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// This function written in JavaScript 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) {
"use strict"
// Working in JavaScript 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...
var k_l = 1.0, k_c = 1.0, k_h = 1.0;
var n = (Math.sqrt(a_1 * a_1 + b_1 * b_1) + Math.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 - Math.sqrt(n / (n + 6103515625.0)));
// Application of the chroma correction factor.
var c_1 = Math.sqrt(a_1 * a_1 * n * n + b_1 * b_1);
var c_2 = Math.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.
var h_1 = Math.atan2(b_1, a_1 * n), h_2 = Math.atan2(b_2, a_2 * n);
h_1 += 2.0 * Math.PI * (h_1 < 0.0);
h_2 += 2.0 * Math.PI * (h_2 < 0.0);
n = Math.abs(h_2 - h_1);
// Cross-implementation consistent rounding.
if (Math.PI - 1E-14 < n && n < Math.PI + 1E-14)
n = Math.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.
var h_m = (h_1 + h_2) * 0.5, h_d = (h_2 - h_1) * 0.5;
if (Math.PI < n) {
h_d += Math.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 += Math.PI;
// h_m += h_m < Math.PI ? Math.PI : -Math.PI;
}
var p = 36.0 * h_m - 55.0 * Math.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.
var r_t = -2.0 * Math.sqrt(n / (n + 6103515625.0))
* Math.sin(Math.PI / 3.0 * Math.exp(p * p / (-25.0 * Math.PI * Math.PI)));
n = (l_1 + l_2) * 0.5;
n = (n - 50.0) * (n - 50.0);
// Lightness.
var l = (l_2 - l_1) / (k_l * (1.0 + 0.015 * n / Math.sqrt(20.0 + n)));
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
var t = 1.0 + 0.24 * Math.sin(2.0 * h_m + Math.PI * 0.5)
+ 0.32 * Math.sin(3.0 * h_m + 8.0 * Math.PI / 15.0)
- 0.17 * Math.sin(h_m + Math.PI / 3.0)
- 0.20 * Math.sin(4.0 * h_m + 3.0 * Math.PI / 20.0);
n = c_1 + c_2;
// Hue.
var h = 2.0 * Math.sqrt(c_1 * c_2) * Math.sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
// Chroma.
var 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 Math.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 = 66.1 a1 = 24.8 b1 = 4.6
// L2 = 66.7 a2 = 30.3 b2 = -4.1
// CIE ΔE00 = 6.0771971996 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 6.0771831645 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.4e-5
// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
// These color conversion functions written in JavaScript are released into the public domain.
// They are provided "as is" without any warranty, express or implied.
// rgb in 0..1
function rgb_to_xyz(r, g, b) {
// Apply a gamma correction to each channel.
r = r < 0.040448236277105097 ? r / 12.92 : Math.pow((r + 0.055) / 1.055, 2.4)
g = g < 0.040448236277105097 ? g / 12.92 : Math.pow((g + 0.055) / 1.055, 2.4)
b = b < 0.040448236277105097 ? b / 12.92 : Math.pow((b + 0.055) / 1.055, 2.4)
// Applying linear transformation using RGB to XYZ transformation matrix.
var x = r * 41.24564390896921145 + g * 35.75760776439090507 + b * 18.04374830853290341
var y = r * 21.26728514056222474 + g * 71.51521552878181013 + b * 7.21749933075596513
var z = r * 1.93338955823293176 + g * 11.91919550818385936 + b * 95.03040770337479886
return [x, y, z]
}
function xyz_to_lab(x, y, z) {
// Reference white point : D65 2° Standard observer
var refX = 95.047
var refY = 100.000
var refZ = 108.883
x /= refX
y /= refY
z /= refZ
// Applying the CIE standard transformation.
x = x < 216.0 / 24389.0 ? ((841.0 / 108.0) * x) + (4.0 / 29.0) : Math.cbrt(x)
y = y < 216.0 / 24389.0 ? ((841.0 / 108.0) * y) + (4.0 / 29.0) : Math.cbrt(y)
z = z < 216.0 / 24389.0 ? ((841.0 / 108.0) * z) + (4.0 / 29.0) : Math.cbrt(z)
var l = (116.0 * y) - 16.0
var a = 500.0 * (x - y)
var b = 200.0 * (y - z)
return [l, a, b]
}
// rgb in 0..1
function rgb_to_lab(r, g, b) {
var xyz = rgb_to_xyz(r, g, b)
return xyz_to_lab(xyz[0], xyz[1], xyz[2])
}
function lab_to_xyz(l, a, b) {
// Reference white point : D65 2° Standard observer
var refX = 95.047
var refY = 100.000
var refZ = 108.883
var y = (l + 16.0) / 116.0
var x = a / 500.0 + y
var z = y - b / 200.0
var x3 = x * x * x
var z3 = z * z * z
x = x3 < 216.0 / 24389.0 ? (x - 4.0 / 29.0) / (841.0 / 108.0) : x3
y = l < 8.0 ? l / (24389.0 / 27.0) : y * y * y
z = z3 < 216.0 / 24389.0 ? (z - 4.0 / 29.0) / (841.0 / 108.0) : z3
return [x * refX, y * refY, z * refZ]
}
// rgb in 0..1
function xyz_to_rgb(x, y, z) {
// Applying linear transformation using the XYZ to RGB transformation matrix.
var r = x * 0.032404541621141049051 + y * -0.015371385127977165753 + z * -0.004985314095560160079
var g = x * -0.009692660305051867686 + y * 0.018760108454466942288 + z * 0.00041556017530349983
var b = x * 0.000556434309591145522 + y * -0.002040259135167538416 + z * 0.010572251882231790398
// Apply gamma correction.
r = r < 0.003130668442500634 ? 12.92 * r : 1.055 * Math.pow(r, 1.0 / 2.4) - 0.055
g = g < 0.003130668442500634 ? 12.92 * g : 1.055 * Math.pow(g, 1.0 / 2.4) - 0.055
b = b < 0.003130668442500634 ? 12.92 * b : 1.055 * Math.pow(b, 1.0 / 2.4) - 0.055
return [r, g, b]
}
// rgb in 0..1
function lab_to_rgb(l, a, b) {
var xyz = lab_to_xyz(l, a, b)
return xyz_to_rgb(xyz[0], xyz[1], xyz[2])
}
// rgb in 0..255
function hex_to_rgb(s) {
// Also support the short syntax (ie "#FFF") as input.
var n = parseInt((s.length === 4 ? s[0] + s[1] + s[1] + s[2] + s[2] + s[3] + s[3] : s).substring(1), 16)
return [n >> 16 & 0xff, n >> 8 & 0xff, n & 0xff]
}
// rgb in 0..255
function rgb_to_hex(r, g, b) {
// Also provide the short syntax (ie "#FFF") as output.
var s = '#' + r.toString(16).padStart(2, '0') + g.toString(16).padStart(2, '0') + b.toString(16).padStart(2, '0')
return s[1] === s[2] && s[3] === s[4] && s[5] === s[6] ? '#' + s[1] + s[3] + s[5] : s
}
//////////////////////////////////////////////////
/////////// /////////////////
/////////// CIE ΔE2000 Demo /////////////////
/////////// /////////////////
//////////////////////////////////////////////////
// The goal of this demo in JavaScript is to use the CIEDE2000 function to compare two hexadecimal colors.
const hex_1 = "#00f"; // blue
const hex_2 = "#483D8B"; // darkslateblue
// 1. hex -> RGB (0..255)
const [r_1, g_1, b_1] = hex_to_rgb(hex_1);
const [r_2, g_2, b_2] = hex_to_rgb(hex_2);
console.log(`${hex_1.padEnd(8)} -> RGB(${r_1}, ${g_1}, ${b_1})`);
console.log(`${hex_2.padEnd(8)} -> RGB(${r_2}, ${g_2}, ${b_2})`);
// 2. RGB -> LAB
const [l_1, a_1, b_1_lab] = rgb_to_lab(r_1 / 255.0, g_1 / 255.0, b_1 / 255.0);
const [l_2, a_2, b_2_lab] = rgb_to_lab(r_2 / 255.0, g_2 / 255.0, b_2 / 255.0);
console.log(`${hex_1.padEnd(8)} -> LAB(L: ${l_1.toFixed(4)}, a: ${a_1.toFixed(4)}, b: ${b_1_lab.toFixed(4)})`);
console.log(`${hex_2.padEnd(8)} -> LAB(L: ${l_2.toFixed(4)}, a: ${a_2.toFixed(4)}, b: ${b_2_lab.toFixed(4)})`);
// 3. Delta E 2000
const delta_e = ciede_2000(l_1, a_1, b_1_lab, l_2, a_2, b_2_lab);
console.log(`ΔE2000 between ${hex_1} and ${hex_2}: ${delta_e.toFixed(4)}`);
// This shows a ΔE2000 of 15.91