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# This function written in R 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.
ciede_2000_classic <- function(l_1, a_1, b_1, l_2, a_2, b_2) {
# This scalar expansion wrapper works with numbers, not vectors.
delta_e <- ciede_2000(c(l_1), c(a_1), c(b_1), c(l_2), c(a_2), c(b_2))
return(delta_e[1])
}
# The classic vectorized 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 <- function(l_1, a_1, b_1, l_2, a_2, b_2) {
# Working in R 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 <- 1.0;
k_c <- 1.0;
k_h <- 1.0;
n <- (sqrt(a_1 * a_1 + b_1 * b_1) + sqrt(a_2 * a_2 + b_2 * b_2)) * 0.5;
n <- n ^ 7.0;
# 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 - sqrt(n / (n + 6103515625.0)));
# Application of the chroma correction factor.
c_1 <- sqrt((a_1 * n) ^ 2.0 + b_1 * b_1);
c_2 <- sqrt((a_2 * n) ^ 2.0 + 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 <- atan2(b_1, a_1 * n);
h_2 <- atan2(b_2, a_2 * n);
h_1 <- h_1 + ifelse(h_1 < 0.0, 2.0 * pi, 0.0)
h_2 <- h_2 + ifelse(h_2 < 0.0, 2.0 * pi, 0.0)
n <- abs(h_2 - h_1);
# Cross-implementation consistent rounding.
n[abs(n - pi) < 1E-14] <- 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.
h_m <- (h_1 + h_2) * 0.5;
h_d <- (h_2 - h_1) * 0.5;
mask <- pi < n;
h_d[mask] <- h_d[mask] + 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[mask] <- h_m[mask] + pi;
# h_m[mask] <- h_m[mask] + ifelse(h_m[mask] < pi, pi, -pi);
p <- 36.0 * h_m - 55.0 * pi;
n <- (c_1 + c_2) * 0.5;
n <- n ^ 7.0;
# 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 * sqrt(n / (n + 6103515625.0)) *
sin(pi / 3.0 * exp(p * p / (-25.0 * pi * 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 / sqrt(20.0 + n)));
# These coefficients adjust the impact of different harmonic
# components on the hue difference calculation.
t <- 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);
n <- c_1 + c_2;
# Hue.
h <- 2.0 * sqrt(c_1 * c_2) * 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.
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 = 9.4 a1 = 41.3 b1 = -1.6
# L2 = 8.9 a2 = 35.1 b2 = 1.6
# CIE ΔE00 = 2.9390853830 (Bruce Lindbloom, Netflix’s VMAF, ...)
# CIE ΔE00 = 2.9390722675 (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.
###############################################
###############################################
####### #######
####### CIEDE 2000 #######
####### Testing Random Colors #######
####### #######
###############################################
###############################################
# This R program outputs a CSV file to standard output, with its length determined by the first CLI argument.
# Each line contains seven columns :
# - Three columns for the random standard L*a*b* color
# - Three columns for the random sample L*a*b* color
# - And the seventh column for the precise Delta E 2000 color difference between the standard and sample
# The output will be correct, this can be verified :
# - With the C driver, which provides a dedicated verification feature
# - By using the JavaScript validator at https://michel-leonard.github.io/ciede2000-color-matching
main <- function(n = 10000, chunk_size = 250000) {
set.seed(NULL)
l1 <- runif(n, 0, 100)
a1 <- runif(n, -128, 128)
b1 <- runif(n, -128, 128)
l2 <- runif(n, 0, 100)
a2 <- runif(n, -128, 128)
b2 <- runif(n, -128, 128)
l1 <- round(l1, sample(0:1, n, replace = TRUE))
a1 <- round(a1, sample(0:1, n, replace = TRUE))
b1 <- round(b1, sample(0:1, n, replace = TRUE))
l2 <- round(l2, sample(0:1, n, replace = TRUE))
a2 <- round(a2, sample(0:1, n, replace = TRUE))
b2 <- round(b2, sample(0:1, n, replace = TRUE))
results <- numeric(n)
for (start in seq(1, n, by = chunk_size)) {
end <- min(start + chunk_size - 1, n)
delta_e_chunk <- ciede_2000(l1[start:end], a1[start:end], b1[start:end], l2[start:end], a2[start:end], b2[start:end])
results[start:end] <- delta_e_chunk
for (i in start:end) {
cat(sprintf("%.1f,%.1f,%.1f,%.1f,%.1f,%.1f,%.17f\n", l1[i], a1[i], b1[i], l2[i], a2[i], b2[i], results[i]))
}
}
}
args <- commandArgs(trailingOnly = TRUE)
if (length(args) > 0) {
input_value <- as.numeric(args[1])
if (!is.na(input_value) && input_value > 0 && input_value == as.integer(input_value)) {
n_iterations <- as.integer(input_value)
} else {
n_iterations <- 10000
}
} else {
n_iterations <- 10000
}
main(n_iterations)