itkRecursiveGaussianImageFilter.h

/*=========================================================================
 *
 *  Copyright NumFOCUS
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         https://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
#ifndef itkRecursiveGaussianImageFilter_h
#define itkRecursiveGaussianImageFilter_h

#include "itkRecursiveSeparableImageFilter.h"
#include "ITKSmoothingExport.h"

namespace itk
{
/** \class RecursiveGaussianImageFilterEnums
 * \brief Contains all enum classes used by RecursiveGaussianImageFilter class.
 * \ingroup ITKSmoothing
 */
class RecursiveGaussianImageFilterEnums
{
public:
  /** \class GaussianOrder
* \ingroup ITKSmoothing
* Enum type that indicates if the filter applies the equivalent operation
of convolving with a gaussian, first derivative of a gaussian or the
second derivative of a gaussian.  */
  enum class GaussianOrder : uint8_t
  {
    ZeroOrder = 0,
    FirstOrder = 1,
    SecondOrder = 2
  };
};
// Define how to print enumeration
extern ITKSmoothing_EXPORT std::ostream &
                           operator<<(std::ostream & out, const RecursiveGaussianImageFilterEnums::GaussianOrder value);

using GaussianOrderEnum = RecursiveGaussianImageFilterEnums::GaussianOrder;
#if !defined(ITK_LEGACY_REMOVE)
/** Enables backwards compatibility for enum values */
using OrderEnumType = GaussianOrderEnum;
using EnumGaussianOrderType = GaussianOrderEnum;
// We need to expose the enum values at the class level
// for backwards compatibility
static constexpr GaussianOrderEnum ZeroOrder = GaussianOrderEnum::ZeroOrder;
static constexpr GaussianOrderEnum FirstOrder = GaussianOrderEnum::FirstOrder;
static constexpr GaussianOrderEnum SecondOrder = GaussianOrderEnum::SecondOrder;
#endif

/**
 * \class RecursiveGaussianImageFilter
 * \brief Base class for computing IIR convolution with an approximation of a  Gaussian kernel.
 *
 *    \f[
 *      \frac{ 1 }{ \sigma \sqrt{ 2 \pi } } \exp{ \left( - \frac{x^2}{ 2 \sigma^2 } \right) }
 *    \f]
 *
 * RecursiveGaussianImageFilter is the base class for recursive filters that
 * approximate convolution with the Gaussian kernel.
 * This class implements the recursive filtering
 * method proposed by R.Deriche in IEEE-PAMI
 * Vol.12, No.1, January 1990, pp 78-87,
 * "Fast Algorithms for Low-Level Vision"
 *
 * Details of the implementation are described in the technical report:
 * R. Deriche, "Recursively Implementing The Gaussian and Its Derivatives",
 * INRIA, 1993, ftp://ftp.inria.fr/INRIA/tech-reports/RR/RR-1893.ps.gz
 *
 * Further improvements of the algorithm are described in:
 * G. Farnebäck & C.-F. Westin, "Improving Deriche-style Recursive Gaussian
 * Filters". J Math Imaging Vis 26, 293–299 (2006).
 * https://doi.org/10.1007/s10851-006-8464-z
 *
 * As compared to itk::DiscreteGaussianImageFilter, this filter tends
 * to be faster for large kernels, and it can take the derivative
 * of the blurred image in one step.  Also, note that we have
 * itk::RecursiveGaussianImageFilter::SetSigma(), but
 * itk::DiscreteGaussianImageFilter::SetVariance().
 *
 * \ingroup ImageEnhancement SingleThreaded
 * \see DiscreteGaussianImageFilter
 * \ingroup ITKSmoothing
 *
 * \sphinx
 * \sphinxexample{Filtering/Smoothing/FindHigherDerivativesOfImage,Find Higher Derivatives Of Image}
 * \endsphinx
 */
template <typename TInputImage, typename TOutputImage = TInputImage>
class ITK_TEMPLATE_EXPORT RecursiveGaussianImageFilter : public RecursiveSeparableImageFilter<TInputImage, TOutputImage>
{
public:
  ITK_DISALLOW_COPY_AND_MOVE(RecursiveGaussianImageFilter);

  /** Standard class type aliases. */
  using Self = RecursiveGaussianImageFilter;
  using Superclass = RecursiveSeparableImageFilter<TInputImage, TOutputImage>;
  using Pointer = SmartPointer<Self>;
  using ConstPointer = SmartPointer<const Self>;

  using typename Superclass::RealType;
  using typename Superclass::ScalarRealType;

  /** Method for creation through the object factory. */
  itkNewMacro(Self);

  /** Type macro that defines a name for this class */
  itkTypeMacro(RecursiveGaussianImageFilter, RecursiveSeparableImageFilter);

  /** Set/Get the Sigma, measured in world coordinates, of the Gaussian
   * kernel.  The default is 1.0. An exception will be generated if
   * the Sigma value is less than or equal to zero.
   */
  itkGetConstMacro(Sigma, ScalarRealType);
  itkSetMacro(Sigma, ScalarRealType);

  /** Type of the output image */
  using OutputImageType = TOutputImage;

#if !defined(ITK_LEGACY_REMOVE)
  /** Enables backwards compatibility for enum values */
  using OrderEnumType = GaussianOrderEnum;
  using EnumGaussianOrderType = GaussianOrderEnum;
  // We need to expose the enum values at the class level
  // for backwards compatibility
  static constexpr GaussianOrderEnum ZeroOrder = GaussianOrderEnum::ZeroOrder;
  static constexpr GaussianOrderEnum FirstOrder = GaussianOrderEnum::FirstOrder;
  static constexpr GaussianOrderEnum SecondOrder = GaussianOrderEnum::SecondOrder;
#endif
  /** Set/Get the flag for normalizing the gaussian over scale-space.

      This flag enables the analysis of the differential shape of
      features independent of their size ( both pixels and physical
      size ). Following the notation of Tony Lindeberg:

      Let \f[ L(x; t) = g(x; t) \ast f(x) \f] be the scale-space
      representation of image \f[ f(x) \f]
      where \f[ g(x; t) = \frac{1}{ \sqrt{ 2 \pi t}  }  \exp{ \left( -\frac{x^2}{ 2 t } \right) } \f] is
      the Gaussian function and \f[\ast\f] denotes convolution. This
      is a change from above with \f[ t = \sigma^2 \f].

      Then the normalized derivative operator for normalized
      coordinates across scale is:

      \f[
            \partial_\xi = \sqrt{t} \partial_x
      \f]

      The resulting scaling factor is
      \f[
            \sigma^N
      \f]
      where N is the order of the derivative.


      When this flag is ON the filter will be normalized in such a way
      that the values of derivatives are not biased by the size of the
      object. That is to say the maximum value a feature reaches across
      scale is independent of the scale of the object.

      For analyzing an image across scale-space you want to enable
      this flag.  It is disabled by default.

      \note Not all scale space axioms are satisfied by this filter,
      some are only approximated. Particularly, at fine scales ( say
      less than 1 pixel ) other methods such as a discrete Gaussian
      kernel should be considered.
     */
  itkSetMacro(NormalizeAcrossScale, bool);
  itkGetConstMacro(NormalizeAcrossScale, bool);
  itkBooleanMacro(NormalizeAcrossScale);

  /** Set/Get the Order of the Gaussian to convolve with.
      \li ZeroOrder is equivalent to convolving with a Gaussian.  This
      is the default.
      \li FirstOrder is equivalent to convolving with the first derivative of a Gaussian.
      \li SecondOrder is equivalent to convolving with the second derivative of a Gaussian.
    */
  itkSetMacro(Order, GaussianOrderEnum);
  itkGetConstMacro(Order, GaussianOrderEnum);

  /** Explicitly set a zeroth order derivative. */
  void
  SetZeroOrder();

  /** Explicitly set a first order derivative. */
  void
  SetFirstOrder();

  /** Explicitly set a second order derivative. */
  void
  SetSecondOrder();

protected:
  RecursiveGaussianImageFilter();
  ~RecursiveGaussianImageFilter() override = default;
  void
  PrintSelf(std::ostream & os, Indent indent) const override;

  /** Set up the coefficients of the filter to approximate a specific kernel.
   * Here it is used to approximate a Gaussian or one of its
   * derivatives. Parameter is the spacing along the dimension to
   * filter. */
  void
  SetUp(ScalarRealType spacing) override;

  /* See superclass for doxygen. This method adds the additional check
   * that sigma is greater than zero. */
  void
  VerifyPreconditions() ITKv5_CONST override;

private:
  /** Compute the N coefficients in the recursive filter. */
  void
  ComputeNCoefficients(ScalarRealType   sigmad,
                       ScalarRealType   A1,
                       ScalarRealType   B1,
                       ScalarRealType   W1,
                       ScalarRealType   L1,
                       ScalarRealType   A2,
                       ScalarRealType   B2,
                       ScalarRealType   W2,
                       ScalarRealType   L2,
                       ScalarRealType & N0,
                       ScalarRealType & N1,
                       ScalarRealType & N2,
                       ScalarRealType & N3,
                       ScalarRealType & SN,
                       ScalarRealType & DN,
                       ScalarRealType & EN);

  /** Compute the D coefficients in the recursive filter. */
  void
  ComputeDCoefficients(ScalarRealType   sigmad,
                       ScalarRealType   W1,
                       ScalarRealType   L1,
                       ScalarRealType   W2,
                       ScalarRealType   L2,
                       ScalarRealType & SD,
                       ScalarRealType & DD,
                       ScalarRealType & ED);

  /** Compute the M coefficients and the boundary coefficients in the
   * recursive filter. */
  void
  ComputeRemainingCoefficients(bool symmetric);

  /** Sigma of the gaussian kernel. */
  ScalarRealType m_Sigma;

  /** Normalize the image across scale space */
  bool m_NormalizeAcrossScale;

  GaussianOrderEnum m_Order;
};
} // end namespace itk

#ifndef ITK_MANUAL_INSTANTIATION
#  include "itkRecursiveGaussianImageFilter.hxx"
#endif

#endif