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-- This function written in Lua 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.
-- Calculates the CIE ΔE2000 color difference between two RGB or hex colors.
-- Accepts RGB values (0–255) and/or hex strings ("#fff" or "#ffffff").
-- Returns the Delta E 2000 value as a numerical difference.
function ciede_2000(r_1, g_1, b_1, r_2, g_2, b_2)
-- Begin : Hex -> RGB
if type(r_1) == "string" then
if type(g_1) == "string" then
if #g_1 == 4 then
r_2 = tonumber(g_1:sub(2, 2) .. g_1:sub(2, 2), 16)
g_2 = tonumber(g_1:sub(3, 3) .. g_1:sub(3, 3), 16)
b_2 = tonumber(g_1:sub(4, 4) .. g_1:sub(4, 4), 16)
else
r_2 = tonumber(g_1:sub(2, 3), 16)
g_2 = tonumber(g_1:sub(4, 5), 16)
b_2 = tonumber(g_1:sub(6, 7), 16)
end
else
b_2, g_2, r_2 = r_2, b_1, g_1
end
if #r_1 == 4 then
b_1 = tonumber(r_1:sub(4, 4) .. r_1:sub(4, 4), 16)
g_1 = tonumber(r_1:sub(3, 3) .. r_1:sub(3, 3), 16)
r_1 = tonumber(r_1:sub(2, 2) .. r_1:sub(2, 2), 16)
else
b_1 = tonumber(r_1:sub(6, 7), 16)
g_1 = tonumber(r_1:sub(4, 5), 16)
r_1 = tonumber(r_1:sub(2, 3), 16)
end
elseif type(r_2) == "string" then
if #r_2 == 4 then
b_2 = tonumber(r_2:sub(4, 4) .. r_2:sub(4, 4), 16)
g_2 = tonumber(r_2:sub(3, 3) .. r_2:sub(3, 3), 16)
r_2 = tonumber(r_2:sub(2, 2) .. r_2:sub(2, 2), 16)
else
b_2 = tonumber(r_2:sub(6, 7), 16)
g_2 = tonumber(r_2:sub(4, 5), 16)
r_2 = tonumber(r_2:sub(2, 3), 16)
end
end
-- End : Hex -> RGB
-- Begin : RGB -> Lab
r_1, g_1, b_1 = r_1 / 255.0, g_1 / 255.0, b_1 / 255.0
r_2, g_2, b_2 = r_2 / 255.0, g_2 / 255.0, b_2 / 255.0
if r_1 < 0.040448236277105097 then r_1 = r_1 / 12.92 else r_1 = ((r_1 + 0.055) / 1.055) ^ 2.4 end
if r_2 < 0.040448236277105097 then r_2 = r_2 / 12.92 else r_2 = ((r_2 + 0.055) / 1.055) ^ 2.4 end
if g_1 < 0.040448236277105097 then g_1 = g_1 / 12.92 else g_1 = ((g_1 + 0.055) / 1.055) ^ 2.4 end
if g_2 < 0.040448236277105097 then g_2 = g_2 / 12.92 else g_2 = ((g_2 + 0.055) / 1.055) ^ 2.4 end
if b_1 < 0.040448236277105097 then b_1 = b_1 / 12.92 else b_1 = ((b_1 + 0.055) / 1.055) ^ 2.4 end
if b_2 < 0.040448236277105097 then b_2 = b_2 / 12.92 else b_2 = ((b_2 + 0.055) / 1.055) ^ 2.4 end
-- Applying linear transformation using RGB to XYZ transformation matrix.
local x_1 = (r_1 * 41.24564390896921145 + g_1 * 35.75760776439090507 + b_1 * 18.04374830853290341) / 95.047
local x_2 = (r_2 * 41.24564390896921145 + g_2 * 35.75760776439090507 + b_2 * 18.04374830853290341) / 95.047
local y_1 = (r_1 * 21.26728514056222474 + g_1 * 71.51521552878181013 + b_1 * 7.21749933075596513) / 100.0
local y_2 = (r_2 * 21.26728514056222474 + g_2 * 71.51521552878181013 + b_2 * 7.21749933075596513) / 100.0
local z_1 = (r_1 * 1.93338955823293176 + g_1 * 11.91919550818385936 + b_1 * 95.03040770337479886) / 108.883
local z_2 = (r_2 * 1.93338955823293176 + g_2 * 11.91919550818385936 + b_2 * 95.03040770337479886) / 108.883
-- Applying the CIE standard transformation.
if x_1 < 216.0 / 24389.0 then x_1 = ((841.0 / 108.0) * x_1) + (4.0 / 29.0) else x_1 = x_1 ^ (1.0 / 3.0) end
if x_2 < 216.0 / 24389.0 then x_2 = ((841.0 / 108.0) * x_2) + (4.0 / 29.0) else x_2 = x_2 ^ (1.0 / 3.0) end
if y_1 < 216.0 / 24389.0 then y_1 = ((841.0 / 108.0) * y_1) + (4.0 / 29.0) else y_1 = y_1 ^ (1.0 / 3.0) end
if y_2 < 216.0 / 24389.0 then y_2 = ((841.0 / 108.0) * y_2) + (4.0 / 29.0) else y_2 = y_2 ^ (1.0 / 3.0) end
if z_1 < 216.0 / 24389.0 then z_1 = ((841.0 / 108.0) * z_1) + (4.0 / 29.0) else z_1 = z_1 ^ (1.0 / 3.0) end
if z_2 < 216.0 / 24389.0 then z_2 = ((841.0 / 108.0) * z_2) + (4.0 / 29.0) else z_2 = z_2 ^ (1.0 / 3.0) end
local l_1 = (116.0 * y_1) - 16.0
local l_2 = (116.0 * y_2) - 16.0
local a_1 = 500.0 * (x_1 - y_1)
local a_2 = 500.0 * (x_2 - y_2)
b_1 = 200.0 * (y_1 - z_1)
b_2 = 200.0 * (y_2 - z_2)
-- End : RGB -> Lab
-- Working in Lua/LuaJIT 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...
local k_l, k_c, k_h = 1.0, 1.0, 1.0;
local 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)));
-- Simulate atan2, as Lua does not originally have this built-in.
local c = a_1 * n;
local c_1 = math.sqrt(c * c + b_1 * b_1);
if 0.0 < a_1 then
h_1 = math.atan(b_1 / c) + (b_1 < 0.0 and 2.0 or 0.0) * math.pi;
elseif a_1 < 0.0 then
h_1 = math.atan(b_1 / c) + math.pi;
else
h_1 = (b_1 < 0.0 and 1.5 or 0.0 < b_1 and 0.5 or 1.0) * math.pi;
end
c = a_2 * n;
local c_2 = math.sqrt(c * c + b_2 * b_2);
if 0.0 < a_2 then
h_2 = math.atan(b_2 / c) + (b_2 < 0.0 and 2.0 or 0.0) * math.pi;
elseif a_2 < 0.0 then
h_2 = math.atan(b_2 / c) + math.pi;
else
h_2 = (b_2 < 0.0 and 1.5 or 0.0 < b_2 and 0.5 or 1.0) * math.pi;
end
-- The atan2 polyfill (customized) is complete.
n = math.abs(h_2 - h_1);
-- Cross-implementation consistent rounding.
if math.pi - 1E-14 < n and n < math.pi + 1E-14 then n = math.pi end;
-- 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.
local h_m = (h_1 + h_2) * 0.5;
local h_d = (h_2 - h_1) * 0.5;
if math.pi < n then
h_d = 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 = h_m + math.pi;
-- h_m = h_m + (h_m < math.pi and math.pi or -math.pi)
end
local 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.
local 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.
local 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.
local 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.
local h = 2.0 * math.sqrt(c_1 * c_2) * math.sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
-- Chroma.
local 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);
end
-- GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
-- Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
-- L1 = 42.5 a1 = 23.6 b1 = -4.4
-- L2 = 45.2 a2 = 18.5 b2 = 3.5
-- CIE ΔE00 = 6.4300403439 (Bruce Lindbloom, Netflix’s VMAF, ...)
-- CIE ΔE00 = 6.4300224381 (Gaurav Sharma, OpenJDK, ...)
-- Deviation between implementations ≈ 1.8e-5
-- See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
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------------- RGB and Hex ------------------------
------------- Color Comparisons ------------------------
------------- ------------------------
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-- For reference, the maximum possible contrast between lime green (#9f0) and dark navy (#006) yields a ΔE2000 value of 119.
-- Lower values indicate more similar colors, making it easy to determine the closest match to a given color.
print(ciede_2000(238, 170, 17, 170, 17, 238)) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000(238, 170, 17, "#a1e")) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000(238, 170, 17, "#aa11ee")) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000("#ea1", 170, 17, 238)) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000("#eeaa11", 170, 17, 238)) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000("#ea1", "#a1e")) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000("#ea1", "#aa11ee")) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000("#eeaa11", "#a1e")) -- Shows a ΔE2000 of 72.464679518244
print(ciede_2000("#eeaa11", "#aa11ee")) -- Shows a ΔE2000 of 72.464679518244