LanczosInterpolation.h

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//     ____   ______ __
//    / __ \ / ____// /
//   / /_/ // /    / /
//  / ____// /___ / /___   PixInsight Class Library
// /_/     \____//_____/   PCL 2.7.0
// ----------------------------------------------------------------------------
// pcl/LanczosInterpolation.h - Released 2024-06-18T15:48:54Z
// ----------------------------------------------------------------------------
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// ----------------------------------------------------------------------------
 
#ifndef __PCL_LanczosInterpolation_h
#define __PCL_LanczosInterpolation_h
 
 
#include <pcl/Defs.h>
#include <pcl/Diagnostics.h>
 
#include <pcl/BidimensionalInterpolation.h>
#include <pcl/Math.h>
#include <pcl/Utility.h>
#include <pcl/Vector.h>
 
namespace pcl
{
 
// ----------------------------------------------------------------------------
 
#define m_width      this->m_width
#define m_height     this->m_height
#define m_fillBorder this->m_fillBorder
#define m_fillValue  this->m_fillValue
#define m_data       this->m_data
 
// ----------------------------------------------------------------------------
 
/*
 * Default clamping threshold for Lanczos interpolation. This value has been
 * selected as the best trade-off for a large set of test linear images.
 */
#ifndef __PCL_LANCZOS_CLAMPING_THRESHOLD
#define __PCL_LANCZOS_CLAMPING_THRESHOLD  0.3F
#endif
 
// ----------------------------------------------------------------------------
 
/*
 * Floating point and integer LUT-based interpolations for 3rd, 4th and 5th
 * order Lanczos functions. LUTs are initialized automatically on-demand by
 * thread-safe internal routines.
 *
 * Real Lanczos LUTs are accurate to +/- 1e-7 DN
 * Integer Lanczos LUTs are accurate to +/- 1 16-bit DN
 */
#define __PCL_LANCZOS_LUT_REAL_RESOLUTION 4096
const double** PCL_FUNC PCL_InitializeLanczosRealLUT( int );
#define __PCL_LANCZOS_LUT_INT_RESOLUTION  65535
const float* PCL_FUNC PCL_InitializeLanczosIntLUT( int );
 
// ----------------------------------------------------------------------------
 
#define PCL_LANCZOS_ACC()        \
         if ( s < 0 )            \
            sn -= s, wn -= L;    \
         else                    \
            sp += s, wp += L;
 
template <typename T>
class PCL_CLASS LanczosInterpolation : public BidimensionalInterpolation<T>
{
private:
 
   struct Default
   {
      template <typename _T> static bool UseLUT( _T* ) { return false; }
      static bool UseLUT( uint8* ) { return true; }
      static bool UseLUT( int8* ) { return true; }
      static bool UseLUT( uint16* ) { return true; }
      static bool UseLUT( int16* ) { return true; }
      static bool UseLUT( float* ) { return true; }
   };
 
public:
 
   LanczosInterpolation( int n = 3, float clamp = __PCL_LANCZOS_CLAMPING_THRESHOLD, bool useLUT = Default::UseLUT( (T*)0 ) )
      : m_n( Max( 1, n ) )
      , m_lut( useLUT ? PCL_InitializeLanczosRealLUT( m_n ) : nullptr )
      , m_Lx( 2*m_n )
      , m_clampTh( Range( clamp, 0.0F, 1.0F ) )
      , m_clampThInv( 1 - m_clampTh )
      , m_clamp( clamp >= 0 )
   {
      PCL_PRECONDITION( n >= 1 )
      PCL_PRECONDITION( clamp < 0 || 0 <= clamp && clamp <= 1 )
   }
 
   LanczosInterpolation( const LanczosInterpolation& ) = default;
 
   ~LanczosInterpolation() override
   {
   }
 
   double operator()( double x, double y ) const override
   {
      PCL_PRECONDITION( m_data != nullptr )
      PCL_PRECONDITION( m_width > 0 && m_height > 0 )
      PCL_PRECONDITION( x >= 0 && x < m_width )
      PCL_PRECONDITION( y >= 0 && y < m_height )
      PCL_CHECK( m_n >= 1 )
 
      // Central grid coordinates
      int x0 = Range( TruncInt( x ), 0, m_width-1 );
      int y0 = Range( TruncInt( y ), 0, m_height-1 );
 
      double sp = 0; // positive filter values
      double sn = 0; // negative filter values
      double wp = 0; // positive filter weight
      double wn = 0; // negative filter weight
      int i;         // row index
 
      if ( m_lut != nullptr )
      {
         // Discrete interpolation increments
         int dx = TruncInt( __PCL_LANCZOS_LUT_REAL_RESOLUTION*(x - x0) );
         int dy = TruncInt( __PCL_LANCZOS_LUT_REAL_RESOLUTION*(y - y0) );
 
         // Precalculate horizontal filter values
         for ( int j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
            m_Lx[k] = m_lut[k][dx];
 
         int k;      // LUT node index
 
         // Clipped rows at top
         for ( i = -m_n + 1, k = 0; i <= m_n; ++i, ++k )
         {
            int y = y0 + i;
            if ( y >= 0 )
               break;
            if ( m_fillBorder )
               FillRow( sp, sn, wp, wn, m_lut[k][dy] );
            else
               InterpolateRow( sp, sn, wp, wn, m_data - 2*int64( y )*m_width, x0, m_lut[k][dy] );
         }
 
         // Unclipped rows
         for ( ; i <= m_n; ++i, ++k )
         {
            int y = y0 + i;
            if ( y == m_height )
               break;
            InterpolateRow( sp, sn, wp, wn, m_data + int64( y )*m_width, x0, m_lut[k][dy] );
         }
 
         // Clipped rows at bottom
         for ( ; i <= m_n; ++i, ++k )
         {
            if ( m_fillBorder )
               FillRow( sp, sn, wp, wn, m_lut[k][dy] );
            else
               InterpolateRow( sp, sn, wp, wn, m_data + int64( 2*m_height - 2 - y0 - i )*m_width, x0, m_lut[k][dy] );
         }
      }
      else
      {
         // Interpolation increments
         double dx = x - x0;
         double dy = y - y0;
 
         // Precalculate horizontal filter values
         for ( int j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
            m_Lx[k] = Lanczos( j - dx );
 
         // Clipped rows at top
         for ( i = -m_n + 1; i <= m_n; ++i )
         {
            int y = y0 + i;
            if ( y >= 0 )
               break;
            if ( m_fillBorder )
               FillRow( sp, sn, wp, wn, Lanczos( i - dy ) );
            else
               InterpolateRow( sp, sn, wp, wn, m_data - 2*int64( y )*m_width, x0, Lanczos( i - dy ) );
         }
 
         // Unclipped rows
         for ( ; i <= m_n; ++i )
         {
            int y = y0 + i;
            if ( y == m_height )
               break;
            InterpolateRow( sp, sn, wp, wn, m_data + int64( y )*m_width, x0, Lanczos( i - dy ) );
         }
 
         // Clipped rows at bottom
         for ( ; i <= m_n; ++i )
         {
            if ( m_fillBorder )
               FillRow( sp, sn, wp, wn, Lanczos( i - dy ) );
            else
               InterpolateRow( sp, sn, wp, wn, m_data + int64( 2*m_height - 2 - y0 - i )*m_width, x0, Lanczos( i - dy ) );
         }
      }
 
      // Clamping
      if ( m_clamp )
      {
         // Empty data?
         if ( sp == 0 )
            return 0;
 
         // Clamping ratio: s-/s+
         double r = sn/sp;
 
         // Clamp for s- >= s+
         if ( r >= 1 )
            return sp/wp;
 
         // Clamp for c < s- < s+
         if ( r > m_clampTh )
         {
            r = (r - m_clampTh)/m_clampThInv;
            double c = 1 - r*r;
            sn *= c, wn *= c;
         }
      }
 
      // Weighted convolution
      return (sp - sn)/(wp - wn);
   }
 
   bool IsClampingEnabled() const noexcept
   {
      return m_clamp;
   }
 
   void EnableClamping( bool enable = true ) noexcept
   {
      m_clamp = enable;
   }
 
   void DisableClamping( bool disable = true ) noexcept
   {
      EnableClamping( !disable );
   }
 
   float ClampingThreshold() const noexcept
   {
      return m_clampTh;
   }
 
   void SetClampingThreshold( float clamp ) noexcept
   {
      PCL_PRECONDITION( 0 <= clamp && clamp <= 1 )
      m_clampTh = Range( clamp, 0.0F, 1.0F );
   }
 
private:
 
           int      m_n;          // filter order
     const double** m_lut;        // precomputed function values
   mutable DVector  m_Lx;         // precalculated row of function values
           double   m_clampTh;    // clamping threshold in [0,1]
           double   m_clampThInv; // 1 - m_clampTh
           bool     m_clamp;      // clamping enabled ?
 
   /*
    * Sinc function for x > 0
    */
   static double Sinc( double x ) noexcept
   {
      x *= Const<double>::pi();
      return (x > 1.0e-07) ? Sin( x )/x : 1.0;
   }
 
   /*
    * Evaluate Lanczos function at x.
    */
   double Lanczos( double x ) const noexcept
   {
      if ( x < 0 )
         x = -x;
      if ( x < m_n )
         return Sinc( x ) * Sinc( x/m_n );
      return 0;
   }
 
   /*
    * Interpolate a row of pixels.
    * Can be either an unclipped row or a mirrored border row.
    */
   void InterpolateRow( double& sp, double& sn, double& wp, double& wn, const T* f, int x0, double Ly ) const noexcept
   {
      int j, k;
 
      // Clipped pixels at the left border
      for ( j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
      {
         int x = x0 + j;
         if ( x >= 0 )
            break;
         double L = m_Lx[k] * Ly;
         double s = (m_fillBorder ? m_fillValue : double( f[-x] )) * L;
         PCL_LANCZOS_ACC()
      }
 
      // Unclipped pixels
      for ( ; j <= m_n; ++j, ++k )
      {
         int x = x0 + j;
         if ( x == m_width )
            break;
         double L = m_Lx[k] * Ly;
         double s = f[x] * L;
         PCL_LANCZOS_ACC()
      }
 
      // Clipped pixels at the right border
      for ( ; j <= m_n; ++j, ++k )
      {
         int x = x0 + j;
         double L = m_Lx[k] * Ly;
         double s = (m_fillBorder ? m_fillValue : double( f[2*m_width - 2 - x] )) * L;
         PCL_LANCZOS_ACC()
      }
   }
 
   /*
    * Interpolate a clipped pixel row with border filling.
    */
   void FillRow( double& sp, double& sn, double& wp, double& wn, double Ly ) const noexcept
   {
      for ( int j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
      {
         double L = m_Lx[k] * Ly;
         double s = m_fillValue * L;
         PCL_LANCZOS_ACC()
      }
   }
};
 
// ----------------------------------------------------------------------------
 
template <typename T, int m_n>
class PCL_CLASS LanczosLUTInterpolationBase : public BidimensionalInterpolation<T>
{
public:
 
   LanczosLUTInterpolationBase( float clamp )
      : m_lut( PCL_InitializeLanczosIntLUT( m_n ) )
      , m_Lx( 2*m_n )
      , m_Ly( 2*m_n )
      , m_clampTh( Range( clamp, 0.0F, 1.0F ) )
      , m_clampThInv( 1 - m_clampTh )
      , m_clamp( clamp >= 0 )
   {
      PCL_PRECONDITION( m_n >= 1 )
      PCL_PRECONDITION( clamp < 0 || 0 <= clamp && clamp <= 1 )
      PCL_CHECK( m_lut != nullptr )
   }
 
   LanczosLUTInterpolationBase( const LanczosLUTInterpolationBase& ) = default;
 
   ~LanczosLUTInterpolationBase() override
   {
   }
 
   double operator()( double x, double y ) const override
   {
      PCL_PRECONDITION( m_data != nullptr )
      PCL_PRECONDITION( m_width > 0 && m_height > 0 )
      PCL_PRECONDITION( x >= 0 && x < m_width )
      PCL_PRECONDITION( y >= 0 && y < m_height )
 
      // Central grid coordinates
      int x0 = Range( TruncInt( x ), 0, m_width-1 );
      int y0 = Range( TruncInt( y ), 0, m_height-1 );
 
      // Precalculate function values
      int dx = RoundInt( (x - x0)*__PCL_LANCZOS_LUT_INT_RESOLUTION );
      int dy = RoundInt( (y - y0)*__PCL_LANCZOS_LUT_INT_RESOLUTION );
      for ( int j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
      {
         int d0 = j*__PCL_LANCZOS_LUT_INT_RESOLUTION;
         m_Lx[k] = m_lut[Abs( d0 - dx )];
         m_Ly[k] = m_lut[Abs( d0 - dy )];
      }
 
      double sp = 0; // positive filter values
      double sn = 0; // negative filter values
      double wp = 0; // positive filter weight
      double wn = 0; // negative filter weight
      int i, k;      // row and coefficient indices
 
      // Clipped rows at top
      for ( i = -m_n + 1, k = 0; i <= m_n; ++i, ++k )
      {
         int y = y0 + i;
         if ( y >= 0 )
            break;
         if ( m_fillBorder )
            FillRow( sp, sn, wp, wn, m_Ly[k] );
         else
            InterpolateRow( sp, sn, wp, wn, m_data - 2*int64( y )*m_width, x0, m_Ly[k] );
      }
 
      // Unclipped rows
      for ( ; i <= m_n; ++i, ++k )
      {
         int y = y0 + i;
         if ( y == m_height )
            break;
         InterpolateRow( sp, sn, wp, wn, m_data + int64( y )*m_width, x0, m_Ly[k] );
      }
 
      // Clipped rows at bottom
      for ( ; i <= m_n; ++i, ++k )
      {
         if ( m_fillBorder )
            FillRow( sp, sn, wp, wn, m_Ly[k] );
         else
            InterpolateRow( sp, sn, wp, wn, m_data + int64( 2*m_height - 2 - y0 - i )*m_width, x0, m_Ly[k] );
      }
 
      // Clamping
      if ( m_clamp )
      {
         // Empty data?
         if ( sp == 0 )
            return 0;
 
         // Clamping ratio: s-/s+
         double r = sn/sp;
 
         // Clamp for s- >= s+
         if ( r >= 1 )
            return sp/wp;
 
         // Clamp for c < s- < s+
         if ( r > m_clampTh )
         {
            r = (r - m_clampTh)/m_clampThInv;
            double c = 1 - r*r;
            sn *= c, wn *= c;
         }
      }
 
      // Weighted convolution
      return (sp - sn)/(wp - wn);
   }
 
   bool IsClampingEnabled() const noexcept
   {
      return m_clamp;
   }
 
   void EnableClamping( bool enable = true ) noexcept
   {
      m_clamp = enable;
   }
 
   void DisableClamping( bool disable = true ) noexcept
   {
      EnableClamping( !disable );
   }
 
   float ClampingThreshold() const noexcept
   {
      return m_clampTh;
   }
 
   void SetClampingThreshold( float clamp ) noexcept
   {
      PCL_PRECONDITION( 0 <= clamp && clamp <= 1 )
      m_clampTh = Range( clamp, 0.0F, 1.0F );
   }
 
private:
 
     const float*  m_lut;        // filter LUT
   mutable FVector m_Lx, m_Ly;   // precalculated function values
           double  m_clampTh;    // clamping threshold in [0,1]
           double  m_clampThInv; // 1 - m_clampTh
           bool    m_clamp;      // clamping enabled ?
 
   /*
    * Interpolate a row of pixels.
    * Can be either an unclipped row or a mirrored border row.
    */
   void InterpolateRow( double& sp, double& sn, double& wp, double& wn, const T* f, int x0, float Ly ) const noexcept
   {
      int j, k;
 
      // Clipped pixels at the left border
      for ( j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
      {
         int x = x0 + j;
         if ( x >= 0 )
            break;
         double L = m_Lx[k] * Ly;
         double s = (m_fillBorder ? m_fillValue : double( f[-x] )) * L;
         PCL_LANCZOS_ACC()
      }
 
      // Unclipped pixels
      for ( ; j <= m_n; ++j, ++k )
      {
         int x = x0 + j;
         if ( x == m_width )
            break;
         double L = m_Lx[k] * Ly;
         double s = f[x] * L;
         PCL_LANCZOS_ACC()
      }
 
      // Clipped pixels at the right border
      for ( ; j <= m_n; ++j, ++k )
      {
         int x = x0 + j;
         double L = m_Lx[k] * Ly;
         double s = (m_fillBorder ? m_fillValue : double( f[2*m_width - 2 - x] )) * L;
         PCL_LANCZOS_ACC()
      }
   }
 
   /*
    * Interpolate a clipped pixel row with border filling.
    */
   void FillRow( double& sp, double& sn, double& wp, double& wn, float Ly ) const noexcept
   {
      for ( int j = -m_n + 1, k = 0; j <= m_n; ++j, ++k )
      {
         double L = m_Lx[k] * Ly;
         double s = m_fillValue * L;
         PCL_LANCZOS_ACC()
      }
   }
};
 
// ----------------------------------------------------------------------------
 
template <typename T>
class PCL_CLASS Lanczos3LUTInterpolation : public LanczosLUTInterpolationBase<T,3>
{
public:
 
   Lanczos3LUTInterpolation( float clamp = __PCL_LANCZOS_CLAMPING_THRESHOLD )
      : LanczosLUTInterpolationBase<T,3>( clamp )
   {
      PCL_PRECONDITION( 0 <= clamp && clamp <= 1 )
   }
 
   Lanczos3LUTInterpolation( const Lanczos3LUTInterpolation& ) = default;
 
   ~Lanczos3LUTInterpolation() override
   {
   }
};
 
// ----------------------------------------------------------------------------
 
template <typename T>
class PCL_CLASS Lanczos4LUTInterpolation : public LanczosLUTInterpolationBase<T,4>
{
public:
 
   Lanczos4LUTInterpolation( float clamp = __PCL_LANCZOS_CLAMPING_THRESHOLD )
      : LanczosLUTInterpolationBase<T,4>( clamp )
   {
      PCL_PRECONDITION( 0 <= clamp && clamp <= 1 )
   }
 
   Lanczos4LUTInterpolation( const Lanczos4LUTInterpolation& ) = default;
 
   ~Lanczos4LUTInterpolation() override
   {
   }
};
 
// ----------------------------------------------------------------------------
 
template <typename T>
class PCL_CLASS Lanczos5LUTInterpolation : public LanczosLUTInterpolationBase<T,5>
{
public:
 
   Lanczos5LUTInterpolation( float clamp = __PCL_LANCZOS_CLAMPING_THRESHOLD )
      : LanczosLUTInterpolationBase<T,5>( clamp )
   {
      PCL_PRECONDITION( 0 <= clamp && clamp <= 1 )
   }
 
   Lanczos5LUTInterpolation( const Lanczos5LUTInterpolation& ) = default;
 
   ~Lanczos5LUTInterpolation() override
   {
   }
};
 
// ----------------------------------------------------------------------------
 
#undef PCL_LANCZOS_ACC
 
#undef m_width
#undef m_height
#undef m_fillBorder
#undef m_fillValue
#undef m_data
 
// ----------------------------------------------------------------------------
 
} // pcl
 
#endif   // __PCL_LanczosInterpolation_h
 
// ----------------------------------------------------------------------------
// EOF pcl/LanczosInterpolation.h - Released 2024-06-18T15:48:54Z