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 *
 *  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 itkCurvatureRegistrationFilter_h
#define itkCurvatureRegistrationFilter_h

#include "itkPDEDeformableRegistrationFilter.h"
#include "itkMeanSquareRegistrationFunction.h"

#if !defined(ITK_USE_CUFFTW) && (defined(ITK_USE_FFTWF) || defined(ITK_USE_FFTWD))
#  include "fftw3.h"

namespace itk
{
/** \class CurvatureRegistrationFilter
 * \brief Deformably register two images using the fast curvature algorithm.
 *
 * CurvatureRegistrationFilter implements the fast (i.e., O(n log n) )
 * registration method described in B. Fischer and J. Modersitzki,
 * "A unified approach to fast image registration and a new curvature
 * based registration technique," Linear Algebra and its Applications,
 * vol. 380, pp. 107-124, 2004.
 *
 * A deformation field is represented as a image whose pixel type is some
 * vector type with at least N elements, where N is the dimension of
 * the fixed image. The vector type must support element access via operator
 * []. It is assumed that the vector elements behave like floating point
 * scalars.
 *
 * This class is templated over the fixed image type, moving image type,
 * the deformation field type, and the images forces function. Fundamentally,
 * any image force function in the PDE framework should work (e.g., mean
 * squares, demons, correlation, mutual information, etc.).
 *
 * The input fixed and moving images are set via methods SetFixedImage
 * and SetMovingImage respectively. An initial deformation field maybe set via
 * SetInitialDisplacementField or SetInput. If no initial field is set,
 * a zero field is used as the initial condition.
 *
 * The output deformation field can be obtained via methods GetOutput
 * or GetDisplacementField.
 *
 * This class makes use of the finite difference solver hierarchy. Update
 * for each iteration is computed in the function class defined by the
 * template parameter TImageForceFunction.
 *
 * The algorithm has three parameters: the number of iteration to be performed,
 * the time step, and the weight of the curvature regularization term in
 * the overall cost function.
 *
 * \warning The algorithm parameters (time step and constraint weight) as
 * given by F&M (dt=100; alpha=0.01) do not seem to work with this implementation.
 * In fact, they seem to be off by orders of magnitude. This may be an
 * effect of different normalization of the image forces, or this implementation
 * may be incorrect. Be aware.
 *
 * \warning This filter assumes that the fixed image type, moving image type
 * and deformation field type all have the same number of dimensions.
 *
 * \warning There is something sketchy going on with the DCT (see FFTW
 * documentation) regarding numerical stability of the "ordinary" DCT.
 * Also, F&M are slightly ambiguous in their use of the DCT operator. So
 * it is quite possible that the implementation of their algorithm is
 * not quite correct. Ultimately, they are saying that the curvature
 * smoother is equivalent to a special low-pass filter that is applied
 * to the DCT coefficients.
 *
 * \note This class was developed with funding from:
 *
 * "CNS Deficits: Interaction of Age and Alcoholism"
 * NIAAA AA05965, PI: A. Pfefferbaum
 *
 * "INIA: Imaging Core"
 * NIAAA AA13521, PI: A. Pfefferbaum
 *
 *
 * \sa CurvatureRegistrationFunction
 * \ingroup DeformableImageRegistration MultiThreaded
 *
 * \author Torsten Rohlfing, SRI International, Neuroscience Program
 * \ingroup ITKPDEDeformableRegistration
 */
template <typename TFixedImage,
          typename TMovingImage,
          typename TDisplacementField,
          typename TImageForceFunction = MeanSquareRegistrationFunction<TFixedImage, TMovingImage, TDisplacementField>>
class ITK_TEMPLATE_EXPORT CurvatureRegistrationFilter
  : public PDEDeformableRegistrationFilter<TFixedImage, TMovingImage, TDisplacementField>
{
public:
  ITK_DISALLOW_COPY_AND_MOVE(CurvatureRegistrationFilter);

  /** Standard class type aliases. */
  using Self = CurvatureRegistrationFilter;
  using Superclass = PDEDeformableRegistrationFilter<TFixedImage, TMovingImage, TDisplacementField>;
  using Pointer = SmartPointer<Self>;
  using ConstPointer = SmartPointer<const Self>;

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

  /** \see LightObject::GetNameOfClass() */
  itkOverrideGetNameOfClassMacro(CurvatureRegistrationFilter);

  /** Inherit types from superclass. */
  using typename Superclass::TimeStepType;

  /** FixedImage image type. */
  using typename Superclass::FixedImageType;
  using typename Superclass::FixedImagePointer;
  static constexpr unsigned int ImageDimension = FixedImageType::ImageDimension;

  /** MovingImage image type. */
  using typename Superclass::MovingImageType;
  using typename Superclass::MovingImagePointer;

  /** Deformation field type. */
  using typename Superclass::DisplacementFieldType;
  using typename Superclass::DisplacementFieldPointer;

  using DisplacementFieldPixelType = typename TDisplacementField::PixelType;
  using DisplacementFieldComponentType = typename DisplacementFieldPixelType::ValueType;
  static constexpr unsigned int DeformationVectorDimension = DisplacementFieldPixelType::Dimension;

#  if defined(ITK_USE_FFTWD)
  // Prefer to use double precision
  using RealTypeDFT = double;
#  else
#    if defined(ITK_USE_FFTWF)
  // Allow to use single precision
#      warning "Using single precision for FFT computations!"
  using RealTypeDFT = double;
#    endif
#  endif

  using DisplacementFieldComponentImageType = Image<RealTypeDFT, TDisplacementField::ImageDimension>;
  using DisplacementFieldComponentImagePointer = typename DisplacementFieldComponentImageType::Pointer;

  /** FiniteDifferenceFunction type. */
  using typename Superclass::FiniteDifferenceFunctionType;

  /** CurvatureRegistrationFilterFunction type. */
  using RegistrationFunctionType = TImageForceFunction;

  /** Set the constraint vs. image forces weight. */
  void
  SetConstraintWeight(const float w)
  {
    m_ConstraintWeight = w;
  }

  /** Set the time step. */
  void
  SetTimeStep(const TimeStepType ts)
  {
    m_TimeStep = ts;
  }

  /** Get the metric value. The metric value is the mean square difference
   * in intensity between the fixed image and transforming moving image
   * computed over the overlapping region between the two images.
   * This is value is only available for the previous iteration and
   * NOT the current iteration. */
  virtual double
  GetMetric() const;

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

  /** Initialize the state of filter before starting first iteration. */
  void
  Initialize() override;

  /** Apply update. */
  void
  ApplyUpdate(const TimeStepType & dt) override;

private:
  unsigned int m_FixedImageDimensions[ImageDimension]{};

  RealTypeDFT * m_DisplacementFieldComponentImage{};
  RealTypeDFT * m_DisplacementFieldComponentImageDCT{};

  float m_ConstraintWeight{};

  fftw_plan m_PlanForwardDCT{};
  fftw_plan m_PlanBackwardDCT{};

  TimeStepType m_TimeStep{};

  RealTypeDFT * m_DiagonalElements[ImageDimension]{};
};
} // end namespace itk

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

#endif // defined(ITK_USE_FFTWF) || defined(ITK_USE_FFTWD)

#endif
