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# This function written in Ruby 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 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_one(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 = 55.2 a1 = 24.1 b1 = 3.4
# L2 = 57.0 a2 = 29.3 b2 = -4.1
# CIE ΔE00 = 5.5717826003 (Bruce Lindbloom, Netflix’s VMAF, ...)
# CIE ΔE00 = 5.5717644472 (Gaurav Sharma, OpenJDK, ...)
# Deviation between implementations ≈ 1.8e-5
# See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
def ciede_2000_two(l1, a1, b1, l2, a2, b2)
# The other function here.
end
########################################################
########################################################
############ #############
############ Compare with #############
############ ___________ #############
############ #############
########################################################
########################################################
## The goal is to demonstrate that the library produces results identical to ___________.
## If the results differ by more than a tolerance of 1E-10, a non-zero value will be returned.
def finite?(f)
!f.nan? && !f.infinite?
end
runs = (ARGV[0] || 10000).to_i
worst = {
diff: 0.0
}
runs.times do |i|
l1 = rand * 100.0
a1 = rand * 256.0 - 128.0
b1 = rand * 256.0 - 128.0
l2 = rand * 100.0
a2 = rand * 256.0 - 128.0
b2 = rand * 256.0 - 128.0
d1 = ciede_2000_one(l1, a1, b1, l2, a2, b2)
d2 = ciede_2000_two(l1, a1, b1, l2, a2, b2)
unless finite?(d1) && finite?(d2)
puts "Non-finite value detected at run #{i}"
exit(1)
end
diff = (d1 - d2).abs
if diff > worst[:diff]
worst = {
l1: l1, a1: a1, b1: b1,
l2: l2, a2: a2, b2: b2,
delta1: d1, delta2: d2,
diff: diff
}
end
end
puts "Total runs : #{runs}"
puts "Worst case : {"
worst.each do |k, v|
if v.is_a?(Float)
puts " %.17g," % v
else
puts " #{k}: #{v},"
end
end
puts "}"