ITK  6.0.0 Insight Toolkit
Examples/Filtering/SecondDerivativeRecursiveGaussianImageFilter.cxx
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// Software Guide : BeginLatex
//
// This example illustrates how to compute second derivatives of
// a 3D image using the \doxygen{RecursiveGaussianImageFilter}.
//
// It's good to be able to compute the raw derivative without any smoothing,
// but this can be problematic in a medical imaging scenario, when images
// will often have a certain amount of noise. It's almost always more
// desirable to include a smoothing step first, where an image is convolved
// with a Gaussian kernel in whichever directions the user desires a
// derivative. The nature of the Gaussian kernel makes it easy to combine
// these two steps into one, using an infinite impulse response (IIR) filter.
// In this example, all the second derivatives are computed independently in
// the same way, as if they were intended to be used for building the Hessian
// matrix of the image (a square matrix of second-order derivatives of an
// image, which is useful in many image processing techniques).
//
// Software Guide : EndLatex
// Software Guide : BeginLatex
//
// First, we will include the relevant header files: the
// itkRecursiveGaussianImageFilter, the image reader, writer, and duplicator.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
#include <string>
// Software Guide : EndCodeSnippet
int
main(int argc, char * argv[])
{
if (argc < 3)
{
std::cerr << "Usage: " << std::endl;
std::cerr << argv[0] << " inputImage outputPrefix [sigma] " << std::endl;
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// Next, we declare our pixel type and output pixel type to be floats, and
// our image dimension to be $3$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using PixelType = float;
using OutputPixelType = float;
constexpr unsigned int Dimension = 3;
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Using these definitions, define the image types, reader and writer
// types, and duplicator types, which are templated over the pixel types
// and dimension. Then, instantiate the reader, writer, and duplicator
// with the \code{New()} method.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using OutputImageType = itk::Image<OutputPixelType, Dimension>;
using DuplicatorType = itk::ImageDuplicator<OutputImageType>;
auto writer = WriterType::New();
auto duplicator = DuplicatorType::New();
// Software Guide : EndCodeSnippet
std::string outputPrefix = argv[2];
std::string outputFileName;
try
{
}
catch (const itk::ExceptionObject & excp)
{
std::cerr << "Problem reading the input file" << std::endl;
std::cerr << excp << std::endl;
return EXIT_FAILURE;
}
// Software Guide : BeginLatex
//
// Here we create three new filters. For each derivative we take, we will
// want to smooth in that direction first. So after the filters are
// created, each is given a dimension, and set to (in this example) the
// same sigma. Note that here, $\sigma$ represents the standard deviation,
// whereas the \doxygen{DiscreteGaussianImageFilter} exposes the
// \code{SetVariance} method.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
auto ga = FilterType::New();
auto gb = FilterType::New();
auto gc = FilterType::New();
ga->SetDirection(0);
gb->SetDirection(1);
gc->SetDirection(2);
if (argc > 3)
{
const float sigma = std::stod(argv[3]);
ga->SetSigma(sigma);
gb->SetSigma(sigma);
gc->SetSigma(sigma);
}
// Software Guide: EndCodeSnippet
// Software Guide : BeginLatex
//
// First we will compute the second derivative of the $z$-direction.
// In order to do this, we smooth in the $x$- and $y$- directions, and
// finally smooth and compute the derivative in the $z$-direction. Taking
// the zero-order derivative is equivalent to simply smoothing in that
// direction. This result is commonly notated $I_{zz}$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
ga->SetZeroOrder();
gb->SetZeroOrder();
gc->SetSecondOrder();
ga->SetInput(inputImage);
gb->SetInput(ga->GetOutput());
gc->SetInput(gb->GetOutput());
duplicator->SetInputImage(gc->GetOutput());
gc->Update();
duplicator->Update();
ImageType::Pointer Izz = duplicator->GetOutput();
// Software Guide: EndCodeSnippet
writer->SetInput(Izz);
outputFileName = outputPrefix + "-Izz.mhd";
writer->SetFileName(outputFileName.c_str());
writer->Update();
// Software Guide : BeginLatex
//
// Recall that \code{gc} is the filter responsible for taking the second
// derivative. We can now take advantage of the pipeline architecture and,
// without much hassle, switch the direction of \code{gc} and \code{gb},
// so that \code{gc} now takes the derivatives in the $y$-direction. Now we
// only need to call \code{Update()} on \code{gc} to re-run the entire
// pipeline from \code{ga} to \code{gc}, obtaining the second-order
// derivative in the $y$-direction, which is commonly notated $I_{yy}$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
gc->SetDirection(1); // gc now works along Y
gb->SetDirection(2); // gb now works along Z
gc->Update();
duplicator->Update();
ImageType::Pointer Iyy = duplicator->GetOutput();
// Software Guide : EndCodeSnippet
writer->SetInput(Iyy);
outputFileName = outputPrefix + "-Iyy.mhd";
writer->SetFileName(outputFileName.c_str());
writer->Update();
// Software Guide : BeginLatex
//
// Now we switch the directions of \code{gc} with that of \code{ga} in
// order to take the derivatives in the $x$-direction. This will give us
// $I_{xx}$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
gc->SetDirection(0); // gc now works along X
ga->SetDirection(1); // ga now works along Y
gc->Update();
duplicator->Update();
ImageType::Pointer Ixx = duplicator->GetOutput();
// Software Guide : EndCodeSnippet
writer->SetInput(Ixx);
outputFileName = outputPrefix + "-Ixx.mhd";
writer->SetFileName(outputFileName.c_str());
writer->Update();
// Software Guide : BeginLatex
//
// Now we can reset the directions to their original values, and compute
// first derivatives in different directions. Since we set both \code{gb}
// and \code{gc} to compute first derivatives, and \code{ga} to zero-order
// (which is only smoothing) we will obtain $I_{yz}$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
ga->SetDirection(0);
gb->SetDirection(1);
gc->SetDirection(2);
ga->SetZeroOrder();
gb->SetFirstOrder();
gc->SetFirstOrder();
gc->Update();
duplicator->Update();
ImageType::Pointer Iyz = duplicator->GetOutput();
// Software Guide : EndCodeSnippet
writer->SetInput(Iyz);
outputFileName = outputPrefix + "-Iyz.mhd";
writer->SetFileName(outputFileName.c_str());
writer->Update();
// Software Guide : BeginLatex
//
// Here is how you may easily obtain $I_{xz}$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
ga->SetDirection(1);
gb->SetDirection(0);
gc->SetDirection(2);
ga->SetZeroOrder();
gb->SetFirstOrder();
gc->SetFirstOrder();
gc->Update();
duplicator->Update();
ImageType::Pointer Ixz = duplicator->GetOutput();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// For the sake of completeness, here is how you may compute
// $I_{xz}$ and $I_{xy}$.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
writer->SetInput(Ixz);
outputFileName = outputPrefix + "-Ixz.mhd";
writer->SetFileName(outputFileName.c_str());
writer->Update();
ga->SetDirection(2);
gb->SetDirection(0);
gc->SetDirection(1);
ga->SetZeroOrder();
gb->SetFirstOrder();
gc->SetFirstOrder();
gc->Update();
duplicator->Update();
ImageType::Pointer Ixy = duplicator->GetOutput();
writer->SetInput(Ixy);
outputFileName = outputPrefix + "-Ixy.mhd";
writer->SetFileName(outputFileName.c_str());
writer->Update();
// Software Guide : EndCodeSnippet
return EXIT_SUCCESS;
}
Pointer
SmartPointer< Self > Pointer
itkRecursiveGaussianImageFilter.h
itk::ImageDuplicator
A helper class which creates an image which is perfect copy of the input image.
Definition: itkImageDuplicator.h:54
Data source that reads image data from a single file.
itk::ImageFileWriter
Writes image data to a single file.
Definition: itkImageFileWriter.h:90
itkImageFileWriter.h
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
New
static Pointer New()
itk::GTest::TypedefsAndConstructors::Dimension2::Dimension
constexpr unsigned int Dimension
Definition: itkGTestTypedefsAndConstructors.h:44
itkImageDuplicator.h