ITK  5.3.0 Insight Toolkit
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"
// Software Guide : BeginLatex
//
// The first step required to use this filter is to include its header file.
//
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// 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
// 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 =
// Software Guide : EndCodeSnippet
// 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
FilterType::Pointer filterX = FilterType::New();
FilterType::Pointer 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
// 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.
//
//
// \frac{ 1 }{ \sigma \sqrt{ 2 \pi } }
//
//
// 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.
//
//
// \frac{ 1 }{ \sigma^2 \sqrt{ 2 \pi } }
//
//
// 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
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 =
RescaleFilterType::Pointer rescaler = RescaleFilterType::New();
rescaler->SetOutputMinimum(0);
rescaler->SetOutputMaximum(255);
WriterType::Pointer 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;
}
itkRecursiveGaussianImageFilter.h
itkImage.h
Data source that reads image data from a single file.
itk::ImageFileWriter
Writes image data to a single file.
Definition: itkImageFileWriter.h:88
itkRescaleIntensityImageFilter.h
itkImageFileWriter.h
itk::RecursiveGaussianImageFilterEnums::GaussianOrder::ZeroOrder
itk::RescaleIntensityImageFilter
Applies a linear transformation to the intensity levels of the input Image.
Definition: itkRescaleIntensityImageFilter.h:147
itk::Image
Templated n-dimensional image class.
Definition: itkImage.h:88
itk::RecursiveGaussianImageFilter
Base class for computing IIR convolution with an approximation of a Gaussian kernel.
Definition: itkRecursiveGaussianImageFilter.h:100