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DoViLutGen: add conversion to BT.709
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@erazortt
erazortt committed Mar 1, 2024
1 parent 826226c commit 2558c99
Showing 1 changed file with 205 additions and 26 deletions.
231 changes: 205 additions & 26 deletions DoViBaker/DoViLutGen.cpp
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Original file line number Diff line number Diff line change
@@ -1,13 +1,14 @@
#include "def.h"
#include <fstream>
#include <algorithm>

double EOTFpq(double ep)
{
static const double m1 = 2610.0 / 4096 / 4;
static const double m2 = 2523.0 / 4096 * 128;
static const double c3 = 2392.0 / 4096 * 32;
static const double c2 = 2413.0 / 4096 * 32;
static const double c1 = c3 - c2 + 1;
static constexpr double m1 = 2610.0 / 4096 / 4;
static constexpr double m2 = 2523.0 / 4096 * 128;
static constexpr double c3 = 2392.0 / 4096 * 32;
static constexpr double c2 = 2413.0 / 4096 * 32;
static constexpr double c1 = c3 - c2 + 1;

const double epower = pow(ep, 1 / m2);
const double num = std::max(epower - c1, 0.0);
Expand All @@ -18,16 +19,16 @@ double EOTFpq(double ep)
double OOTFhlgInv(double fd, double yd)
{
if (yd > 0) {
static const double power = (1 - 1.2) / 1.2;
static constexpr double power = (1 - 1.2) / 1.2;
return fd * pow(yd, power);
}
return 0;
}

double OETFhlg(double e)
{
static const double a = 0.17883277;
static const double b = 1 - 4 * a;
static constexpr double a = 0.17883277;
static constexpr double b = 1 - 4 * a;
static const double c = 0.5 - a * std::log(4 * a);

if (e * 12 < 1) {
Expand All @@ -36,6 +37,26 @@ double OETFhlg(double e)
return a * std::log(12 * e - b) + c;
}

double OETFsdr(double l) {
static constexpr double a = 1.099296827;
static constexpr double b = 0.018053969;
static constexpr double c = a - b - 1;

if (l < b)
return 4.5 * l;
return a * std::pow(l, 0.45) - (a - 1);
}

double EOTFsdr(double g) {
static constexpr double a = 1.099296827;
static constexpr double b = 0.018053969;
static constexpr double c = a - b - 1;

if (g < c)
return g/4.5;
return std::pow((g + (a - 1))/a, 1.0/0.45);
}


// this function maps the hlg signal above 203 nits to the sdr signal range until it runs out of sdr signal range at 267.6nits hlg
// thus when the sdr is viewed it appears idential to the hlg as long as the hlg stays below these 267.6 nits
Expand Down Expand Up @@ -82,6 +103,132 @@ double hlg2sdr(double x, double kS, double m1Factor) {
return x * matchHlg2Sdr(x);
}

bool outOfRange(double r, double g, double b) {
return b < 0 || b > 1 || g < 0 || g > 1 || r < 0 || r > 1;
}

void xyzFromRgb2020(double& x, double& y, double& z, double rl, double gl, double bl) {
x = 0.636958048 * rl + 0.144616904 * gl + 0.168880975 * bl;
y = 0.262700212 * rl + 0.677998072 * gl + 0.059301716 * bl;
z = 0.000000000 * rl + 0.028072693 * gl + 1.060985058 * bl;
}
void rgb2020FromXYZ(double& rl, double& gl, double& bl, double x, double y, double z) {
rl = 1.716651188 * x - 0.355670784 * y - 0.253366281 * z;
gl = -0.666684352 * x + 1.616481237 * y + 0.015768546 * z;
bl = 0.017639857 * x - 0.042770613 * y + 0.942103121 * z;
}

void xyzFromRgb709(double& x, double& y, double& z, double rl, double gl, double bl) {
x = 0.412390799 * rl + 0.357584339 * gl + 0.180480788 * bl;
y = 0.212639006 * rl + 0.715168679 * gl + 0.072192315 * bl;
z = 0.019330819 * rl + 0.119194780 * gl + 0.950532152 * bl;
}
void rgb709FromXYZ(double& rl, double& gl, double& bl, double x, double y, double z) {
rl = 3.240969942 * x - 1.537383178 * y - 0.498610760 * z;
gl = -0.969243636 * x + 1.875967502 * y + 0.041555057 * z;
bl = 0.055630080 * x - 0.203976959 * y + 1.056971514 * z;
}

void lmsFromXYZ(double& l, double& m, double& s, double x, double y, double z) {
l = 0.8189330101 * x + 0.3618667424 * y - 0.1288597137 * z;
m = 0.0329845436 * x + 0.9293118715 * y + 0.0361456387 * z;
s = 0.0482003018 * x + 0.2643662691 * y + 0.6338517070 * z;
}
void XYZfromLms(double& x, double& y, double& z, double l, double m, double s) {
x = 1.227013851 * l - 0.557799981 * m + 0.281256149 * s;
y = -0.040580178 * l + 1.11225687 * m - 0.071676679 * s;
z = -0.076381285 * l - 0.421481978 * m + 1.58616322 * s;
}

void labFromLms(double& L, double& a, double& b, double l, double m, double s) {
l = std::pow(l, 0.33333333);
m = std::pow(m, 0.33333333);
s = std::pow(s, 0.33333333);
L = 0.2104542553 * l + 0.7936177850 * m - 0.0040720468 * s;
a = 1.9779984951 * l - 2.4285922050 * m + 0.4505937099 * s;
b = 0.0259040371 * l + 0.7827717662 * m - 0.8086757660 * s;
}
void lmsFromLab(double& l, double& m, double& s, double L, double a, double b) {
l = 1.000000000 * L + 0.396337792 * a + 0.215803758 * b;
m = 1.000000000 * L - 0.105561342 * a - 0.063854175 * b;
s = 1.000000000 * L - 0.089484182 * a - 1.291485538 * b;
l = l*l*l;
m = m*m*m;
s = s*s*s;
}

void labFromRgb2020(double& L, double& a, double& b, double rl, double gl, double bl) {
double x, y, z;
xyzFromRgb2020(x, y, z, rl, gl, bl);
double l, m, s;
lmsFromXYZ(l, m, s, x, y, z);
labFromLms(L, a, b, l, m, s);
}
void labFromRgb709(double& L, double& a, double& b, double rl, double gl, double bl) {
double x, y, z;
xyzFromRgb709(x, y, z, rl, gl, bl);
double l, m, s;
lmsFromXYZ(l, m, s, x, y, z);
labFromLms(L, a, b, l, m, s);
}
void rgb2020fromLab(double& rl, double& gl, double& bl, double L, double a, double b) {
double l, m, s;
lmsFromLab(l, m, s, L, a, b);
double x, y, z;
XYZfromLms(x, y, z, l, m, s);
rgb2020FromXYZ(rl, gl, bl, x, y, z);
}
void rgb709fromLab(double& rl, double& gl, double& bl, double L, double a, double b) {
double l, m, s;
lmsFromLab(l, m, s, L, a, b);
double x, y, z;
XYZfromLms(x, y, z, l, m, s);
rgb709FromXYZ(rl, gl, bl, x, y, z);
}

void convert2020To709(double& rl, double& gl, double& bl) {
double x, y, z;
xyzFromRgb2020(x, y, z, rl, gl, bl);
rgb709FromXYZ(rl, gl, bl, x, y, z);
}

void clip2020Chroma(double& rl, double& gl, double& bl) {
double L, a, b;
labFromRgb2020(L, a, b, rl, gl, bl);
double f=0.5;
for (int d = 4; d < 16385; d *= 2) {
rgb2020fromLab(rl, gl, bl, L, a*f, b*f);
if (outOfRange(rl, gl, bl)) {
f -= 1.0 / d;
}
else {
f += 1.0 / d;
}
}
}

void clip709Chroma(double& rl, double& gl, double& bl) {
double L, a, b;
labFromRgb709(L, a, b, rl, gl, bl);
double f = 0.5;
for (int d = 4; d < 8193; d *= 2) {
rgb709fromLab(rl, gl, bl, L, a * f, b * f);
if (outOfRange(rl, gl, bl)) {
f -= 1.0 / d;
}
else {
f += 1.0 / d;
}
}
}

void reduceChroma(double& rl, double& gl, double& bl) {
double L, a, b;
labFromRgb2020(L, a, b, rl, gl, bl);
double f = 0.9418;
rgb2020fromLab(rl, gl, bl, L, a * f, b * f);
}

void showBestLutSizes() {
printf("For unnormalized PQ inputs only the following LUT sizes should be used:\n");
for (int s = 2; s < 139; s++) {
Expand Down Expand Up @@ -111,9 +258,13 @@ int main(int argc, char* argv[])
printf("DoViLutGen.exe pq2hlg.cube 65\n");
printf("DoViLutGen.exe pq2hlg_normalizedInput.cube 50 1\n");
printf("\n");
printf("examples for PQ to SDR conversions:\n");
printf("DoViLutGen.exe pq2sdr.cube 65 0 1\n");
printf("DoViLutGen.exe pq2sdr_normalizedInput.cube 50 1 1\n");
printf("examples for PQ to BT.2020 SDR conversions:\n");
printf("DoViLutGen.exe pq2sdr2020.cube 65 0 1\n");
printf("DoViLutGen.exe pq2sdr2020_normalizedInput.cube 50 1 1\n");
printf("\n");
printf("examples for PQ to BT.709 SDR conversions:\n");
printf("DoViLutGen.exe pq2sdr709.cube 65 0 2\n");
printf("DoViLutGen.exe pq2sdr709_normalizedInput.cube 50 1 2\n");
printf("\n");
showBestLutSizes();
return 1;
Expand All @@ -133,13 +284,18 @@ int main(int argc, char* argv[])
}

std::string mode = "HLG";
bool sdr = false;
int sdr = false;
double sdrGain = 0.0;
double sdrCompression = 0.0;
if (argc > 4) {
sdr = std::atoi(argv[4]);
if (sdr) {
mode = "SDR";
if (sdr > 1) {
mode = "BT.709 SDR";
}
else {
mode = "BT.2020 SDR";
}
}
if (argc > 5) {
sdrGain = std::atof(argv[5]);
Expand Down Expand Up @@ -178,7 +334,7 @@ int main(int argc, char* argv[])
fsCube << "# midtone gain: " << sdrGain << " (kS=" << sdrKneeStart << ")" << std::endl;
fsCube << "# highlight compression: " << sdrCompression << " (m1Factor=" << sdrKneeEndTangentFactor << ")" << std::endl;
printf("Producing a LUT for PQ -> SDR conversions of size %i\n", lutSize);
fsCube << "# LUT for conversions from BT.2100 HDR PQ to BT.2020 SDR" << std::endl;
fsCube << "# LUT for conversions from BT.2100 HDR PQ to " << mode << std::endl;
}
else {
printf("Producing LUT for PQ -> HLG conversions of size %i\n", lutSize);
Expand All @@ -190,11 +346,11 @@ int main(int argc, char* argv[])
printf("The LUT will expect the PQ input to be re-normalized to 1000 nits\n");
inputScale = 0.7518271;
fsCube << "# ATTENTION: This special LUT expects the PQ input to be re-normalized to 1000nits max brightness!" << std::endl;
fsCube << "TITLE \"PQ_renorm_1000nits_to_" << mode << "\"" << std::endl;
fsCube << "TITLE \"PQ renorm 1000nits to " << mode << "\"" << std::endl;
}
else {
printf("The LUT will expect usual PQ input\n");
fsCube << "TITLE \"PQ_to_" << mode << "\"" << std::endl;
fsCube << "TITLE \"PQ to " << mode << "\"" << std::endl;
}
fsCube << "LUT_3D_SIZE " << lutSize << std::endl;

Expand All @@ -213,22 +369,45 @@ int main(int argc, char* argv[])
rd = (rd > 1) ? 1 : rd;

double yd = 0.2627 * rd + 0.6780 * gd + 0.0593 * bd;
double bs = OOTFhlgInv(bd, yd);
double gs = OOTFhlgInv(gd, yd);
double rs = OOTFhlgInv(rd, yd);
double bg = OETFhlg(bs);
double gg = OETFhlg(gs);
double gs = OOTFhlgInv(gd, yd);
double bs = OOTFhlgInv(bd, yd);

/*if (outOfRange(rs, gs, bs)) {
clip2020Chroma(rs, gs, bs);
}*/

double rg = OETFhlg(rs);
double gg = OETFhlg(gs);
double bg = OETFhlg(bs);

bg = std::clamp(bg, 0.0, 1.0);
gg = std::clamp(gg, 0.0, 1.0);
rg = std::clamp(rg, 0.0, 1.0);

if (sdr) {
bg = hlg2sdr(bg, sdrKneeStart, sdrKneeEndTangentFactor);
gg = hlg2sdr(gg, sdrKneeStart, sdrKneeEndTangentFactor);
rg = hlg2sdr(rg, sdrKneeStart, sdrKneeEndTangentFactor);
}
gg = hlg2sdr(gg, sdrKneeStart, sdrKneeEndTangentFactor);
bg = hlg2sdr(bg, sdrKneeStart, sdrKneeEndTangentFactor);

if (sdr>1) {
double rl = EOTFsdr(rg);
double gl = EOTFsdr(gg);
double bl = EOTFsdr(bg);
reduceChroma(rl, gl, bl);
convert2020To709(rl, gl, bl);
/*if (outOfRange(rl, gl, bl)) {
clip709Chroma(rl, gl, bl);
}*/
rg = OETFsdr(rl);
gg = OETFsdr(gl);
bg = OETFsdr(bl);
}

bg = (bg > 1) ? 1 : bg;
gg = (gg > 1) ? 1 : gg;
rg = (rg > 1) ? 1 : rg;
bg = std::clamp(bg, 0.0, 1.0);
gg = std::clamp(gg, 0.0, 1.0);
rg = std::clamp(rg, 0.0, 1.0);
}

fsCube << rg << " " << gg << " " << bg << std::endl;
}
Expand Down

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