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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
import math
const M_PI = 3.14159265358979323846264338328
# The generic 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.
proc ciede_2000[T: SomeFloat](l_1, a_1, b_1, l_2, a_2, b_2: T): T =
# Working in Nim 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...
let k_l = T(1.0);
let k_c = T(1.0);
let k_h = T(1.0);
var n = (sqrt(a_1 * a_1 + b_1 * b_1) + sqrt(a_2 * a_2 + b_2 * b_2)) * T(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 = T(1.0) + T(0.5) * (T(1.0) - sqrt(n / (n + T(6103515625.0))));
# Application of the chroma correction factor.
let c_1 = sqrt(a_1 * a_1 * n * n + b_1 * b_1);
let 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.
var h_1 = arctan2(b_1, a_1 * n);
var h_2 = arctan2(b_2, a_2 * n);
if h_1 < T(0.0) :
h_1 += T(2.0) * T(M_PI);
if h_2 < T(0.0) :
h_2 += T(2.0) * T(M_PI);
n = abs(h_2 - h_1);
# Cross-implementation consistent rounding.
if T(M_PI) - T(1E-14) < n and n < T(M_PI) + T(1E-14) :
n = T(M_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.
var h_m = (h_1 + h_2) * T(0.5);
var h_d = (h_2 - h_1) * T(0.5);
if T(M_PI) < n :
h_d += T(M_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 += T(M_PI);
# h_m += (if h_m < T(M_PI) : T(M_PI) else : T(-M_PI));
let p = T(36.0) * h_m - T(55.0) * T(M_PI);
n = (c_1 + c_2) * T(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.
let r_t = T(-2.0) * sqrt(n / (n + T(6103515625.0))) *
sin(T(M_PI) / T(3.0) * exp(p * p / (T(-25.0) * T(M_PI) * T(M_PI))));
n = (l_1 + l_2) * T(0.5);
n = (n - T(50.0)) * (n - T(50.0));
# Lightness.
let l = (l_2 - l_1) / (k_l * (T(1.0) + T(0.015) * n / sqrt(T(20.0) + n)));
# These coefficients adjust the impact of different harmonic
# components on the hue difference calculation.
let t = T(1.0) + T(0.24) * sin(T(2.0) * h_m + T(M_PI) * T(0.5)) +
T(0.32) * sin(T(3.0) * h_m + T(8.0) * T(M_PI) / T(15.0)) -
T(0.17) * sin(h_m + T(M_PI) / T(3.0)) -
T(0.20) * sin(T(4.0) * h_m + T(3.0) * T(M_PI) / T(20.0));
n = c_1 + c_2;
# Hue.
let h = T(2.0) * sqrt(c_1 * c_2) *
sin(h_d) / (k_h * (T(1.0) + T(0.0075) * n * t));
# Chroma.
let c = (c_2 - c_1) / (k_c * (T(1.0) + T(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 sqrt(l * l + h * h + c * c + c * h * r_t);
# GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
# Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
# L1 = 68.8 a1 = 21.6 b1 = -2.4
# L2 = 67.3 a2 = 15.7 b2 = 2.4
# CIE ΔE00 = 5.0609566750 (Bruce Lindbloom, Netflix’s VMAF, ...)
# CIE ΔE00 = 5.0609436595 (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 Nim 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 : 65,107,1,51.3,58,-18.3
## Corresponding output line : 65,107,1,51.3,58,-18.3,18.134308412944345843174051109052
import os, strutils, sequtils
proc main() =
if paramCount() < 1:
quit("Usage: program filename")
let filename = paramStr(1)
for line in lines(filename):
let parts = line.split(',').mapIt(it.strip())
let vals = parts.mapIt(parseFloat(it).float64)
let deltaE = ciede_2000(vals[0], vals[1], vals[2], vals[3], vals[4], vals[5])
echo line & "," & $(deltaE)
when isMainModule:
main()