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// ____ ______ __
// / __ \ / ____// /
// / /_/ // / / /
// / ____// /___ / /___ PixInsight Class Library
// /_/ \____//_____/ PCL 2.4.23
// ----------------------------------------------------------------------------
// pcl/BicubicInterpolation.h - Released 2022-03-12T18:59:29Z
// ----------------------------------------------------------------------------
// This file is part of the PixInsight Class Library (PCL).
// PCL is a multiplatform C++ framework for development of PixInsight modules.
//
// Copyright (c) 2003-2022 Pleiades Astrophoto S.L. All Rights Reserved.
//
// Redistribution and use in both source and binary forms, with or without
// modification, is permitted provided that the following conditions are met:
//
// 1. All redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. All redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the names "PixInsight" and "Pleiades Astrophoto", nor the names
// of their contributors, may be used to endorse or promote products derived
// from this software without specific prior written permission. For written
// permission, please contact info@pixinsight.com.
//
// 4. All products derived from this software, in any form whatsoever, must
// reproduce the following acknowledgment in the end-user documentation
// and/or other materials provided with the product:
//
// "This product is based on software from the PixInsight project, developed
// by Pleiades Astrophoto and its contributors (https://pixinsight.com/)."
//
// Alternatively, if that is where third-party acknowledgments normally
// appear, this acknowledgment must be reproduced in the product itself.
//
// THIS SOFTWARE IS PROVIDED BY PLEIADES ASTROPHOTO AND ITS CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL PLEIADES ASTROPHOTO OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, BUSINESS
// INTERRUPTION; PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; AND LOSS OF USE,
// DATA OR PROFITS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
// ----------------------------------------------------------------------------
#ifndef __PCL_BicubicInterpolation_h
#define __PCL_BicubicInterpolation_h
/// \file pcl/BicubicInterpolation.h
#include <pcl/Defs.h>
#include <pcl/Diagnostics.h>
#include <pcl/BidimensionalInterpolation.h>
#include <pcl/Math.h>
#include <pcl/Utility.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
// ----------------------------------------------------------------------------
/*!
* \class BicubicInterpolationBase
* \brief Base class for bicubic interpolation algorithm implementations
*
* %BicubicInterpolationBase is a base class for BicubicSplineInterpolation and
* BicubicBSplineInterpolation.
*
* \sa BicubicSplineInterpolation, BicubicBSplineInterpolation
*/
template <typename T>
class PCL_CLASS BicubicInterpolationBase : public BidimensionalInterpolation<T>
{
public:
/*!
* Constructs a new %BicubicInterpolationBase instance.
*/
BicubicInterpolationBase() = default;
/*!
* Copy constructor.
*/
BicubicInterpolationBase( const BicubicInterpolationBase& ) = default;
protected:
void InitXY( int& i1, int& j1, double* p0, double* p1, double* p2, double* p3, double x, double y ) const noexcept
{
PCL_PRECONDITION( int( x ) >= 0 )
PCL_PRECONDITION( int( x ) < m_width )
PCL_PRECONDITION( int( y ) >= 0 )
PCL_PRECONDITION( int( y ) < m_height )
// Central grid coordinates
i1 = pcl::Range( TruncInt( y ), 0, m_height-1 );
j1 = pcl::Range( TruncInt( x ), 0, m_width-1 );
// Set up source matrix
int j0 = j1 - 1;
int i0 = i1 - 1;
int j2 = j1 + 1;
int i2 = i1 + 1;
int j3 = j1 + 2;
int i3 = i1 + 2;
const T* fp = m_data + (int64( i0 )*m_width + j0);
// Row 0
if ( i0 < 0 )
{
fp += m_width;
if ( m_fillBorder )
{
p0[0] = p0[1] = p0[2] = p0[3] = m_fillValue;
goto __row1;
}
}
GetRow( p0, fp, j0, j2, j3 );
if ( i0 >= 0 )
fp += m_width;
__row1: // Row 1
GetRow( p1, fp, j0, j2, j3 );
// Row 2
if ( i2 < m_height )
fp += m_width;
GetRow( p2, fp, j0, j2, j3 );
// Row 3
if ( i3 < m_height )
fp += m_width;
else if ( m_fillBorder )
{
p3[0] = p3[1] = p3[2] = p3[3] = m_fillValue;
goto __done;
}
GetRow( p3, fp, j0, j2, j3 );
__done:
;
}
void InitYX( int& i1, int& j1, double* p0, double* p1, double* p2, double* p3, double x, double y ) const noexcept
{
PCL_PRECONDITION( int( x ) >= 0 )
PCL_PRECONDITION( int( x ) < m_width )
PCL_PRECONDITION( int( y ) >= 0 )
PCL_PRECONDITION( int( y ) < m_height )
// Central grid coordinates
i1 = pcl::Range( TruncInt( y ), 0, m_height-1 );
j1 = pcl::Range( TruncInt( x ), 0, m_width-1 );
// Set up source matrix
int j0 = j1 - 1;
int i0 = i1 - 1;
int j2 = j1 + 1;
int i2 = i1 + 1;
int j3 = j1 + 2;
int i3 = i1 + 2;
const T* fp = m_data + (int64( i0 )*m_width + j0);
// Column 0
if ( j0 < 0 )
{
++fp;
if ( m_fillBorder )
{
p0[0] = p0[1] = p0[2] = p0[3] = m_fillValue;
goto __col1;
}
}
GetColumn( p0, fp, i0, i2, i3 );
if ( j0 >= 0 )
++fp;
__col1: // Column 1
GetColumn( p1, fp, i0, i2, i3 );
// Column 2
if ( j2 < m_width )
++fp;
GetColumn( p2, fp, i0, i2, i3 );
// Column 3
if ( j3 < m_width )
++fp;
else if ( m_fillBorder )
{
p3[0] = p3[1] = p3[2] = p3[3] = m_fillValue;
goto __done;
}
GetColumn( p3, fp, i0, i2, i3 );
__done:
;
}
private:
void GetRow( double* p, const T* fp, int j0, int j2, int j3 ) const noexcept
{
if ( m_fillBorder )
{
*p = (j0 >= 0) ? *fp : m_fillValue;
*++p = *++fp;
if ( j2 < m_width )
{
*++p = *++fp;
*++p = (j3 < m_width) ? *++fp : m_fillValue;
}
else
p[1] = p[2] = m_fillValue;
}
else
{
if ( j0 < 0 )
++fp;
*p = *fp;
if ( j0 >= 0 )
++fp;
*++p = *fp;
if ( j2 < m_width )
{
*++p = *++fp;
if ( j3 < m_width )
++fp;
*++p = *fp;
}
else
{
*++p = *fp;
*++p = *(fp - 1);
}
}
}
void GetColumn( double* p, const T* fp, int i0, int i2, int i3 ) const noexcept
{
if ( m_fillBorder )
{
*p = (i0 >= 0) ? *fp : m_fillValue;
*++p = *(fp += m_width);
if ( i2 < m_height )
{
*++p = *(fp += m_width);
*++p = (i3 < m_height) ? *(fp += m_width) : m_fillValue;
}
else
p[1] = p[2] = m_fillValue;
}
else
{
if ( i0 < 0 )
fp += m_width;
*p = *fp;
if ( i0 >= 0 )
fp += m_width;
*++p = *fp;
if ( i2 < m_height )
{
*++p = *(fp += m_width);
if ( i3 < m_height )
fp += m_width;
*++p = *fp;
}
else
{
*++p = *fp;
*++p = *(fp - m_width);
}
}
}
};
// ----------------------------------------------------------------------------
#define InitXY this->InitXY
#define InitYX this->InitYX
/*
* Undefine the following to use any free constant value a != -1/2
*/
#define __PCL_BICUBIC_SPLINE_A_IS_MINUS_ONE_HALF 1
/*
* The "a" constant controls the depth of the negative lobes in the bicubic
* spline interpolation function, -1 <= a < 0. Larger values of a (in absolute
* value) lead to more ringing (sharpness). The default is -1/2, as recommended
* in [Keys 1981].
*/
#define __PCL_BICUBIC_SPLINE_A -0.5
/*
* Default clamping threshold for linear images. This value has been optimized
* for a = -1/2. If you use another value for a, this must also be fine tuned.
*/
#ifndef __PCL_BICUBIC_SPLINE_CLAMPING_THRESHOLD
#define __PCL_BICUBIC_SPLINE_CLAMPING_THRESHOLD 0.3F
#endif
/*!
* \class BicubicSplineInterpolation
* \brief Bicubic spline interpolation algorithm
*
* Bicubic interpolation algorithms interpolate from the nearest sixteen mapped
* source data items. Our implementation uses the following cubic spline
* function as a separable filter to perform a convolution interpolation:
*
* <pre>
* f(x) = (a+2)*x^3 - (a+3)*x^2 + 1 for 0 <= x <= 1
* f(x) = a*x^3 - 5*a*x^2 + 8*a*x - 4*a for 1 < x <= 2
* f(x) = 0 otherwise
* </pre>
*
* Reference: Keys, R. G. (1981), <em>%Cubic %Convolution %Interpolation for
* %Digital %Image %Processing</em>, IEEE Trans. %Acoustics, %Speech & %Signal
* Proc., Vol. 29, pp. 1153-1160.
*
* The a constant parameter of the cubic spline (-1 <= a < 0) controls the
* depth of the negative lobes of the interpolation function. In this
* implementation we have set a fixed value <em>a</em>=-1/2.
*
* Our implementation includes an automatic <em>linear clamping</em> mechanism
* to avoid discontinuity problems when interpolating linear images. The cubic
* spline function has negative lobes that can cause undershoot (aka ringing)
* artifacts when they fall over bright pixels. This happens frequently with
* linear CCD images. See the documentation for the
* BicubicSplineInterpolation::SetClampingThreshold( float ) function for a
* more detailed description of the linear clamping mechanism.
*/
template <typename T>
class PCL_CLASS BicubicSplineInterpolation : public BicubicInterpolationBase<T>
{
public:
/*!
* Constructs a %BicubicSplineInterpolation instance.
*
* The optional \e clamp parameter defines a threshold to trigger the
* <em>linear clamping</em> mechanism. See the documentation for the
* SetClampingThreshold( float ) function for a detailed description of the
* automatic linear clamping mechanism. The default value of \e clamp = 0.1
* is appropriate for most linear images.
*/
BicubicSplineInterpolation( float clamp = __PCL_BICUBIC_SPLINE_CLAMPING_THRESHOLD )
: m_clamp( Range( clamp, 0.0F, 1.0F ) )
{
PCL_PRECONDITION( 0 <= clamp && clamp <= 1 )
}
/*!
* Copy constructor.
*/
BicubicSplineInterpolation( const BicubicSplineInterpolation& ) = default;
/*!
* Virtual destructor.
*/
virtual ~BicubicSplineInterpolation()
{
}
/*!
* Returns an interpolated value at {\a x,\a y} location.
*
* \param x,y %Coordinates of the interpolation point (horizontal,
* vertical).
*
* This function performs a two-dimensional interpolation via a convolution
* with the separable cubic spline filter.
*/
double operator()( double x, double y ) const override
{
PCL_PRECONDITION( m_data != nullptr )
PCL_PRECONDITION( m_width > 0 && m_height > 0 )
// Initialize grid coordinates and source matrix
int i1, j1;
double p0[ 4 ], p1[ 4 ], p2[ 4 ], p3[ 4 ];
InitXY( i1, j1, p0, p1, p2, p3, x, y );
// Cubic spline coefficients
double C[ 4 ];
GetSplineCoefficients( C, x-j1 );
// Interpolate neighbor rows
double c[ 4 ];
c[0] = Interpolate( p0, C );
c[1] = Interpolate( p1, C );
c[2] = Interpolate( p2, C );
c[3] = Interpolate( p3, C );
// Interpolate result vertically
GetSplineCoefficients( C, y-i1 );
return Interpolate( c, C );
}
/*!
* Horizontal interpolation.
*
* \param x,y %Coordinates of the interpolation point (horizontal,
* vertical).
*
* \param[out] fx Address of the first element of a vector where the four
* interpolated X-values will be stored.
*
* This function interpolates horizontally the four neighbor rows for the
* specified \a x, \a y coordinates. This is useful when this interpolation
* algorithm is being used to interpolate an image on the horizontal axis
* exclusively.
*/
void InterpolateX( double fx[], double x, double y ) const noexcept
{
PCL_PRECONDITION( m_data != nullptr )
PCL_PRECONDITION( m_width > 0 && m_height > 0 )
// Initialize grid coordinates and source matrix
int i1, j1;
double p0[ 4 ], p1[ 4 ], p2[ 4 ], p3[ 4 ];
InitXY( i1, j1, p0, p1, p2, p3, x, y );
// Cubic spline coefficients
double C[ 4 ];
GetSplineCoefficients( C, x-j1 );
// Interpolate neighbor rows
fx[0] = Interpolate( p0, C );
fx[1] = Interpolate( p1, C );
fx[2] = Interpolate( p2, C );
fx[3] = Interpolate( p3, C );
}
/*!
* Vertical interpolation.
*
* \param x,y %Coordinates of the interpolation point (horizontal,
* vertical).
*
* \param[out] fy Address of the first element of a vector where the four
* interpolated Y-values will be stored.
*
* This function interpolates vertically the four neighbor columns for the
* specified \a x, \a y coordinates. This is useful when this interpolation
* algorithm is being used to interpolate an image on the vertical axis
* exclusively.
*/
void InterpolateY( double fy[], double x, double y ) const noexcept
{
PCL_PRECONDITION( m_data != nullptr )
PCL_PRECONDITION( m_width > 0 && m_height > 0 )
// Initialize grid coordinates and source matrix
int i1, j1;
double p0[ 4 ], p1[ 4 ], p2[ 4 ], p3[ 4 ];
InitYX( i1, j1, p0, p1, p2, p3, x, y );
// Cubic spline coefficients
double C[ 4 ];
GetSplineCoefficients( C, y-i1 );
// Interpolate neighbor columns
fy[0] = Interpolate( p0, C );
fy[1] = Interpolate( p1, C );
fy[2] = Interpolate( p2, C );
fy[3] = Interpolate( p3, C );
}
/*!
* %Vector interpolation.
*
* \param c Address of the first element of a vector of four data points.
*
* \param dx %Interpolation point in the range [0,+1[. A value of zero
* corresponds to the second element in the f vector.
*
* This function interpolates four neighbor rows or columns by direct
* convolution with the cubic spline function. The four elements of the \a c
* vector can be raw data points, to use cubic spline interpolation in one
* dimension, or they can be interpolated rows or columns from an arbitrary
* 2-D matrix. For example, \a c can be generated by a previous call to
* InterpolateX() or InterpolateY(), respectively to provide source
* interpolated rows or columns, or by equivalent functions from a different
* separable cubic interpolation algorithm. This is useful to mix cubic
* spline interpolation with other interpolation algorithms, which allows
* for flexible interpolation schemes.
*/
double InterpolateVector( const double c[], double dx ) const noexcept
{
double C[ 4 ];
GetSplineCoefficients( C, dx );
return Interpolate( c, C );
}
/*!
* Returns the current <em>linear clamping threshold</em> for this
* interpolation object.
*
* See the documentation for SetClampingThreshold( float ) for a detailed
* description of the automatic linear clamping mechanism.
*/
float ClampingThreshold() const noexcept
{
return m_clamp;
}
/*!
* Defines a threshold to trigger the <em>linear clamping</em> mechanism.
* The clamping mechanism automatically switches to linear interpolation
* when the differences between neighbor pixels are so large that the cubic
* interpolation function may cause ringing artifacts. Ringing occurs when
* the negative lobes of the cubic spline interpolation function fall over
* isolated bright source pixels or bright edges. For example, ringing
* problems happen frequently around stars in linear CCD images. For
* nonlinear images, linear clamping is almost never necessary, as in
* nonlinear images (e.g., stretched deep-sky images, or diurnal images)
* there are normally no such large variations between neighbor pixels.
*
* Linear clamping works on a per-row or per-column basis within the
* interpolation neighborhood of 16 pixels. This means that when the
* clamping mechanism selects linear interpolation, it restricts its use to
* the affected (by too strong variations) row or column, without changing
* the bicubic interpolation scheme as a whole. This ensures artifact-free
* interpolated images without degrading the overall performance of bicubic
* spline interpolation.
*
* The specified clamping threshold \e clamp must be in the [0,1] range.
* Lower values cause a more aggressive deringing effect.
*/
void SetClampingThreshold( float c ) noexcept
{
PCL_PRECONDITION( 0 <= c && c <= 1 )
m_clamp = Range( c, 0.0F, 1.0F );
}
private:
double m_clamp;
PCL_HOT_FUNCTION
double Interpolate( const double* __restrict__ p, const double* __restrict__ C ) const noexcept
{
// Unclamped code:
//return p[0]*C[0] + p[1]*C[1] + p[2]*C[2] + p[3]*C[3];
double f12 = p[1]*C[1] + p[2]*C[2];
double f03 = p[0]*C[0] + p[3]*C[3];
return (-f03 < f12*m_clamp) ? f12 + f03 : f12/(C[1] + C[2]);
}
PCL_HOT_FUNCTION
void GetSplineCoefficients( double* __restrict__ C, double dx ) const noexcept
{
double dx2 = dx*dx;
double dx3 = dx2*dx;
#ifdef __PCL_BICUBIC_SPLINE_A_IS_MINUS_ONE_HALF
// Optimized code for a = -1/2
// We *really* need optimization here since this routine is called twice
// for each interpolated pixel.
double dx1_2 = dx/2;
double dx2_2 = dx2/2;
double dx3_2 = dx3/2;
double dx22 = dx2 + dx2;
double dx315 = dx3 + dx3_2;
C[0] = dx2 - dx3_2 - dx1_2;
C[1] = dx315 - dx22 - dx2_2 + 1;
C[2] = dx22 - dx315 + dx1_2;
C[3] = dx3_2 - dx2_2;
#else
# define a (__PCL_BICUBIC_SPLINE_A)
C[0] = a*dx3 - 2*a*dx2 + a*dx;
C[1] = (a + 2)*dx3 - (a + 3)*dx2 + 1;
C[2] = -(a + 2)*dx3 + (2*a + 3)*dx2 - a*dx;
C[3] = -a*dx3 + a*dx2;
# undef a
#endif
}
};
/*!
* \class BicubicInterpolation
* \brief Bicubic interpolation - an alias for BicubicSplineInterpolation
*
* %BicubicInterpolation is a synonym for the BicubicSplineInterpolation class.
*
* \deprecated This class exists to support old PCL-based code; all new code
* should use the BicubicSplineInterpolation class.
*
* \sa BicubicSplineInterpolation
*/
template <typename T>
class PCL_CLASS BicubicInterpolation : public BicubicSplineInterpolation<T>
{
public:
/*!
* Constructs a %BicubicInterpolation instance.
*/
BicubicInterpolation() = default;
/*!
* Copy constructor.
*/
BicubicInterpolation( const BicubicInterpolation& ) = default;
/*!
* Virtual destructor.
*/
virtual ~BicubicInterpolation()
{
}
};
// ----------------------------------------------------------------------------
/*!
* \class BicubicBSplineInterpolation
* \brief Bicubic B-Spline Interpolation Algorithm
*
* Like bicubic spline interpolation, the bicubic B-spline interpolation
* algorithm also interpolates from the nearest sixteen data items. However,
* this algorithm uses B-spline interpolating functions instead of cubic
* splines, which yields quite (too?) smooth results.
*
* This implementation is based on <em>Bicubic %Interpolation for %Image
* Scaling</em>, by Paul Bourke. It performs a convolution with a nonseparable
* 2-D filter, so its performance is O(n^2).
*
* \sa BicubicSplineInterpolation, BicubicInterpolation, BilinearInterpolation,
* NearestNeighborInterpolation
*/
template <typename T>
class PCL_CLASS BicubicBSplineInterpolation : public BicubicInterpolationBase<T>
{
public:
/*!
* Constructs a %BicubicBSplineInterpolation instance.
*/
BicubicBSplineInterpolation() = default;
/*!
* Copy constructor.
*/
BicubicBSplineInterpolation( const BicubicBSplineInterpolation& ) = default;
/*!
* Virtual destructor.
*/
virtual ~BicubicBSplineInterpolation()
{
}
/*!
* Interpolated value at \a {x,y} location.
*
* \param x,y %Coordinates of the interpolation point (horizontal,
* vertical).
*/
double operator()( double x, double y ) const override
{
PCL_PRECONDITION( f != 0 )
PCL_PRECONDITION( m_width > 0 && m_height > 0 )
// Initialize grid coordinates and source matrix
int i1, j1;
double p0[ 4 ], p1[ 4 ], p2[ 4 ], p3[ 4 ];
InitXY( i1, j1, p0, p1, p2, p3, x, y );
// Bicubic B-Spline interpolation functions
double dx = x - j1;
double dx0 = -1 - dx;
double dx1 = -dx;
double dx2 = 1 - dx;
double dx3 = 2 - dx;
double dy = y - i1;
double dy0 = -1 - dy;
double dy1 = -dy;
double dy2 = 1 - dy;
double dy3 = 2 - dy;
return
BXY( p0, 0, dx0, dy0 ) +
BXY( p0, 1, dx1, dy0 ) +
BXY( p0, 2, dx2, dy0 ) +
BXY( p0, 3, dx3, dy0 ) +
BXY( p1, 0, dx0, dy1 ) +
BXY( p1, 1, dx1, dy1 ) +
BXY( p1, 2, dx2, dy1 ) +
BXY( p1, 3, dx3, dy1 ) +
BXY( p2, 0, dx0, dy2 ) +
BXY( p2, 1, dx1, dy2 ) +
BXY( p2, 2, dx2, dy2 ) +
BXY( p2, 3, dx3, dy2 ) +
BXY( p3, 0, dx0, dy3 ) +
BXY( p3, 1, dx1, dy3 ) +
BXY( p3, 2, dx2, dy3 ) +
BXY( p3, 3, dx3, dy3 );
}
private:
double BXY( const double* __restrict__ p, int j, double x, double y ) const noexcept
{
return p[j]*B( x )*B( y );
}
double B( double x ) const noexcept
{
double fx = (x > 0) ? x*x*x : 0;
double fxp1 = x + 1;
fxp1 = (fxp1 > 0) ? fxp1*fxp1*fxp1 : 0;
double fxp2 = x + 2;
fxp2 = (fxp2 > 0) ? fxp2*fxp2*fxp2 : 0;
double fxm1 = x - 1;
fxm1 = (fxm1 > 0) ? fxm1*fxm1*fxm1 : 0;
return (fxp2 - 4*fxp1 + 6*fx - 4*fxm1)/6;
}
};
// ----------------------------------------------------------------------------
#undef InitXY
#undef InitYX
// ----------------------------------------------------------------------------
#undef m_width
#undef m_height
#undef m_fillBorder
#undef m_fillValue
#undef m_data
// ----------------------------------------------------------------------------
} // pcl
#endif // __PCL_BicubicInterpolation_h
// ----------------------------------------------------------------------------
// EOF pcl/BicubicInterpolation.h - Released 2022-03-12T18:59:29Z
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