Java / ciede-2000.java 💾

// This function written in Java 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.
static double ciede_2000(final double l_1, final double a_1, final double b_1, final double l_2, final double a_2, final double b_2) {
	// Working in Java 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...
	final double k_l = 1.0, k_c = 1.0, k_h = 1.0;
	double 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.
	final double c_1 = Math.sqrt(a_1 * a_1 * n * n + b_1 * b_1);
	final double 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.
	double h_1 = Math.atan2(b_1, a_1 * n), h_2 = Math.atan2(b_2, a_2 * n);
	h_1 += 2.0 * Math.PI * Boolean.compare(h_1 < 0.0, false);
	h_2 += 2.0 * Math.PI * Boolean.compare(h_2 < 0.0, false);
	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.
	double 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;
	}
	final double 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.
	final double 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.
	final double 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.
	final double 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.
	final double h = 2.0 * Math.sqrt(c_1 * c_2) * Math.sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
	// Chroma.
	final double 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 = 24.8   a1 = 36.7   b1 = -3.4
// L2 = 23.9   a2 = 31.4   b2 = 4.1
// CIE ΔE00 = 4.9864120463 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 4.9863986991 (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.