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icc_formeln.cpp
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icc_formeln.cpp
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/*
* ICC Examin ist eine ICC Profil Betrachter
*
* Copyright (C) 2004-2011 Kai-Uwe Behrmann
*
* Autor: Kai-Uwe Behrmann <ku.b@gmx.de>
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*
* -----------------------------------------------------------------------------
*
* some mathematical formulas
*
*/
// Date: 26. 08. 2004
#if 0
# ifndef DEBUG
# define DEBUG
# endif
# define DEBUG_ICCFORMELN
#endif
#include "icc_formeln.h"
#include <cmath>
#include <cstring>
#ifdef DEBUG_ICCFORMELN
# define DBG_v(x) DBG_NUM_V(x)
#else
# define DBG_v(x)
#endif
double
gradATAN(const double b, const double a)
{
if ((b) == 0 && (a) == 0) {
return 0.0;
} else {
double d = atan2 ((b),(a));
if (d < 0.0)
d = d + 2.0*M_PI;
if (d > 2.0*M_PI)
d = d - 2.0*M_PI;
d = d * 180.0/M_PI;
return d;
}
}
double
dE2000 (const Lab_s & Lab1_n, const Lab_s & Lab2_n,
const double kL, const double kC, const double kH) // (1)
{
// convert to CIE*Lab
Lab_s Lab1, Lab2;
Lab1.L = Lab1_n.L * 100.;
Lab2.L = Lab2_n.L * 100.;
Lab1.a = Lab1_n.a * 256. - 128.;
Lab2.a = Lab2_n.a * 256. - 128.;
Lab1.b = Lab1_n.b * 256. - 128.;
Lab2.b = Lab2_n.b * 256. - 128.;
/*
* Aus: "The CIEDE2000 Color-Difference Formula:
* Implementation Notes, Supplementary Test
* Data, and Mathematical Observations "
* Gaurav Sharma, Wencheng Wu, Edul N. Dalal
*
* in ciede2000noteCRNA.pdf
*/
# define nachRAD(grad) (M_PI*(grad)/180.0)
# define QUAD(num) (num)*(num)
double Cs1ab = sqrt( QUAD(Lab1.a) + QUAD(Lab1.b)); DBG_v (Cs1ab)
double Cs2ab = sqrt( QUAD(Lab2.a) + QUAD(Lab2.b)); DBG_v (Cs2ab) // (2)
double Cab = (Cs1ab + Cs2ab) / 2; DBG_v (Cab) // (3)
double G = 0.5 * (1.0 - sqrt( pow(Cab,7) / (pow(Cab,7) + pow((double)25,7)))); DBG_v (G)
// (4)
double a1 = (1.0+G) * Lab1.a; DBG_v (a1)
double a2 = (1.0+G) * Lab2.a; DBG_v (a2) // (5)
double C1 = sqrt( QUAD(a1) + QUAD(Lab1.b)); DBG_v (C1)
double C2 = sqrt( QUAD(a2) + QUAD(Lab2.b)); DBG_v (C2) // (6)
double h1 = gradATAN(Lab1.b, a1);
double h2 = gradATAN(Lab2.b, a2); DBG_v (h1) DBG_v (h2) // (7)
//------------------------------------------------------
double dL = Lab2.L - Lab1.L; DBG_v (dL) // (8)
double dC = C2 - C1; DBG_v (dC) // (9)
double dh = 0.0; // (C1*C2 == 0.0)
if (C1*C2 != 0.0) {
if ((h2 - h1) < -180.0) {
dh = (h2 - h1) + 360.0; DBG_v (dh)
} else if ((h2 - h1) <= 180.0) {
dh = h2 - h1; DBG_v (dh <<" "<< h2 <<" "<< h1)
} else {// if ((h2 - h1) > 180.0) {
dh = (h2 - h1) - 360.0; DBG_v (dh)
}
} DBG_v (dh) // (10)
double dH = 2.0 * sqrt(C1 * C2) * sin (nachRAD(dh / 2.0)); DBG_v (dH)//(11)
//------------------------------------------------------
double aL = (Lab1.L + Lab2.L) / 2.0; DBG_v (aL) // (12)
double aC = (C1 + C2) / 2.0; DBG_v (aC) // (13)
double mean_h= (h1 + h2); // (C1*C2 == 0.0)
# if 1
if (C1*C2 != 0.0) {
if (fabs(h1 - h2) <= 180.0) {
mean_h= (h1 + h2) / 2.0; DBG_v (mean_h)
} else {// if ((h1 - h2) > 180.0) {
if ((h1 + h2) < 360.0) {
mean_h= (h1 + h2) / 2.0 + 180.0; DBG_v (mean_h)
} else {
mean_h= (h1 + h2) / 2.0 - 180.0; DBG_v (mean_h)
}
}
} DBG_v (mean_h) // (14)
# else
if ( fabs(h1-h2) > 180.0 ) {
mean_h = MAX(h1,h2) + (360.0 - fabs ( h1-h2 )) / 2.0; DBG_v (mean_h)
} else {
mean_h = MIN(h1,h2) + fabs ( h1-h2 ) / 2.0; DBG_v (mean_h)
}
while (mean_h > 360.0)
mean_h = mean_h - 360.0; DBG_v (mean_h) // (14)
# endif
double T = 1.0 - 0.17 * cos (nachRAD(mean_h - 30.0))
+ 0.24 * cos (nachRAD(2.0 * mean_h))
+ 0.32 * cos (nachRAD(3.0 * mean_h + 6.0))
- 0.20 * cos (nachRAD(4.0 * mean_h - 63.0));DBG_v (T)//(15)
double dTheta= 30.0 * exp (- QUAD((mean_h - 275.0)/25.0)); DBG_v (dTheta)
// (16)
double RC = 2.0 * sqrt( pow(aC,7)/(pow(aC,7) + pow((double)25, 7))); DBG_v (RC)
// (17)
double SL = 1.0 + (0.015 * QUAD(aL - 50.0))
/ sqrt(20.0 + QUAD(aL - 50.0)); DBG_v (SL) // (18)
double SC = 1.0 + 0.045 * aC; DBG_v (SC) // (19)
double SH = 1.0 + 0.015 * aC * T; DBG_v (SH) // (20)
double RT = - sin (nachRAD(2.0 * dTheta)) * RC; DBG_v (RT) // (21)
double de2000= sqrt(
QUAD(dL / (kL * SL))
+ QUAD(dC / (kC * SC))
+ QUAD(dH / (kH * SH))
+ RT * dC / (kC * SC)
* dH / (kH * SH)
); // (22)
DBG_v ( de2000 )
return de2000;
}
double
dE ( const Lab_s Lab1, const Lab_s Lab2 )
{
double l1[3], l2[3];
LabToCIELab( Lab1, l1 );
LabToCIELab( Lab2, l2 );
return dE( l1, l2 );
}
double
dE ( const double * l1, const Lab_s Lab2 )
{
double l2[3];
LabToCIELab( Lab2, l2 );
return dE( l1, l2 );
}
double
dE ( const double * l1, const double * l2 )
{
return HYP3( l1[0]-l2[0], l1[1]-l2[1], l1[2]-l2[2] );
}
void
LabtoXYZ (const Lab_s &lab, XYZ_s &XYZ)
{
double l[3];
//double e = 216./24389.; // 0.0088565
//double k = 24389./27.; // 903.30
double d = 6./29.; // 0.20690
double Xn = 0.964294;
double Yn = 1.000000;
double Zn = 0.825104;
LabToCIELab(lab, l);
double fy = (l[0] + 16) / 116.;
double fx = fy + l[1] / 500.;
double fz = fy - l[2] / 200.;
if(fy > d)
XYZ.Y = Yn * pow( fy, 3 );
else
XYZ.Y = (fy - 16./116.) * 3 * pow( d, 2 ) * Yn;
if(fx > d)
XYZ.X = Xn * pow( fx, 3 );
else
XYZ.X = (fx - 16./116.) * 3 * pow( d, 2 ) * Xn;
if(fz > d)
XYZ.Z = Zn * pow( fz, 3 );
else
XYZ.Z = (fz - 16./116.) * 3 * pow( d, 2 ) * Zn;
}
void
XYZtoLab (const XYZ_s &xyz, Lab_s &lab)
{
/* white point D50 [0.964294 , 1.000000 , 0.825104]
* XYZ->Lab is defined as (found with the help of Marti Maria):
*
* L* = 116*f(Y/Yn) - 16 0 <= L* <= 100
* a* = 500*[f(X/Xn) - f(Y/Yn)]
* b* = 200*[f(Y/Yn) - f(Z/Zn)]
*
* and
*
* f(t) = t^(1/3) 1 >= t > 0.008856
* 7.787*t + (16/116) 0 <= t <= 0.008856
*/
double gamma = 1.0/3.0; // standard is 1.0/3.0
XYZ_s xyz_;
double K = 24389./27.;
double k = K/116.; // 7.787
double e = 216./24389.; // 0.008856
// CIE XYZ -> CIE*Lab (D50)
xyz_.X = xyz.X / 0.964294;
xyz_.Y = xyz.Y / 1.000000;
xyz_.Z = xyz.Z / 0.825104;
if ( xyz_.X > e)
xyz_.X = pow (xyz_.X, gamma);
else
xyz_.X = k * xyz_.X + (16.0/116.0);
if ( xyz_.Y > e)
xyz_.Y = pow ( xyz_.Y, gamma);
else
xyz_.Y = k * xyz_.Y + (16.0/116.0);
if ( xyz_.Z > e)
xyz_.Z = pow ( xyz_.Z, gamma);
else
xyz_.Z = k * xyz_.Z + (16.0/116.0);
// auf 0.0-1.0 normalise ------v
lab.L = (116.0* xyz_.Y - 16.0) / 100.0;
lab.a = (500.0*( xyz_.X - xyz_.Y) + 128.0) / 256.0 ;
lab.b = (200.0*( xyz_.Y - xyz_.Z) + 128.0) / 256.0 ;
}
void
XYZtoLab (const double* xyz, double* lab, int n)
{
XYZ_s xyz_;
Lab_s lab_;
for(int i = 0; i < n; ++i) {
xyz_.X = xyz[i*3+0];
xyz_.Y = xyz[i*3+1];
xyz_.Z = xyz[i*3+2];
XYZtoLab (xyz_, lab_);
lab[i*3+0] = lab_.L;
lab[i*3+1] = lab_.a;
lab[i*3+2] = lab_.b;
}
}
void
CIELabToLab (const double* cielab, double* lab, int n)
{
for(int i = 0; i < n; ++i)
{
lab[i*3+0] = cielab[i*3+0] / 100.0;
lab[i*3+1] = (cielab[i*3+1] + 128.0) / 256.0;
lab[i*3+2] = (cielab[i*3+2] + 128.0) / 256.0;
}
}
void
CIELabToLab (const double* cielab, Lab_s & lab)
{
lab.L = cielab[0] / 100.0;
lab.a = (cielab[1] + 128.0) / 256.0;
lab.b = (cielab[2] + 128.0) / 256.0;
}
void
LabToCIELab (const double* lab, double* cielab, int n)
{
for(int i = 0; i < n; ++i)
{
cielab[i*3+0] = lab[i*3+0] * 100.0;
cielab[i*3+1] = (lab[i*3+1] * 256.0) - 128.0;
cielab[i*3+2] = (lab[i*3+2] * 256.0) - 128.0;
//DBG_NUM_V( lab[i*3+0] <<" "<< lab[i*3+1] <<" "<< lab[i*3+2] )
//DBG_NUM_V( cielab[i*3+0] <<" "<< cielab[i*3+1] <<" "<< cielab[i*3+2] )
}
}
void
LabToCIELab (const Lab_s & lab, double* cielab)
{
cielab[0] = lab.L * 100.0;
cielab[1] = (lab.a * 256.0) - 128.0;
cielab[2] = (lab.b * 256.0) - 128.0;
}
void
FarbeZuDouble (double* d_xyz, XYZ_s xyz)
{ DBG_PROG
d_xyz[0] = xyz.X;
d_xyz[1] = xyz.Y;
d_xyz[2] = xyz.Z;
}
void
FarbeZuDouble (XYZ_s *xyz, double* d_xyz)
{ DBG_PROG
xyz->X = d_xyz[0];
xyz->Y = d_xyz[1];
xyz->Z = d_xyz[2];
}
void
FarbeZuDouble (double* d_lab, Lab_s lab)
{ DBG_PROG
d_lab[0] = lab.L;
d_lab[1] = lab.a;
d_lab[2] = lab.b;
}
void
FarbeZuDouble (Lab_s *lab, double* d_lab)
{ DBG_PROG
lab->L = d_lab[0];
lab->a = d_lab[1];
lab->b = d_lab[2];
}
void
FarbeZuDouble (double* d_rgb, RGB_s rgb)
{ DBG_PROG
d_rgb[0] = rgb.R;
d_rgb[1] = rgb.G;
d_rgb[2] = rgb.B;
}
void
FarbeZuDouble (RGB_s *rgb, double* d_rgb)
{ DBG_PROG
rgb->R = d_rgb[0];
rgb->G = d_rgb[1];
rgb->B = d_rgb[2];
}
void
FarbeZuDouble (double* d_cmyk, CMYK_s cmyk)
{ DBG_PROG
d_cmyk[0] = cmyk.C;
d_cmyk[1] = cmyk.M;
d_cmyk[2] = cmyk.Y;
d_cmyk[3] = cmyk.K;
}
void
FarbeZuDouble (CMYK_s *cmyk, double* d_cmyk)
{ DBG_PROG
cmyk->C = d_cmyk[0];
cmyk->M = d_cmyk[1];
cmyk->Y = d_cmyk[2];
cmyk->K = d_cmyk[3];
}