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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
# 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.
def ciede_2000(l_1, a_1, b_1, l_2, a_2, b_2)
# Working in Ruby 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 = k_c = k_h = 1.0
n = (Math.sqrt(a_1 * a_1 + b_1 * b_1) + Math.sqrt(a_2 * a_2 + b_2 * b_2)) * 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 = 1.0 + 0.5 * (1.0 - Math.sqrt(n / (n + 6103515625.0)))
# Application of the chroma correction factor.
c_1 = Math.sqrt(a_1 * a_1 * n * n + b_1 * b_1)
c_2 = Math.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 = Math.atan2(b_1, a_1 * n)
h_2 = Math.atan2(b_2, a_2 * n)
h_1 += 2.0 * Math::PI if h_1 < 0.0
h_2 += 2.0 * Math::PI if h_2 < 0.0
n = (h_2 - h_1).abs
# Cross-implementation consistent rounding.
n = Math::PI if Math::PI - 1E-14 < n && n < Math::PI + 1E-14
# 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
if Math::PI < n
h_d += Math::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 += Math::PI
# h_m += h_m < Math::PI ? Math::PI : -Math::PI
end
p = 36.0 * h_m - 55.0 * Math::PI
n = (c_1 + c_2) * 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.
r_t = -2.0 * Math.sqrt(n / (n + 6103515625.0)) \
* Math.sin(Math::PI / 3.0 * Math.exp(p * p / (-25.0 * Math::PI * Math::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 / Math.sqrt(20.0 + n)))
# These coefficients adjust the impact of different harmonic
# components on the hue difference calculation.
t = 1.0 + 0.24 * Math.sin(2.0 * h_m + Math::PI * 0.5) \
+ 0.32 * Math.sin(3.0 * h_m + 8.0 * Math::PI / 15.0) \
- 0.17 * Math.sin(h_m + Math::PI / 3.0) \
- 0.20 * Math.sin(4.0 * h_m + 3.0 * Math::PI / 20.0)
n = c_1 + c_2
# Hue.
h = 2.0 * Math.sqrt(c_1 * c_2) * Math.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.
Math.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 = 79.8 a1 = 22.6 b1 = 5.5
# L2 = 79.7 a2 = 17.0 b2 = -3.2
# CIE ΔE00 = 6.6045017438 (Bruce Lindbloom, Netflix’s VMAF, ...)
# CIE ΔE00 = 6.6045175269 (Gaurav Sharma, OpenJDK, ...)
# Deviation between implementations ≈ 1.6e-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 Ruby 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 : 86,-21,107.5,93.6,11,117
# Corresponding output line : 86,-21,107.5,93.6,11,117,16.282425530248471855629868453553
if ARGV[0]
File.foreach(ARGV[0]) do |line|
line.chomp!
fields = line.split(',')
l1, a1, b1, l2, a2, b2 = fields.map(&:to_f)
delta_e = ciede_2000(l1, a1, b1, l2, a2, b2)
puts "#{line},#{'%.17f' % delta_e}"
end
end