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# This function written in TCL 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.
proc ciede_2000 { l_1 a_1 b_1 l_2 a_2 b_2 } {
# Working in TCL 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...
set k_l 1.0
set k_c 1.0
set k_h 1.0
set pi 3.14159265358979323846264338328
set n [expr { (sqrt($a_1 * $a_1 + $b_1 * $b_1) + sqrt($a_2 * $a_2 + $b_2 * $b_2)) * 0.5 }]
set n [expr { $n * $n * $n * $n * $n * $n * $n }]
# A factor involving chroma raised to the power of 7 designed to make
# the influence of chroma on the total color difference more accurate.
set n [expr { 1.0 + 0.5 * (1.0 - sqrt($n / ($n + 6103515625.0))) }]
# Application of the chroma correction factor.
set c_1 [expr { sqrt($a_1 * $a_1 * $n * $n + $b_1 * $b_1) }]
set c_2 [expr { sqrt($a_2 * $a_2 * $n * $n + $b_2 * $b_2) }]
# atan2 is preferred over atan because it accurately computes the angle of
# a point (x, y) in all quadrants, handling the signs of both coordinates.
set h_1 [expr { atan2($b_1, $a_1 * $n) }]
set h_2 [expr { atan2($b_2, $a_2 * $n) }]
if { $h_1 < 0.0 } { set h_1 [expr { $h_1 + 2.0 * $pi }] }
if { $h_2 < 0.0 } { set h_2 [expr { $h_2 + 2.0 * $pi }] }
set n [expr { abs($h_2 - $h_1) }]
# Cross-implementation consistent rounding.
if { $pi - 1E-14 < $n && $n < $pi + 1E-14 } {
set n $pi
}
# When the hue angles lie in different quadrants, the straightforward
# average can produce a mean that incorrectly suggests a hue angle in
# the wrong quadrant, the next lines handle this issue.
set h_m [expr { ($h_1 + $h_2) * 0.5 }]
set h_d [expr { ($h_2 - $h_1) * 0.5 }]
if { $pi < $n } {
set h_d [expr { $h_d + $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.
set h_m [expr { $h_m + $pi }]
# set h_m [expr {$h_m + ($h_m < $pi ? $pi : -$pi)}]
}
set p [expr { 36.0 * $h_m - 55.0 * $pi }]
set n [expr { ($c_1 + $c_2) * 0.5 }]
set n [expr { $n * $n * $n * $n * $n * $n * $n }]
# The hue rotation correction term is designed to account for the
# non-linear behavior of hue differences in the blue region.
set r_t [expr { -2.0 * sqrt($n / ($n + 6103515625.0))
* sin($pi / 3.0 * exp($p * $p / (-25.0 * $pi * $pi))) }]
set n [expr { ($l_1 + $l_2) * 0.5 }]
set n [expr { ($n - 50.0) * ($n - 50.0) }]
# Lightness.
set l [expr { ($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.
set t [expr { 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) }]
set n [expr { $c_1 + $c_2 }]
# Hue.
set h [expr { 2.0 * sqrt($c_1 * $c_2) * sin($h_d) / ($k_h * (1.0 + 0.0075 * $n * $t)) }]
# Chroma.
set c [expr { ($c_2 - $c_1) / ($k_c * (1.0 + 0.0225 * $n)) }]
# Returning the square root ensures that dE00 accurately reflects the
# geometric distance in color space, which can range from 0 to around 185.
return [expr { sqrt($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 = 12.0 a1 = 25.9 b1 = -4.3
# L2 = 13.7 a2 = 20.0 b2 = 4.4
# CIE ΔE00 = 6.5762883529 (Bruce Lindbloom, Netflix’s VMAF, ...)
# CIE ΔE00 = 6.5762728956 (Gaurav Sharma, OpenJDK, ...)
# Deviation between implementations ≈ 1.5e-5
# See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.