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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. -- 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))); -- 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.