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// This function written in Go 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.
package main
import (
"fmt"
"math"
"math/rand"
"os"
"strconv"
"time"
)
// 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.
func ciede_2000(l_1 float64, a_1 float64, b_1 float64, l_2 float64, a_2 float64, b_2 float64) float64 {
// Working in Go with the CIEDE2000 color-difference formula.
const (
// 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 := (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)
if h_1 < 0.0 { h_1 += 2.0 * math.Pi }
if h_2 < 0.0 { h_2 += 2.0 * math.Pi }
n = math.Abs(h_2 - h_1)
// Cross-implementation consistent rounding.
if math.Pi - 1E-14 < n && n < math.Pi + 1E-14 { n = 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.
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
// if h_m < math.Pi { h_m += math.Pi } else { h_m -= math.Pi }
}
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.
return math.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 = 25.3 a1 = 34.4 b1 = -3.8
// L2 = 27.8 a2 = 39.4 b2 = 4.5
// CIE ΔE00 = 5.4334495584 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 5.4334652121 (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.
///////////////////////////////////////////////
///////////////////////////////////////////////
/////// ///////
/////// CIEDE 2000 ///////
/////// Testing Random Colors ///////
/////// ///////
///////////////////////////////////////////////
///////////////////////////////////////////////
// This Go 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
func randInRange(min, max float64) float64 {
n := min + (max-min)*rand.Float64()
switch rand.Intn(3) {
case 0: return math.Round(n)
case 1: return math.Round(n*10.0) / 10.0
default: return math.Round(n*100.0) / 100.0
}
}
func main() {
rand.Seed(time.Now().UnixNano())
nIterations := 10000
if len(os.Args) > 1 {
if parsed, err := strconv.Atoi(os.Args[1]); err == nil && parsed > 0 {
nIterations = parsed
}
}
for i := 0; i < nIterations; i++ {
l1 := randInRange(0.0, 100.0)
a1 := randInRange(-128.0, 128.0)
b1 := randInRange(-128.0, 128.0)
l2 := randInRange(0.0, 100.0)
a2 := randInRange(-128.0, 128.0)
b2 := randInRange(-128.0, 128.0)
deltaE := ciede_2000(l1, a1, b1, l2, a2, b2)
fmt.Printf("%g,%g,%g,%g,%g,%g,%.17g\n", l1, a1, b1, l2, a2, b2, deltaE)
}
}