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%%%%%%% CIEDE 2000 %%%%%%%
%%%%%%% Testing Random Colors %%%%%%%
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%% This MATLAB program outputs a CSV file to standard output, with its length determined by the first CLI argument.
%% Each line contains seven columns :
%% - Three columns for the random standard L*a*b* color
%% - Three columns for the random sample L*a*b* color
%% - And the seventh column for the precise Delta E 2000 color difference between the standard and sample
%% The output will be correct, this can be verified :
%% - With the C driver, which provides a dedicated verification feature
%% - By using the JavaScript validator at https://michel-leonard.github.io/ciede2000-color-matching
function run_ciede2000_random(varargin)
n_iterations = 10000;
if nargin >= 1
n = varargin{1};
if !isnan(n) && n > 0
n_iterations = n;
end
end
% Each chunk will use up to 128 Megabytes of memory.
chunk_size = 1000000;
for start_idx = 1:chunk_size:n_iterations
end_idx = min(start_idx + chunk_size - 1, n_iterations);
current_chunk_size = end_idx - start_idx + 1;
l_1 = randi([0, 10000], current_chunk_size, 1) / 100.0;
a_1 = randi([-12800, 12800], current_chunk_size, 1) / 100.0;
b_1 = randi([-12800, 12800], current_chunk_size, 1) / 100.0;
l_2 = randi([0, 10000], current_chunk_size, 1) / 100.0;
a_2 = randi([-12800, 12800], current_chunk_size, 1) / 100.0;
b_2 = randi([-12800, 12800], current_chunk_size, 1) / 100.0;
delta_e = ciede_2000(l_1, a_1, b_1, l_2, a_2, b_2);
output = [l_1, a_1, b_1, l_2, a_2, b_2, delta_e];
fprintf('%.2f,%.2f,%.2f,%.2f,%.2f,%.2f,%.17f\n', output');
end
end
% 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 = 87.6 a1 = 53.8 b1 = 4.4
% L2 = 90.3 a2 = 60.0 b2 = -4.3
% CIE ΔE00 = 4.7658989768 (Bruce Lindbloom, Netflix’s VMAF, ...)
% CIE ΔE00 = 4.7658852489 (Gaurav Sharma, OpenJDK, ...)
% Deviation between implementations ≈ 1.4e-5
% See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.