ITK  5.4.0 Insight Toolkit
Examples/Filtering/SigmoidImageFilter.cxx
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// Software Guide : BeginCommandLineArgs
// INPUTS: {BrainProtonDensitySlice.png}
// OUTPUTS: {SigmoidImageFilterOutput.png}
// ARGUMENTS: 10 240 10 170
// Software Guide : EndCommandLineArgs
// Software Guide : BeginLatex
//
// The \doxygen{SigmoidImageFilter} is commonly used as an intensity
// transform. It maps a specific range of intensity values into a new
// intensity range by making a very smooth and continuous transition in the
// borders of the range. Sigmoids are widely used as a mechanism for
// focusing attention on a particular set of values and progressively
// attenuating the values outside that range. In order to extend the
// flexibility of the Sigmoid filter, its implementation in ITK includes four
// parameters that can be tuned to select its input and output intensity
// ranges. The following equation represents the Sigmoid intensity
// transformation, applied pixel-wise.
//
//
// I' = (Max-Min)\cdot \frac{1}{\left(1+e^{-\left(\frac{ I - \beta }{\alpha }
// \right)} \right)} + Min
//
// In the equation above, $I$ is the intensity of the input pixel, $I'$ the
// intensity of the output pixel, $Min,Max$ are the minimum and maximum
// values of the output image, $\alpha$ defines the width of the input
// intensity range, and $\beta$ defines the intensity around which the range
// is centered. Figure~\ref{fig:SigmoidParameters} illustrates the
// significance of each parameter.
//
// \begin{figure} \center
// \includegraphics[width=0.44\textwidth]{SigmoidParameterAlpha}
// \includegraphics[width=0.44\textwidth]{SigmoidParameterBeta}
// \itkcaption[Sigmoid Parameters]{Effects of the various parameters in the
// SigmoidImageFilter. The alpha parameter defines the width of the intensity
// window. The beta parameter defines the center of the intensity window.}
// \label{fig:SigmoidParameters} \end{figure}
//
// This filter will work on images of any dimension and will take advantage
// of multiple processors when available.
//
// \index{itk::SigmoidImageFilter }
//
// Software Guide : EndLatex
#include "itkImage.h"
// Software Guide : BeginLatex
//
// The header file corresponding to this filter should be included first.
//
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
int
main(int argc, char * argv[])
{
if (argc < 7)
{
std::cerr << "Usage: " << std::endl;
std::cerr << argv[0] << " inputImageFile outputImageFile";
std::cerr << " OutputMin OutputMax SigmoidAlpha SigmoidBeta" << std::endl;
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// Then pixel and image types for the filter input and output must be
// defined.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using InputPixelType = unsigned char;
using OutputPixelType = unsigned char;
using InputImageType = itk::Image<InputPixelType, 2>;
using OutputImageType = itk::Image<OutputPixelType, 2>;
// Software Guide : EndCodeSnippet
auto writer = WriterType::New();
writer->SetFileName(argv[2]);
// Software Guide : BeginLatex
//
// Using the image types, we instantiate the filter type
// and create the filter object.
//
// \index{itk::SigmoidImageFilter!instantiation}
// \index{itk::SigmoidImageFilter!New()}
// \index{itk::SigmoidImageFilter!Pointer}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using SigmoidFilterType =
auto sigmoidFilter = SigmoidFilterType::New();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The minimum and maximum values desired in the output are defined using
// the methods \code{SetOutputMinimum()} and \code{SetOutputMaximum()}.
//
// \index{itk::SigmoidImageFilter!SetOutputMaximum()}
// \index{itk::SigmoidImageFilter!SetOutputMinimum()}
//
// Software Guide : EndLatex
const OutputPixelType outputMinimum = std::stoi(argv[3]);
const OutputPixelType outputMaximum = std::stoi(argv[4]);
// Software Guide : BeginCodeSnippet
sigmoidFilter->SetOutputMinimum(outputMinimum);
sigmoidFilter->SetOutputMaximum(outputMaximum);
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The coefficients $\alpha$ and $\beta$ are set with the methods
// \code{SetAlpha()} and \code{SetBeta()}. Note that $\alpha$ is
// proportional to the width of the input intensity window. As rule of
// thumb, we may say that the window is the interval $[-3\alpha, 3\alpha]$.
// The boundaries of the intensity window are not sharp. The $\alpha$
// curve approaches its extrema smoothly, as shown in
// the same terms as when taking a range in a population of measures by
// defining an interval of $[-3 \sigma, +3 \sigma]$ around the population
// mean.
//
// \index{itk::SigmoidImageFilter!SetAlpha()}
// \index{itk::SigmoidImageFilter!SetBeta()}
//
// Software Guide : EndLatex
const double alpha = std::stod(argv[5]);
const double beta = std::stod(argv[6]);
// Software Guide : BeginCodeSnippet
sigmoidFilter->SetAlpha(alpha);
sigmoidFilter->SetBeta(beta);
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The input to the SigmoidImageFilter can be taken from any other filter,
// such as an image file reader, for example. The output can be passed down
// the pipeline to other filters, like an image file writer. An
// \code{Update()} call on any downstream filter will trigger the execution
// of the Sigmoid filter.
//
// \index{itk::SigmoidImageFilter!SetInput()}
// \index{itk::SigmoidImageFilter!GetOutput()}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
writer->SetInput(sigmoidFilter->GetOutput());
writer->Update();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// \begin{figure}
// \center
// \includegraphics[width=0.44\textwidth]{BrainProtonDensitySlice}
// \includegraphics[width=0.44\textwidth]{SigmoidImageFilterOutput}
// \itkcaption[Effect of the Sigmoid filter.]{Effect of the Sigmoid filter
// on a slice from a MRI proton density brain image.}
// \label{fig:SigmoidImageFilterOutput}
// \end{figure}
//
// Figure~\ref{fig:SigmoidImageFilterOutput} illustrates the effect of this
// filter on a slice of MRI brain image using the following parameters.
//
// \begin{itemize}
// \item Minimum = 10
// \item Maximum = 240
// \item $\alpha$ = 10
// \item $\beta$ = 170
// \end{itemize}
//
// As can be seen from the figure, the intensities of the white matter
// were expanded in their dynamic range, while intensity values lower than
// $\beta - 3 \alpha$ and higher than $\beta + 3\alpha$ became
// progressively mapped to the minimum and maximum output values. This is
// the way in which a Sigmoid can be used for performing smooth intensity
// windowing.
//
// Note that both $\alpha$ and $\beta$ can be positive and negative. A
// negative $\alpha$ will have the effect of \emph{negating} the image.
// This is illustrated on the left side of
// Figure~\ref{fig:SigmoidParameters}. An application of the Sigmoid filter
// as preprocessing for segmentation is presented in
// Section~\ref{sec:FastMarchingImageFilter}.
//
// Sigmoid curves are common in the natural world. They represent the
// plot of sensitivity to a stimulus. They are also the integral curve of
// the Gaussian and, therefore, appear naturally as the response to signals
// whose distribution is Gaussian.
//
// Software Guide : EndLatex
return EXIT_SUCCESS;
}
itkSigmoidImageFilter.h
itkImage.h
itk::SigmoidImageFilter
Computes the sigmoid function pixel-wise.
Definition: itkSigmoidImageFilter.h:144