixedImageType;
typedef itk::Image< PixelType, Dimension > MovingImageType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The transform that will map the fixed image space into the moving image
// space is defined below.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::TranslationTransform< double, Dimension > TransformType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// An optimizer is required to explore the parameter space of the transform
// in search of optimal values of the metric.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::RegularStepGradientDescentOptimizer OptimizerType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The metric will compare how well the two images match each other. Metric
// types are usually templated over the image types as seen in
// the following type declaration.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::MeanSquaresImageToImageMetric<
FixedImageType,
MovingImageType > MetricType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Finally, the type of the interpolator is declared. The interpolator will
// evaluate the intensities of the moving image at non-grid positions.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk:: LinearInterpolateImageFunction<
MovingImageType,
double > InterpolatorType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The registration method type is instantiated using the types of the
// fixed and moving images. This class is responsible for interconnecting
// all the components that we have described so far.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::ImageRegistrationMethod<
FixedImageType,
MovingImageType > RegistrationType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Each one of the registration components is created using its
// \code{New()} method and is assigned to its respective
// \doxygen{SmartPointer}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
MetricType::Pointer metric = MetricType::New();
TransformType::Pointer transform = TransformType::New();
OptimizerType::Pointer optimizer = OptimizerType::New();
InterpolatorType::Pointer interpolator = InterpolatorType::New();
RegistrationType::Pointer registration = RegistrationType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Each component is now connected to the instance of the registration method.
// \index{itk::RegistrationMethod!SetMetric()}
// \index{itk::RegistrationMethod!SetOptimizer()}
// \index{itk::RegistrationMethod!SetTransform()}
// \index{itk::RegistrationMethod!SetFixedImage()}
// \index{itk::RegistrationMethod!SetMovingImage()}
// \index{itk::RegistrationMethod!SetInterpolator()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
registration->SetMetric( metric );
registration->SetOptimizer( optimizer );
registration->SetTransform( transform );
registration->SetInterpolator( interpolator );
// 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] );
// Software Guide : BeginLatex
//
// In this example, the fixed and moving images are read from files. This
// requires the \doxygen{ImageRegistrationMethod} to acquire its inputs from
// the output of the readers.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
registration->SetFixedImage( fixedImageReader->GetOutput() );
registration->SetMovingImage( movingImageReader->GetOutput() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The registration can be restricted to consider only a particular region
// of the fixed image as input to the metric computation. This region is
// defined with the \code{SetFixedImageRegion()} method. You could use this
// feature to reduce the computational time of the registration or to avoid
// unwanted objects present in the image from affecting the registration outcome.
// In this example we use the full available content of the image. This
// region is identified by the \code{BufferedRegion} of the fixed image.
// Note that for this region to be valid the reader must first invoke its
// \code{Update()} method.
//
// \index{itk::ImageRegistrationMethod!SetFixedImageRegion()}
// \index{itk::Image!GetBufferedRegion()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
fixedImageReader->Update();
registration->SetFixedImageRegion(
fixedImageReader->GetOutput()->GetBufferedRegion() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The parameters of the transform are initialized by passing them in an
// array. This can be used to setup an initial known correction of the
// misalignment. In this particular case, a translation transform is
// being used for the registration. The array of parameters for this
// transform is simply composed of the translation values along each
// dimension. Setting the values of the parameters to zero
// initializes the transform to an \emph{Identity} transform. Note that the
// array constructor requires the number of elements to be passed as an
// argument.
//
// \index{itk::TranslationTransform!GetNumberOfParameters()}
// \index{itk::RegistrationMethod!SetInitialTransformParameters()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef RegistrationType::ParametersType ParametersType;
ParametersType initialParameters( transform->GetNumberOfParameters() );
initialParameters[0] = 0.0; // Initial offset in mm along X
initialParameters[1] = 0.0; // Initial offset in mm along Y
registration->SetInitialTransformParameters( initialParameters );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// At this point the registration method is ready for execution. The
// optimizer is the component that drives the execution of the
// registration. However, the ImageRegistrationMethod class
// orchestrates the ensemble to make sure that everything is in place
// before control is passed to the optimizer.
//
// It is usually desirable to fine tune the parameters of the optimizer.
// Each optimizer has particular parameters that must be interpreted in the
// context of the optimization strategy it implements. The optimizer used in
// this example is a variant of gradient descent that attempts to prevent it
// from taking steps that are too large. At each iteration, this optimizer
// will take a step along the direction of the \doxygen{ImageToImageMetric}
// derivative. The initial length of the step is defined by the user. Each
// time the direction of the derivative abruptly changes, the optimizer
// assumes that a local extrema has been passed and reacts by reducing the
// step length by a half. After several reductions of the step length, the
// optimizer may be moving in a very restricted area of the transform
// parameter space. The user can define how small the step length should be
// to consider convergence to have been reached. This is equivalent to defining
// the precision with which the final transform should be known.
//
// The initial step length is defined with the method
// \code{SetMaximumStepLength()}, while the tolerance for convergence is
// defined with the method \code{SetMinimumStepLength()}.
//
// \index{itk::Regular\-Setp\-Gradient\-Descent\-Optimizer!SetMaximumStepLength()}
// \index{itk::Regular\-Step\-Gradient\-Descent\-Optimizer!SetMinimumStepLength()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
optimizer->SetMaximumStepLength( 4.00 );
optimizer->SetMinimumStepLength( 0.01 );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// In case the optimizer never succeeds reaching the desired
// precision tolerance, it is prudent to establish a limit on the number of
// iterations to be performed. This maximum number is defined with the
// method \code{SetNumberOfIterations()}.
//
// \index{itk::Regular\-Setp\-Gradient\-Descent\-Optimizer!SetNumberOfIterations()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
optimizer->SetNumberOfIterations( 200 );
// Software Guide : EndCodeSnippet
// Connect an observer
CommandIterationUpdate::Pointer observer = CommandIterationUpdate::New();
optimizer->AddObserver( itk::IterationEvent(), observer );
// Software Guide : BeginLatex
//
// The registration process is triggered by an invocation to the
// \code{Update()} method. If something goes wrong during the
// initialization or execution of the registration an exception will be
// thrown. We should therefore place the \code{Update()} method
// inside a \code{try/catch} block as illustrated in the following lines.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
try
{
registration->Update();
}
catch( itk::ExceptionObject & err )
{
std::cerr << "ExceptionObject caught !" << std::endl;
std::cerr << err << std::endl;
return EXIT_FAILURE;
}
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// In a real life application, you may attempt to recover from the error by
// taking more effective actions in the catch block. Here we are simply
// printing out a message and then terminating the execution of the program.
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// The result of the registration process is an array of parameters that
// defines the spatial transformation in an unique way. This final result is
// obtained using the \code{GetLastTransformParameters()} method.
//
// \index{itk::RegistrationMethod!GetLastTransformParameters()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
ParametersType finalParameters = registration->GetLastTransformParameters();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// In the case of the \doxygen{TranslationTransform}, there is a
// straightforward interpretation of the parameters. Each element of the
// array corresponds to a translation along one spatial dimension.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
const double TranslationAlongX = finalParameters[0];
const double TranslationAlongY = finalParameters[1];
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The optimizer can be queried for the actual number of iterations
// performed to reach convergence. The \code{GetCurrentIteration()}
// method returns this value. A large number of iterations may be an
// indication that the maximum step length has been set too small, which
// is undesirable since it results in long computational times.
//
// \index{itk::Regular\-Setp\-Gradient\-Descent\-Optimizer!GetCurrentIteration()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
const unsigned int numberOfIterations = optimizer->GetCurrentIteration();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The value of the image metric corresponding to the last set of parameters
// can be obtained with the \code{GetValue()} method of the optimizer.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
const double bestValue = optimizer->GetValue();
// Software Guide : EndCodeSnippet
// Print out results
//
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;
// 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{BrainProtonDensitySliceShifted13x17y.png}
// \end{itemize}
//
// The second image is the result of intentionally translating the first
// image by $(13,17)$ millimeters. Both images have unit-spacing and
// are shown in Figure \ref{fig:FixedMovingImageRegistration1}. The
// registration takes 18 iterations and the resulting transform parameters are:
//
// \begin{verbatim}
// Translation X = 12.9959
// Translation Y = 17.0001
// \end{verbatim}
//
// As expected, these values match quite well the misalignment that we
// intentionally introduced in the moving image.
//
// \begin{figure}
// \center
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceBorder20}
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceShifted13x17y}
// \itkcaption[Fixed and Moving images in registration framework]{Fixed and
// Moving image provided as input to the registration method.}
// \label{fig:FixedMovingImageRegistration1}
// \end{figure}
//
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// It is common, as the last step of a registration task, to use the
// resulting transform to map the moving image into the fixed image space.
// This is easily done with the \doxygen{ResampleImageFilter}. Please
// refer to Section~\ref{sec:ResampleImageFilter} for details on the use
// of this filter. First, a ResampleImageFilter type is instantiated
// using the image types. It is convenient to use the fixed image type as
// the output type since it is likely that the transformed moving image
// will be compared with the fixed image.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::ResampleImageFilter<
MovingImageType,
FixedImageType > ResampleFilterType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// A resampling filter is created and the moving image is connected as
// its input.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
ResampleFilterType::Pointer resampler = ResampleFilterType::New();
resampler->SetInput( movingImageReader->GetOutput() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The Transform that is produced as output of the Registration method is
// also passed as input to the resampling filter. Note the use of the
// methods \code{GetOutput()} and \code{Get()}. This combination is needed
// here because the registration method acts as a filter whose output is a
// transform decorated in the form of a \doxygen{DataObject}. For details in
// this construction you may want to read the documentation of the
// \doxygen{DataObjectDecorator}.
//
// \index{itk::ImageRegistrationMethod!Resampling image}
// \index{itk::ImageRegistrationMethod!Pipeline}
// \index{itk::ImageRegistrationMethod!DataObjectDecorator}
// \index{itk::ImageRegistrationMethod!GetOutput()}
// \index{itk::DataObjectDecorator!Use in Registration}
// \index{itk::DataObjectDecorator!Get()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
resampler->SetTransform( registration->GetOutput()->Get() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// As described in Section \ref{sec:ResampleImageFilter}, the
// ResampleImageFilter requires additional parameters to be specified, in
// particular, the spacing, origin and size of the output image. The default
// pixel value is also set to a distinct gray level in order to highlight
// the regions that are mapped outside of the moving image.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
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 );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// \begin{figure}
// \center
// \includegraphics[width=0.32\textwidth]{ImageRegistration1Output}
// \includegraphics[width=0.32\textwidth]{ImageRegistration1DifferenceBefore}
// \includegraphics[width=0.32\textwidth]{ImageRegistration1DifferenceAfter}
// \itkcaption[HelloWorld registration output images]{Mapped moving image and its
// difference with the fixed image before and after registration}
// \label{fig:ImageRegistration1Output}
// \end{figure}
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// The output of the filter is passed to a writer that will store the
// image in a file. An \doxygen{CastImageFilter} is used to convert the
// pixel type of the resampled image to the final type used by the
// writer. The cast and writer filters are instantiated below.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef unsigned char OutputPixelType;
typedef itk::Image< OutputPixelType, Dimension > OutputImageType;
typedef itk::CastImageFilter<
FixedImageType,
OutputImageType > CastFilterType;
typedef itk::ImageFileWriter< OutputImageType > WriterType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The filters are created by invoking their \code{New()}
// method.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
WriterType::Pointer writer = WriterType::New();
CastFilterType::Pointer caster = CastFilterType::New();
// Software Guide : EndCodeSnippet
writer->SetFileName( argv[3] );
// Software Guide : BeginLatex
//
// The filters are connected together and the \code{Update()} method of the
// writer is invoked in order to trigger the execution of the pipeline.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
caster->SetInput( resampler->GetOutput() );
writer->SetInput( caster->GetOutput() );
writer->Update();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// \begin{figure}
// \center
// \includegraphics[width=\textwidth]{ImageRegistration1Pipeline}
// \itkcaption[Pipeline structure of the registration example]{Pipeline
// structure of the registration example.}
// \label{fig:ImageRegistration1Pipeline}
// \end{figure}
//
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// The fixed image and the transformed moving image can easily be compared
// using the \doxygen{SubtractImageFilter}. This pixel-wise filter computes
// the difference between homologous pixels of its two input images.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::SubtractImageFilter<
FixedImageType,
FixedImageType,
FixedImageType > DifferenceFilterType;
DifferenceFilterType::Pointer difference = DifferenceFilterType::New();
difference->SetInput1( fixedImageReader->GetOutput() );
difference->SetInput2( resampler->GetOutput() );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Note that the use of subtraction as a method for comparing the images is
// appropriate here because we chose to represent the images using a pixel
// type \code{float}. A different filter would have been used if the pixel
// type of the images were any of the \code{unsigned} integer type.
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// Since the differences between the two images may correspond to very low
// values of intensity, we rescale those intensities with a
// \doxygen{RescaleIntensityImageFilter} in order to make them more visible.
// This rescaling will also make possible to visualize the negative values
// even if we save the difference image in a file format that only support
// unsigned pixel values\footnote{This is the case of PNG, BMP, JPEG and
// TIFF among other common file formats.}. We also reduce the
// \code{DefaultPixelValue} to ``1'' in order to prevent that value from
// absorbing the dynamic range of the differences between the two images.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::RescaleIntensityImageFilter<
FixedImageType,
OutputImageType > RescalerType;
RescalerType::Pointer intensityRescaler = RescalerType::New();
intensityRescaler->SetInput( difference->GetOutput() );
intensityRescaler->SetOutputMinimum( 0 );
intensityRescaler->SetOutputMaximum( 255 );
resampler->SetDefaultPixelValue( 1 );
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Its output can be passed to another writer.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
WriterType::Pointer writer2 = WriterType::New();
writer2->SetInput( intensityRescaler->GetOutput() );
// Software Guide : EndCodeSnippet
if( argc > 4 )
{
writer2->SetFileName( argv[4] );
writer2->Update();
}
// Software Guide : BeginLatex
//
// For the purpose of comparison, the difference between the fixed image and
// the moving image before registration can also be computed by simply
// setting the transform to an identity transform. Note that the resampling
// is still necessary because the moving image does not necessarily have the
// same spacing, origin and number of pixels as the fixed image. Therefore a
// pixel-by-pixel operation cannot in general be performed. The resampling
// process with an identity transform will ensure that we have a
// representation of the moving image in the grid of the fixed image.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
TransformType::Pointer identityTransform = TransformType::New();
identityTransform->SetIdentity();
resampler->SetTransform( identityTransform );
// Software Guide : EndCodeSnippet
if( argc > 5 )
{
writer2->SetFileName( argv[5] );
writer2->Update();
}
// Software Guide : BeginLatex
//
// The complete pipeline structure of the current example is presented in
// Figure~\ref{fig:ImageRegistration1Pipeline}. The components of the
// registration method are depicted as well. Figure
// \ref{fig:ImageRegistration1Output} (left) shows the result of resampling
// the moving image in order to map it onto the fixed image space. The top
// and right borders of the image appear in the gray level selected with the
// \code{SetDefaultPixelValue()} in the ResampleImageFilter. The center
// image shows the difference between the fixed image and the original
// moving image. That is, the difference before the registration is
// performed. The right image shows the difference between the fixed image
// and the transformed moving image. That is, after the registration has
// been performed. Both difference images have been rescaled in intensity
// in order to highlight those pixels where differences exist. Note that
// the final registration is still off by a fraction of a pixel, which
// results in bands around edges of anatomical structures to appear in the
// difference image. A perfect registration would have produced a null
// difference image.
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// \begin{figure}
// \center
// \includegraphics[height=0.44\textwidth]{ImageRegistration1TraceTranslations}
// \includegraphics[height=0.44\textwidth]{ImageRegistration1TraceMetric}
// \itkcaption[Trace of translations and metrics during registration]{The sequence
// of translations and metric values at each iteration of the optimizer.}
// \label{fig:ImageRegistration1Trace}
// \end{figure}
//
// It is always useful to keep in mind that registration is essentially an
// optimization problem. Figure \ref{fig:ImageRegistration1Trace} helps to
// reinforce this notion by showing the trace of translations and values of
// the image metric at each iteration of the optimizer. It can be seen from
// the top figure that the step length is reduced progressively as the
// optimizer gets closer to the metric extrema. The bottom plot clearly
// shows how the metric value decreases as the optimization advances. The
// log plot helps to highlight the normal oscillations of the optimizer
// around the extrema value.
//
// Software Guide : EndLatex
return EXIT_SUCCESS;
}