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 *
 *  Copyright Insight Software Consortium
 *
 *  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
 *
 *         http://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 itkWindowedSincInterpolateImageFunction_h
#define itkWindowedSincInterpolateImageFunction_h

#include "itkConstNeighborhoodIterator.h"
#include "itkZeroFluxNeumannBoundaryCondition.h"
#include "itkInterpolateImageFunction.h"

namespace itk
{
namespace Function
{
/**
 * \class CosineWindowFunction
 * \brief Window function for sinc interpolation.
 * \f[ w(x) = cos(\frac{\pi x}{2 m} ) \f]
 * \sa WindowedSincInterpolateImageFunction
 * \ingroup ITKImageFunction
 */
template< unsigned int VRadius,
          typename TInput = double, typename TOutput = double >
class CosineWindowFunction
{
public:
  inline TOutput operator()(const TInput & A) const
  { return static_cast<TOutput>(std::cos(A * m_Factor)); }

private:
  /** Equal to \f$ \frac{\pi}{2 m} \f$ */
  static const double m_Factor;
};

/**
 * \class HammingWindowFunction
 * \brief Window function for sinc interpolation.
 * \f[ w(x) = 0.54 + 0.46 cos(\frac{\pi x}{m} ) \f]
 * \sa WindowedSincInterpolateImageFunction
 * \ingroup ITKImageFunction
 */
template< unsigned int VRadius,
          typename TInput = double, typename TOutput = double >
class HammingWindowFunction
{
public:
  inline TOutput operator()(const TInput & A) const
  { return static_cast<TOutput>(0.54 + 0.46 * std::cos(A * m_Factor) ); }

private:
  /** Equal to \f$ \frac{\pi}{m} \f$ */
  static const double m_Factor;
};

/**
 * \class WelchWindowFunction
 * \brief Window function for sinc interpolation.
 * \f[ w(x) = 1 - ( \frac{x^2}{m^2} ) \f]
 * \sa WindowedSincInterpolateImageFunction
 * \ingroup ITKImageFunction
 */
template< unsigned int VRadius,
          typename TInput = double, typename TOutput = double >
class WelchWindowFunction
{
public:
  inline TOutput operator()(const TInput & A) const
  { return static_cast<TOutput>( 1.0 - A * m_Factor * A ); }

private:
  /** Equal to \f$ \frac{1}{m^2} \f$ */
  static const double m_Factor;
};

/**
 * \class LanczosWindowFunction
 * \brief Window function for sinc interpolation.
 * \f[ w(x) = \textrm{sinc} ( \frac{x}{m} ) \f]
 * Note: Paper referenced in WindowedSincInterpolateImageFunction gives
 * an incorrect definition of this window function.
 * \sa WindowedSincInterpolateImageFunction
 * \ingroup ITKImageFunction
 */
template< unsigned int VRadius,
          typename TInput = double, typename TOutput = double >
class LanczosWindowFunction
{
public:
  inline TOutput operator()(const TInput & A) const
  {
    if ( A == 0.0 ) { return static_cast<TOutput>(1.0); }
    double z = m_Factor * A;
    return static_cast<TOutput>( std::sin(z) / z );
  }

private:
  /** Equal to \f$ \frac{\pi}{m} \f$ */
  static const double m_Factor;
};

/**
 * \class BlackmanWindowFunction
 * \brief Window function for sinc interpolation.
 * \f[ w(x) = 0.42 + 0.5 cos(\frac{\pi x}{m}) + 0.08 cos(\frac{2 \pi x}{m}) \f]
 * \sa WindowedSincInterpolateImageFunction
 * \ingroup ITKImageFunction
 */
template< unsigned int VRadius,
          typename TInput = double, typename TOutput = double >
class BlackmanWindowFunction
{
public:
  inline TOutput operator()(const TInput & A) const
  {
    return static_cast<TOutput>
           ( 0.42 + 0.5 * std::cos(A * m_Factor1) + 0.08 * std::cos(A * m_Factor2) );
  }

private:
  /** Equal to \f$ \frac{\pi}{m} \f$ */
  static const double m_Factor1;

  /** Equal to \f$ \frac{2 \pi}{m} \f$  */
  static const double m_Factor2;
};
} // namespace Function

/**
 * \class WindowedSincInterpolateImageFunction
 * \brief Use the windowed sinc function to interpolate
 * \author Paul A. Yushkevich
 *
 * \par THEORY
 *
 * This function is intended to provide an interpolation function that
 * has minimum aliasing artifacts, in contrast to linear interpolation.
 * According to sampling theory, the infinite-support sinc filter,
 * whose Fourier transform is the box filter, is optimal for resampling
 * a function. In practice, the infinite support sinc filter is
 * approximated using a limited support 'windowed' sinc filter.
 *
 * \par
 * This function is based on the following publication:
 *
 * \par
 * Erik H. W. Meijering, Wiro J. Niessen, Josien P. W. Pluim,
 * Max A. Viergever: Quantitative Comparison of Sinc-Approximating
 * Kernels for Medical Image Interpolation. MICCAI 1999, pp. 210-217
 *
 * \par
 * In this work, several 'windows' are estimated. In two dimensions, the
 * interpolation at a position (x,y) is given by the following
 * expression:
 *
 * \par
 * \f[
 *   I(x,y) =
 *     \sum_{i = \lfloor x \rfloor + 1 - m}^{\lfloor x \rfloor + m}
 *     \sum_{j = \lfloor y \rfloor + 1 - m}^{\lfloor y \rfloor + m}
 *     I_{i,j} K(x-i) K(y-j),
 * \f]
 *
 * \par
 * where m is the 'radius' of the window, (3,4 are reasonable numbers),
 * and K(t) is the kernel function, composed of the sinc function and
 * one of several possible window functions:
 *
 * \par
 * \f[
 *   K(t) = w(t) \textrm{sinc}(t) = w(t) \frac{\sin(\pi t)}{\pi t}
 * \f]
 *
 * \par
 * Several window functions are provided here in the itk::Function
 * namespace. The conclusions of the referenced paper suggest to use the
 * Welch, Cosine, Kaiser, and Lanczos windows for m = 4,5. These are based
 * on error in rotating medical images w.r.t. the linear interpolation
 * method. In some cases the results achieve a 20-fold improvement in
 * accuracy.
 *
 * \par USING THIS FILTER
 *
 * Use this filter the way you would use any ImageInterpolationFunction,
 * so for instance, you can plug it into the ResampleImageFilter class.
 * In order to initialize the filter you must choose several template
 * parameters.
 *
 * \par
 * The first (TInputImage) is the image type, that's standard.
 *
 * \par
 * The second (VRadius) is the radius of the kernel, i.e., the
 * \f$ m \f$ from the formula above.
 *
 * \par
 * The third (TWindowFunction) is the window function object, which you
 * can choose from about five different functions defined in this
 * header. The default is the Hamming window, which is commonly used
 * but not optimal according to the cited paper.
 *
 * \par
 * The fourth (TBoundaryCondition) is the boundary condition class used
 * to determine the values of pixels that fall off the image boundary.
 * This class has the same meaning here as in the NeighborhoodItetator
 * classes.
 *
 * \par
 * The fifth (TCoordRep) is again standard for interpolating functions,
 * and should be float or double.
 *
 * \par CAVEATS
 *
 * There are a few improvements that an enthusiasting ITK developer
 * could make to this filter. One issue is with the way that the kernel
 * is applied. The computational expense comes from two sources:
 * computing the kernel weights K(t) and multiplying the pixels in the
 * window by the kernel weights. The first is done more or less
 * efficiently in \f$ 2 m d \f$ operations (where d is the
 * dimensionality of the image). The second can be done
 * better. Presently, each pixel \f$ I(i,j,k) \f$ is multiplied by the
 * weights \f$ K(x-i), K(y-j), K(z-k) \f$ and added to the running
 * total. This results in \f$ d (2m)^d \f$ multiplication
 * operations. However, by keeping intermediate sums, it would be
 * possible to do the operation in \f$ O ( (2m)^d ) \f$
 * operations. This would require some creative coding. In addition, in
 * the case when one of the coordinates is integer, the computation
 * could be reduced by an order of magnitude.
 *
 * \sa LinearInterpolateImageFunction ResampleImageFilter
 * \sa Function::HammingWindowFunction
 * \sa Function::CosineWindowFunction
 * \sa Function::WelchWindowFunction
 * \sa Function::LanczosWindowFunction
 * \sa Function::BlackmanWindowFunction
 * \ingroup ImageFunctions ImageInterpolators
 * \ingroup ITKImageFunction
 */
template<
  typename TInputImage,
  unsigned int VRadius,
  typename TWindowFunction = Function::HammingWindowFunction< VRadius >,
  class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition< TInputImage, TInputImage >,
  class TCoordRep = double >
class WindowedSincInterpolateImageFunction:
  public InterpolateImageFunction< TInputImage, TCoordRep >
{
public:
  /** Standard class typedefs. */
  typedef WindowedSincInterpolateImageFunction               Self;
  typedef InterpolateImageFunction< TInputImage, TCoordRep > Superclass;

  typedef SmartPointer< Self >       Pointer;
  typedef SmartPointer< const Self > ConstPointer;

  /** Run-time type information (and related methods). */
  itkTypeMacro(WindowedSincInterpolateImageFunction,
               InterpolateImageFunction);

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

  /** OutputType typedef support. */
  typedef typename Superclass::OutputType OutputType;

  /** InputImageType typedef support. */
  typedef typename Superclass::InputImageType InputImageType;

  /** RealType typedef support. */
  typedef typename Superclass::RealType RealType;

  /** Dimension underlying input image. */
  itkStaticConstMacro(ImageDimension, unsigned int, Superclass::ImageDimension);

  /** Index typedef support. */
  typedef typename Superclass::IndexType      IndexType;
  typedef typename Superclass::IndexValueType IndexValueType;

  /** Image type definition */
  typedef TInputImage ImageType;

  /** ContinuousIndex typedef support. */
  typedef typename Superclass::ContinuousIndexType ContinuousIndexType;

  virtual void SetInputImage(const ImageType *image) ITK_OVERRIDE;

  /** Evaluate the function at a ContinuousIndex position
   *
   * Returns the interpolated image intensity at a
   * specified point position.  Bounds checking is based on the
   * type of the TBoundaryCondition specified.
   */
  virtual OutputType EvaluateAtContinuousIndex(
    const ContinuousIndexType & index) const ITK_OVERRIDE;

protected:
  WindowedSincInterpolateImageFunction();
  virtual ~WindowedSincInterpolateImageFunction();
  void PrintSelf(std::ostream & os, Indent indent) const ITK_OVERRIDE;

private:
  WindowedSincInterpolateImageFunction(const Self &); //not implemented
  void operator=(const Self &) ITK_DELETE_FUNCTION;

  // Internal typedefs
  typedef ConstNeighborhoodIterator<
    ImageType, TBoundaryCondition > IteratorType;

  // Constant to store twice the radius
  static const unsigned int m_WindowSize;

  /** The function object, used to compute window */
  TWindowFunction m_WindowFunction;

  /** The offset array, used to keep a list of relevant
   * offsets in the neihborhoodIterator */
  unsigned int *m_OffsetTable;

  /** Size of the offset table */
  unsigned int m_OffsetTableSize;

  /** Index into the weights array for each offset */
  unsigned int **m_WeightOffsetTable;

  /** The sinc function */
  inline double Sinc(double x) const
  {
    double px = itk::Math::pi * x;

    return ( x == 0.0 ) ? 1.0 : std::sin(px) / px;
  }
};
} // namespace itk

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

#endif // _itkWindowedSincInterpolateImageFunction_h
