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% This function written in MATLAB 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 vectorized 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 delta_e = ciede_2000(l_1, a_1, b_1, l_2, a_2, b_2) % Working in MATLAB 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 = 1.0; k_c = 1.0; k_h = 1.0; % The memory requirement for a call to this function is 128 bytes for each pair of colors. n = ((sqrt(a_1 .* a_1 + b_1 .* b_1) + sqrt(a_2 .* a_2 + b_2 .* b_2)) * 0.5) .^ 7.0; % 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); % Vectorized conditionals mask = h_1 < 0.0; h_1(mask) = h_1(mask) + 2.0 * pi; mask = h_2 < 0.0; h_2(mask) = h_2(mask) + 2.0 * pi; n = abs(h_2 - h_1); % Cross-implementation consistent rounding. n((pi - 1E-14 < n) & (n < pi + 1E-14)) = 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; % Vectorized conditionals mask = pi < n; h_d(mask) = h_d(mask) + 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(mask) = h_m(mask) + pi; % h_m(mask) = h_m(mask) + ((h_m(mask) < pi) - (pi <= h_m(mask))) * pi; p = 36.0 * h_m - 55.0 * pi; n = ((c_1 + c_2) * 0.5) .^ 7.0; % 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(pi / 3.0 * exp((p .* p) / (-25.0 * pi * 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 + pi * 0.5) ... + 0.32 * sin(3.0 * h_m + 8.0 * pi / 15.0) ... - 0.17 .* sin(h_m + pi / 3.0) ... - 0.20 * sin(4.0 * h_m + 3.0 * 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. delta_e = 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 = 0.6 a1 = 43.9 b1 = 3.1 % L2 = 3.1 a2 = 49.2 b2 = -3.1 % CIE ΔE00 = 3.9300830879 (Bruce Lindbloom, Netflix’s VMAF, ...) % CIE ΔE00 = 3.9300699597 (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.