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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
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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 MATLAB 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 : 69.7,-18,82.1,73,7,101
% Corresponding output line : 69.7,-18,82.1,73,7,101,14.363601648949024026421493363468
function main(filename)
fid = fopen(filename,'r');
% Each chunk will use up to 128 Megabytes of memory.
chunk_size = 1000000;
fmt = '%.17g,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g\n';
while true
data = textscan(fid, '%f%f%f%f%f%f', chunk_size, 'Delimiter', ',','CollectOutput',true);
if isempty(data{1}) || isempty(data{1})
break;
end
lab = data{1}; % Nx6 double matrix
deltaE = ciede_2000(lab(:,1), lab(:,2), lab(:,3), lab(:,4), lab(:,5), lab(:,6));
% Write chunk to stdout, formatting with max precision
fprintf(fmt, [lab'; deltaE']);
end
fclose(fid);
end
% 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 = 85.1 a1 = 49.1 b1 = 2.3
% L2 = 85.6 a2 = 54.7 b2 = -2.5
% CIE ΔE00 = 2.9171506379 (Bruce Lindbloom, Netflix’s VMAF, ...)
% CIE ΔE00 = 2.9171372087 (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.