Examples/Filtering/SmoothingRecursiveGaussianImageFilter.cxx

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//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {SmoothingRecursiveGaussianImageFilterOutput3.png}
//    ARGUMENTS:    3
//  Software Guide : EndCommandLineArgs
//  Software Guide : BeginCommandLineArgs
//    INPUTS:  {BrainProtonDensitySlice.png}
//    OUTPUTS: {SmoothingRecursiveGaussianImageFilterOutput5.png}
//    ARGUMENTS:    5
//  Software Guide : EndCommandLineArgs
 
//  Software Guide : BeginLatex
//
//  The classical method of smoothing an image by convolution with a Gaussian
//  kernel has the drawback that it is slow when the standard deviation
//  $\sigma$ of the Gaussian is large.  This is due to the larger size of the
//  kernel, which results in a higher number of computations per pixel.
//
//  The \doxygen{RecursiveGaussianImageFilter} implements an approximation of
//  convolution with the Gaussian and its derivatives by using
//  IIR\footnote{Infinite Impulse Response} filters. In practice this filter
//  requires a constant number of operations for approximating the
//  convolution, regardless of the $\sigma$ value
//  \cite{Deriche1990,Deriche1993}.
//
//  \index{itk::RecursiveGaussianImageFilter}
//
//  Software Guide : EndLatex
 
 
#include "itkImage.h"
#include "itkImageFileReader.h"
#include "itkImageFileWriter.h"
#include "itkRescaleIntensityImageFilter.h"
 
//  Software Guide : BeginLatex
//
//  The first step required to use this filter is to include its header file.
//
//  \index{itk::RecursiveGaussianImageFilter!header}
//
//  Software Guide : EndLatex
 
// Software Guide : BeginCodeSnippet
#include "itkRecursiveGaussianImageFilter.h"
// Software Guide : EndCodeSnippet
 
 
int
main(int argc, char * argv[])
{
  if (argc < 4)
  {
    std::cerr << "Usage: " << std::endl;
    std::cerr << argv[0] << "  inputImageFile  outputImageFile  sigma "
              << std::endl;
    return EXIT_FAILURE;
  }
 
 
  //  Software Guide : BeginLatex
  //
  //  Types should be selected on the desired input and output pixel types.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using InputPixelType = float;
  using OutputPixelType = float;
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  The input and output image types are instantiated using the pixel types.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using InputImageType = itk::Image<InputPixelType, 2>;
  using OutputImageType = itk::Image<OutputPixelType, 2>;
  // Software Guide : EndCodeSnippet
 
 
  using ReaderType = itk::ImageFileReader<InputImageType>;
 
 
  //  Software Guide : BeginLatex
  //
  //  The filter type is now instantiated using both the input image and the
  //  output image types.
  //
  //  \index{itk::RecursiveGaussianImageFilter!Instantiation}
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  using FilterType =
    itk::RecursiveGaussianImageFilter<InputImageType, OutputImageType>;
  // Software Guide : EndCodeSnippet
 
 
  auto reader = ReaderType::New();
  reader->SetFileName(argv[1]);
 
 
  //  Software Guide : BeginLatex
  //
  //  This filter applies the approximation of the convolution along a single
  //  dimension. It is therefore necessary to concatenate several of these
  //  filters to produce smoothing in all directions.  In this example, we
  //  create a pair of filters since we are processing a $2D$ image.  The
  //  filters are created by invoking the \code{New()} method and assigning
  //  the result to a \doxygen{SmartPointer}.
  //
  //  \index{itk::RecursiveGaussianImageFilter!New()}
  //  \index{itk::RecursiveGaussianImageFilter!Pointer}
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  auto filterX = FilterType::New();
  auto filterY = FilterType::New();
  // Software Guide : EndCodeSnippet
 
  //  Software Guide : BeginLatex
  //
  //  Since each one of the newly created filters has the potential to perform
  //  filtering along any dimension, we have to restrict each one to a
  //  particular direction. This is done with the \code{SetDirection()}
  //  method.
  //
  //  \index{RecursiveGaussianImageFilter!SetDirection()}
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  filterX->SetDirection(0); // 0 --> X direction
  filterY->SetDirection(1); // 1 --> Y direction
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  The \doxygen{RecursiveGaussianImageFilter} can approximate the
  //  convolution with the Gaussian or with its first and second
  //  derivatives. We select one of these options by using the
  //  \code{SetOrder()} method. Note that the argument is an \code{enum} whose
  //  values can be \code{ZeroOrder}, \code{FirstOrder} and
  //  \code{SecondOrder}. For example, to compute the $x$ partial derivative
  //  we should select \code{FirstOrder} for $x$ and \code{ZeroOrder} for $y$.
  //  Here we want only to smooth in $x$ and $y$, so we select
  //  \code{ZeroOrder} in both directions.
  //
  //  \index{RecursiveGaussianImageFilter!SetOrder()}
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  filterX->SetOrder(itk::GaussianOrderEnum::ZeroOrder);
  filterY->SetOrder(itk::GaussianOrderEnum::ZeroOrder);
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  There are two typical ways of normalizing Gaussians depending on their
  //  application. For scale-space analysis it is desirable to use a
  //  normalization that will preserve the maximum value of the input. This
  //  normalization is represented by the following equation.
  //
  //  \begin{equation}
  //          \frac{ 1 }{ \sigma  \sqrt{ 2 \pi } }
  //  \end{equation}
  //
  //  In applications that use the Gaussian as a solution of the diffusion
  //  equation it is desirable to use a normalization that preserve the
  //  integral of the signal. This last approach can be seen as a conservation
  //  of mass principle. This is represented by the following equation.
  //
  //  \begin{equation}
  //          \frac{ 1 }{ \sigma^2  \sqrt{ 2 \pi } }
  //  \end{equation}
  //
  //  The \doxygen{RecursiveGaussianImageFilter} has a boolean flag that
  //  allows users to select between these two normalization options.
  //  Selection is done with the method \code{SetNormalizeAcrossScale()}.
  //  Enable this flag to analyzing an image across scale-space.  In the
  //  current example, this setting has no impact because we are actually
  //  renormalizing the output to the dynamic range of the reader, so we
  //  simply disable the flag.
  //
  //  \index{RecursiveGaussianImageFilter!SetNormalizeAcrossScale()}
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  filterX->SetNormalizeAcrossScale(false);
  filterY->SetNormalizeAcrossScale(false);
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  The input image can be obtained from the output of another
  //  filter. Here, an image reader is used as the source. The image is passed
  //  to the $x$ filter and then to the $y$ filter. The reason for keeping
  //  these two filters separate is that it is usual in scale-space
  //  applications to compute not only the smoothing but also combinations of
  //  derivatives at different orders and smoothing. Some factorization is
  //  possible when separate filters are used to generate the intermediate
  //  results. Here this capability is less interesting, though, since we only
  //  want to smooth the image in all directions.
  //
  //  Software Guide : EndLatex
 
  // Software Guide : BeginCodeSnippet
  filterX->SetInput(reader->GetOutput());
  filterY->SetInput(filterX->GetOutput());
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  It is now time to select the $\sigma$ of the Gaussian used to smooth the
  //  data.  Note that $\sigma$ must be passed to both filters and that sigma
  //  is considered to be in millimeters. That is, at the moment of applying
  //  the smoothing process, the filter will take into account the spacing
  //  values defined in the image.
  //
  //  \index{itk::RecursiveGaussianImageFilter!SetSigma()}
  //  \index{SetSigma()!itk::RecursiveGaussianImageFilter}
  //
  //  Software Guide : EndLatex
 
  const double sigma = std::stod(argv[3]);
 
  // Software Guide : BeginCodeSnippet
  filterX->SetSigma(sigma);
  filterY->SetSigma(sigma);
  // Software Guide : EndCodeSnippet
 
 
  //  Software Guide : BeginLatex
  //
  //  Finally the pipeline is executed by invoking the \code{Update()} method.
  //
  //  \index{itk::RecursiveGaussianImageFilter!Update()}
  //
  //  Software Guide : EndLatex
 
 
  // Software Guide : BeginCodeSnippet
  filterY->Update();
  // Software Guide : EndCodeSnippet
 
 
  using WritePixelType = unsigned char;
  using WriteImageType = itk::Image<WritePixelType, 2>;
  using RescaleFilterType =
    itk::RescaleIntensityImageFilter<OutputImageType, WriteImageType>;
 
  auto rescaler = RescaleFilterType::New();
 
  rescaler->SetOutputMinimum(0);
  rescaler->SetOutputMaximum(255);
  using WriterType = itk::ImageFileWriter<WriteImageType>;
  auto writer = WriterType::New();
  writer->SetFileName(argv[2]);
 
  rescaler->SetInput(filterY->GetOutput());
  writer->SetInput(rescaler->GetOutput());
  writer->Update();
 
 
  //  Software Guide : BeginLatex
  //
  // \begin{figure}
  // \center
  // \includegraphics[width=0.44\textwidth]{SmoothingRecursiveGaussianImageFilterOutput3}
  // \includegraphics[width=0.44\textwidth]{SmoothingRecursiveGaussianImageFilterOutput5}
  // \itkcaption[Output of the SmoothingRecursiveGaussianImageFilter.]{Effect
  // of the SmoothingRecursiveGaussianImageFilter on a slice from a MRI proton
  // density image of the brain.}
  // \label{fig:SmoothingRecursiveGaussianImageFilterInputOutput}
  // \end{figure}
  //
  //  Figure~\ref{fig:SmoothingRecursiveGaussianImageFilterInputOutput}
  //  illustrates the effect of this filter on a MRI proton density image of
  //  the brain using
  //  $\sigma$ values of $3$ (left) and $5$ (right).  The figure shows how the
  //  attenuation of noise can be regulated by selecting the appropriate
  //  standard deviation.  This type of scale-tunable filter is suitable for
  //  performing scale-space analysis.
  //
  //  The RecursiveGaussianFilters can also be applied on multi-component
  //  images. For instance, the above filter could have applied with RGBPixel
  //  as the pixel type. Each component is then independently filtered.
  //  However the RescaleIntensityImageFilter will not work on RGBPixels since
  //  it does not mathematically make sense to rescale the output of
  //  multi-component images.
  //
  //  Software Guide : EndLatex
 
 
  return EXIT_SUCCESS;
}