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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
:- initialization(main).
:- use_module(library(apply)).
:- use_module(library(readutil)).
% 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.
ciede_2000(L1, A1, B1, L2, A2, B2, DeltaE2000) :-
% Working in Prolog 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 is 1.0,
K_C is 1.0,
K_H is 1.0,
Pi_1 is 3.14159265358979323846,
Pi_3 is 1.04719755119659774615,
% 1. Compute chroma magnitudes ... a and b usually range from -128 to +127
A1_sq is A1 * A1,
B1_sq is B1 * B1,
C_orig_1 is sqrt(A1_sq + B1_sq),
A2_sq is A2 * A2,
B2_sq is B2 * B2,
C_orig_2 is sqrt(A2_sq + B2_sq),
% 2. Compute chroma mean and apply G compensation
C_avg is 0.5 * (C_orig_1 + C_orig_2),
C_avg_3 is C_avg * C_avg * C_avg,
C_avg_7 is C_avg_3 * C_avg_3 * C_avg,
G_denom is C_avg_7 + 6103515625.0,
G_ratio is C_avg_7 / G_denom,
G_sqrt is sqrt(G_ratio),
G_factor is 1.0 + 0.5 * (1.0 - G_sqrt),
% 3. Apply G correction to a components, compute corrected chroma
A1_prime is A1 * G_factor,
C1_prime_sq is A1_prime * A1_prime + B1 * B1,
C1_prime is sqrt(C1_prime_sq),
A2_prime is A2 * G_factor,
C2_prime_sq is A2_prime * A2_prime + B2 * B2,
C2_prime is sqrt(C2_prime_sq),
% 4. Compute hue angles in radians, adjust for negatives and wrap
H1_raw is atan2(B1, A1_prime),
H2_raw is atan2(B2, A2_prime),
(H1_raw < 0.0 -> H1_adj is H1_raw + 2.0 * Pi_1 ; H1_adj = H1_raw),
(H2_raw < 0.0 -> H2_adj is H2_raw + 2.0 * Pi_1 ; H2_adj = H2_raw),
Delta_h is abs(H1_adj - H2_adj),
H_mean_raw is 0.5 * (H1_adj + H2_adj),
H_diff_raw is 0.5 * (H2_adj - H1_adj),
% Check if hue mean wraps around pi (180 deg)
Wrap_dist is abs(Pi_1 - Delta_h),
(1.0e-14 < Wrap_dist, Pi_1 < Delta_h -> Hue_wrap = 1.0 ; Hue_wrap = 0),
H_diff is H_diff_raw + Hue_wrap * Pi_1,
% 📜 Sharma’s formulation doesn’t use the next line, but the three after it,
% and these two variants differ by ±0.0003 on the final color differences.
H_mean is H_mean_raw + Hue_wrap * Pi_1,
% (Hue_wrap =:= 1, H_mean_raw < Pi_1 -> H_mean_hi = Pi_1 ; H_mean_hi = 0.0),
% (Hue_wrap =:= 1, H_mean_hi =:= 0.0 -> H_mean_lo = Pi_1 ; H_mean_lo = 0.0),
% H_mean is H_mean_raw + H_mean_hi - H_mean_lo,
% 5. Compute hue rotation correction factor R_T
C_bar is 0.5 * (C1_prime + C2_prime),
C_bar_3 is C_bar * C_bar * C_bar,
C_bar_7 is C_bar_3 * C_bar_3 * C_bar,
Rc_denom is C_bar_7 + 6103515625.0,
R_C is sqrt(C_bar_7 / Rc_denom),
Theta is 36.0 * H_mean - 55.0 * Pi_1,
Theta_denom is -25.0 * Pi_1 * Pi_1,
Exp_argument is Theta * Theta / Theta_denom,
Exp_term is exp(Exp_argument),
Delta_theta is Pi_3 * Exp_term,
Sin_term is sin(Delta_theta),
% Rotation factor ... cross-effect between chroma and hue
R_T is -2.0 * R_C * Sin_term,
% 6. Compute lightness term ... L nominally ranges from 0 to 100
L_avg is 0.5 * (L1 + L2),
L_delta_sq is (L_avg - 50.0) * (L_avg - 50.0),
L_delta is L2 - L1,
% Adaptation to the non-linearity of light perception ... S_L
S_l_num is 0.015 * L_delta_sq,
S_l_denom is sqrt(20.0 + L_delta_sq),
S_L is 1.0 + S_l_num / S_l_denom,
L_term is L_delta / (K_L * S_L),
% 7. Compute chroma-related trig terms and factor T
Trig_1 is 0.17 * sin(H_mean + Pi_3),
Trig_2 is 0.24 * sin(2.0 * H_mean + 0.5 * Pi_1),
Trig_3 is 0.32 * sin(3.0 * H_mean + 1.6 * Pi_3),
Trig_4 is 0.2 * sin(4.0 * H_mean + 0.15 * Pi_1),
T is 1.0 - Trig_1 + Trig_2 + Trig_3 - Trig_4,
C_sum is C1_prime + C2_prime,
C_product is C1_prime * C2_prime,
C_geo_mean is sqrt(C_product),
% 8. Compute hue difference and scaling factor S_H
Sin_h_diff is sin(H_diff),
S_H is 1.0 + 0.0075 * C_sum * T,
H_term is 2.0 * C_geo_mean * Sin_h_diff / (K_H * S_H),
% 9. Compute chroma difference and scaling factor S_C
C_delta is C2_prime - C1_prime,
S_C is 1.0 + 0.0225 * C_sum,
C_term is C_delta / (K_C * S_C),
% 10. Combine lightness, chroma, hue, and interaction terms
L_part is L_term * L_term,
C_part is C_term * C_term,
H_part is H_term * H_term,
Interaction is C_term * H_term * R_T,
Delta_e_squared is L_part + C_part + H_part + Interaction,
DeltaE2000 is sqrt(Delta_e_squared).
% GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
% Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
% L1 = 57.8 a1 = 17.3 b1 = 4.5
% L2 = 55.3 a2 = 11.2 b2 = -2.7
% CIE ΔE00 = 7.1494588687 (Bruce Lindbloom, Netflix’s VMAF, ...)
% CIE ΔE00 = 7.1494719070 (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.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% %%%%%%%%%%%%
%%%%%%%%%%%% CIEDE2000 Driver %%%%%%%%%%%%
%%%%%%%%%%%% %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Reads a CSV file specified as the first command-line argument. For each line, this program
% in Prolog 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 : 52.6,45,7,53,27.7,-23
% Corresponding output line : 52.6,45,7,53,27.7,-23,17.961306147819260693696398178126
main :-
current_prolog_flag(argv, Argv),
( Argv = [Filename|_] ->
open(Filename, read, Stream),
repeat,
read_line_to_string(Stream, Line),
( Line == end_of_file -> ! ;
process(Line),
fail
),
close(Stream)
;
writeln('Usage: swipl -q -s ciede-2000-driver.pro -- <filename>'),
halt(1)
).
process(Line) :-
split_string(Line, ",", " ", Explode),
maplist(number_string, [L1,A1,B1,L2,A2,B2], Explode),
ciede_2000(L1, A1, B1, L2, A2, B2, DeltaE2000),
format("~s,~w~n", [Line, DeltaE2000]).