ITK  4.13.0 Insight Segmentation and Registration 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
typedef float InputPixelType;
typedef float OutputPixelType;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The input and output image types are instantiated using the pixel types.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
typedef itk::Image< InputPixelType, 2 > InputImageType;
typedef itk::Image< OutputPixelType, 2 > OutputImageType;
// 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
InputImageType, OutputImageType > 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
filterX->SetOrder( FilterType::ZeroOrder );
filterY->SetOrder( FilterType::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.
//
//
// \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 = atof( 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
typedef unsigned char WritePixelType;
typedef itk::Image< WritePixelType, 2 > WriteImageType;
OutputImageType, WriteImageType > 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;
}