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<?php
// This function written in PHP is not affiliated with the CIE (International Commission on Illumination),
// and is released into the public domain. It is provided "as is" without any warranty, express or implied.
// The classic CIE ΔE2000 implementation, which operates on two L*a*b* colors, and returns their difference.
// "l" ranges from 0 to 100, while "a" and "b" are unbounded and commonly clamped to the range of -128 to 127.
function ciede_2000($l_1, $a_1, $b_1, $l_2, $a_2, $b_2) {
// Working in PHP with the CIEDE2000 color-difference formula.
// k_l, k_c, k_h are parametric factors to be adjusted according to
// different viewing parameters such as textures, backgrounds...
$k_l = $k_c = $k_h = 1.0;
$n = (sqrt($a_1 * $a_1 + $b_1 * $b_1) + sqrt($a_2 * $a_2 + $b_2 * $b_2)) * 0.5;
$n = $n * $n * $n * $n * $n * $n * $n;
// A factor involving chroma raised to the power of 7 designed to make
// the influence of chroma on the total color difference more accurate.
$n = 1.0 + 0.5 * (1.0 - sqrt($n / ($n + 6103515625.0)));
// Application of the chroma correction factor.
$c_1 = sqrt($a_1 * $a_1 * $n * $n + $b_1 * $b_1);
$c_2 = sqrt($a_2 * $a_2 * $n * $n + $b_2 * $b_2);
// atan2 is preferred over atan because it accurately computes the angle of
// a point (x, y) in all quadrants, handling the signs of both coordinates.
$h_1 = atan2($b_1, $a_1 * $n);
$h_2 = atan2($b_2, $a_2 * $n);
$h_1 += 2.0 * M_PI * ($h_1 < 0.0);
$h_2 += 2.0 * M_PI * ($h_2 < 0.0);
$n = abs($h_2 - $h_1);
// Cross-implementation consistent rounding.
if (M_PI - 1E-14 < $n && $n < M_PI + 1E-14)
$n = M_PI;
// When the hue angles lie in different quadrants, the straightforward
// average can produce a mean that incorrectly suggests a hue angle in
// the wrong quadrant, the next lines handle this issue.
$h_m = ($h_1 + $h_2) * 0.5;
$h_d = ($h_2 - $h_1) * 0.5;
if (M_PI < $n) {
$h_d += M_PI;
// 📜 Sharma’s formulation doesn’t use the next line, but the one after it,
// and these two variants differ by ±0.0003 on the final color differences.
$h_m += M_PI;
// $h_m += $h_m < M_PI ? M_PI : -M_PI;
}
$p = 36.0 * $h_m - 55.0 * M_PI;
$n = ($c_1 + $c_2) * 0.5;
$n = $n * $n * $n * $n * $n * $n * $n;
// The hue rotation correction term is designed to account for the
// non-linear behavior of hue differences in the blue region.
$r_t = -2.0 * sqrt($n / ($n + 6103515625.0))
* sin(M_PI / 3.0 * exp($p * $p / (-25.0 * M_PI * M_PI)));
$n = ($l_1 + $l_2) * 0.5;
$n = ($n - 50.0) * ($n - 50.0);
// Lightness.
$l = ($l_2 - $l_1) / ($k_l * (1.0 + 0.015 * $n / sqrt(20.0 + $n)));
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
$t = 1.0 + 0.24 * sin(2.0 * $h_m + M_PI * 0.5)
+ 0.32 * sin(3.0 * $h_m + 8.0 * M_PI / 15.0)
- 0.17 * sin($h_m + M_PI / 3.0)
- 0.20 * sin(4.0 * $h_m + 3.0 * M_PI / 20.0);
$n = $c_1 + $c_2;
// Hue.
$h = 2.0 * sqrt($c_1 * $c_2) * sin($h_d) / ($k_h * (1.0 + 0.0075 * $n * $t));
// Chroma.
$c = ($c_2 - $c_1) / ($k_c * (1.0 + 0.0225 * $n));
// Returning the square root ensures that dE00 accurately reflects the
// geometric distance in color space, which can range from 0 to around 185.
return sqrt($l * $l + $h * $h + $c * $c + $c * $h * $r_t);
}
// GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
// Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
// L1 = 48.0 a1 = 17.3 b1 = 3.4
// L2 = 46.3 a2 = 21.3 b2 = -3.7
// CIE ΔE00 = 5.5770786128 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 5.5770655241 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.3e-5
// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
///////////////////////////////////////////////
///////////////////////////////////////////////
/////// ///////
/////// CIEDE 2000 ///////
/////// Testing Random Colors ///////
/////// ///////
///////////////////////////////////////////////
///////////////////////////////////////////////
// This PHP program outputs a CSV file to standard output, with its length determined by the first CLI argument.
// Each line contains seven columns :
// - Three columns for the random standard L*a*b* color
// - Three columns for the random sample L*a*b* color
// - And the seventh column for the precise Delta E 2000 color difference between the standard and sample
// The output will be correct, this can be verified :
// - With the C driver, which provides a dedicated verification feature
// - By using the JavaScript validator at https://michel-leonard.github.io/ciede2000-color-matching
$n_iterations = 10000;
if (1 < $argc)
$n_iterations = (int) $argv[1] ;
if ($n_iterations < 1)
$n_iterations = 10000;
for($i = 0; $i < $n_iterations; ++$i) {
$l_1 = mt_rand(0, 10000) / 100.0 ;
$a_1 = mt_rand(-12800, 12800) / 100.0 ;
$b_1 = mt_rand(-12800, 12800) / 100.0 ;
$l_2 = mt_rand(0, 10000) / 100.0 ;
$a_2 = mt_rand(-12800, 12800) / 100.0 ;
$b_2 = mt_rand(-12800, 12800) / 100.0 ;
$delta_e = ciede_2000($l_1, $a_1, $b_1, $l_2, $a_2, $b_2);
echo "$l_1,$a_1,$b_1,$l_2,$a_2,$b_2,$delta_e\n";
}