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-- Limited Use License – March 1, 2025
-- This source code is provided for public use under the following conditions :
-- It may be downloaded, compiled, and executed, including in publicly accessible environments.
-- Modification is strictly prohibited without the express written permission of the author.
-- © Michel Leonard 2025
-- 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 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)));
-- Application of the chroma correction factor.
local c_1 = math.sqrt(a_1 * a_1 * n * n + b_1 * b_1);
local 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.
local h_1 = math.atan2(b_1, a_1 * n);
local h_2 = math.atan2(b_2, a_2 * n);
if h_1 < 0.0 then h_1 = h_1 + 2.0 * math.pi end;
if h_2 < 0.0 then h_2 = h_2 + 2.0 * math.pi end;
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 = 82.1 a1 = 24.3 b1 = 2.4
-- L2 = 82.3 a2 = 29.2 b2 = -2.5
-- CIE ΔE00 = 3.8700515572 (Bruce Lindbloom, Netflix’s VMAF, ...)
-- CIE ΔE00 = 3.8700367580 (Gaurav Sharma, OpenJDK, ...)
-- Deviation between implementations ≈ 1.5e-5
-- See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
-------------------------------------------------
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------------ ------------
------------ CIEDE2000 Driver ------------
------------ ------------
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-- Reads a CSV file specified as the first command-line argument. For each line, this program
-- in Lua/LuaJIT displays the original line with the computed Delta E 2000 color difference appended.
-- The C driver can offer CSV files to process and programmatically check the calculations performed there.
-- Example of a CSV input line : 78.7,111,2.2,79,124,-14
-- Corresponding output line : 78.7,111,2.2,79,124,-14,5.068663981450850511625256703627
local input_filename = arg[1]
if input_filename then
local file = io.open(input_filename, "r")
-- Old Lua may not support 'io.lines(file)', so we use this form.
for line in file:lines() do
local L1, a1, b1, L2, a2, b2 = line:match("([^,]+),([^,]+),([^,]+),([^,]+),([^,]+),([^,]+)")
L1, a1, b1 = tonumber(L1), tonumber(a1), tonumber(b1)
L2, a2, b2 = tonumber(L2), tonumber(a2), tonumber(b2)
local delta_e = ciede_2000(L1, a1, b1, L2, a2, b2)
io.write(string.format("%s,%.17f\n", line, delta_e))
end
file:close()
end