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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
object Main extends App {
import scala.math._
// 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: Double, a_1: Double, b_1: Double, l_2: Double, a_2: Double, b_2: Double): Double = {
// Working in Scala 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...
val k_l: Double = 1.0
val k_c: Double = 1.0
val k_h: Double = 1.0
var n: Double = (sqrt(a_1 * a_1 + b_1 * b_1) + 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 - sqrt(n / (n + 6103515625.0)))
// Application of the chroma correction factor.
val c_1: Double = sqrt(a_1 * a_1 * n * n + b_1 * b_1)
val c_2: Double = 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: Double = atan2(b_1, a_1 * n)
var h_2: Double = atan2(b_2, a_2 * n)
if (h_1 < 0.0) h_1 += 2.0 * scala.math.Pi
if (h_2 < 0.0) h_2 += 2.0 * scala.math.Pi
n = abs(h_2 - h_1)
// Cross-implementation consistent rounding.
if (scala.math.Pi - 1E-14 < n && n < scala.math.Pi + 1E-14)
n = scala.math.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: Double = (h_1 + h_2) * 0.5
var h_d: Double = (h_2 - h_1) * 0.5
if (scala.math.Pi < n) {
h_d += scala.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 += scala.math.Pi
// if (h_m < scala.math.Pi) h_m += scala.math.Pi else h_m -= scala.math.Pi
}
val p: Double = 36.0 * h_m - 55.0 * scala.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.
val r_t: Double = -2.0 * sqrt(n / (n + 6103515625.0)) *
sin(scala.math.Pi / 3.0 * exp(p * p / (-25.0 * scala.math.Pi * scala.math.Pi)))
n = (l_1 + l_2) * 0.5
n = (n - 50.0) * (n - 50.0)
// Lightness.
val l: Double = (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.
val t:Double = 1.0 + 0.24 * sin(2.0 * h_m + scala.math.Pi / 2.0) +
0.32 * sin(3.0 * h_m + 8.0 * scala.math.Pi / 15.0) -
0.17 * sin(h_m + scala.math.Pi / 3.0) -
0.20 * sin(4.0 * h_m + 3.0 * scala.math.Pi / 20.0)
n = c_1 + c_2
// Hue.
val h: Double = 2.0 * sqrt(c_1 * c_2) * sin(h_d) / (k_h * (1.0 + 0.0075 * n * t))
// Chroma.
val c: Double = (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.
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 = 30.1 a1 = 36.4 b1 = 4.3
// L2 = 30.6 a2 = 40.7 b2 = -4.4
// CIE ΔE00 = 5.1668780685 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 5.1668645784 (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 ////////////
//////////// ////////////
/////////////////////////////////////////////////
/////////////////////////////////////////////////
// This file is renamed "Main.scala" when it is used for compiling.
// Reads a CSV file specified as the first command-line argument. For each line, this program
// in Scala 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 : 18.2,112,9,4,126.7,-16
// Corresponding output line : 18.2,112,9,4,126.7,-16,11.770722517869416697582472242161
if (args.length < 1) {
println("Usage : scala Main <filename>")
sys.exit(1)
}
val source = scala.io.Source.fromFile(args(0))
try {
for (line <- source.getLines()) {
val v: Array[String] = line.split(",")
if (v.length == 6) {
val dE: Double = ciede_2000( v(0).toDouble, v(1).toDouble, v(2).toDouble,
v(3).toDouble, v(4).toDouble, v(5).toDouble)
printf("%s,%.15f\n", line.trim(), dE)
}
}
} finally {
source.close()
}
}