colorjs.io/src/deltaE/deltaE2000.js

Let’s get serious about color

import lab from "../spaces/lab.js";
import lch from "../spaces/lch.js";

// deltaE2000 is a statistically significant improvement
// and is recommended by the CIE and Idealliance
// especially for color differences less than 10 deltaE76
// but is wicked complicated
// and many implementations have small errors!
// DeltaE2000 is also discontinuous; in case this
// matters to you, use deltaECMC instead.

const Gfactor = 25 ** 7;
const π = Math.PI;
const r2d = 180 / π;
const d2r = π / 180;

export default function (color, sample, {kL = 1, kC = 1, kH = 1} = {}) {
	// Given this color as the reference
	// and the function parameter as the sample,
	// calculate deltaE 2000.

	// This implementation assumes the parametric
	// weighting factors kL, kC and kH
	// for the influence of viewing conditions
	// are all 1, as sadly seems typical.
	// kL should be increased for lightness texture or noise
	// and kC increased for chroma noise

	let [L1, a1, b1] = lab.from(color);
	let C1 = lch.from(lab, [L1, a1, b1])[1];
	let [L2, a2, b2] = lab.from(sample);
	let C2 = lch.from(lab, [L2, a2, b2])[1];

	// Check for negative Chroma,
	// which might happen through
	// direct user input of LCH values

	if (C1 < 0) {
		C1 = 0;
	}
	if (C2 < 0) {
		C2 = 0;
	}

	let Cbar = (C1 + C2)/2; // mean Chroma

	// calculate a-axis asymmetry factor from mean Chroma
	// this turns JND ellipses for near-neutral colors back into circles
	let C7 = Cbar ** 7;

	let G = 0.5 * (1 - Math.sqrt(C7/(C7 + Gfactor)));

	// scale a axes by asymmetry factor
	// this by the way is why there is no Lab2000 colorspace
	let adash1 = (1 + G) * a1;
	let adash2 = (1 + G) * a2;

	// calculate new Chroma from scaled a and original b axes
	let Cdash1 = Math.sqrt(adash1 ** 2 + b1 ** 2);
	let Cdash2 = Math.sqrt(adash2 ** 2 + b2 ** 2);

	// calculate new hues, with zero hue for true neutrals
	// and in degrees, not radians

	let h1 = (adash1 === 0 && b1 === 0)? 0: Math.atan2(b1, adash1);
	let h2 = (adash2 === 0 && b2 === 0)? 0: Math.atan2(b2, adash2);

	if (h1 < 0) {
		h1 += 2 * π;
	}
	if (h2 < 0) {
		h2 += 2 * π;
	}

	h1 *= r2d;
	h2 *= r2d;

	// Lightness and Chroma differences; sign matters
	let ΔL = L2 - L1;
	let ΔC = Cdash2 - Cdash1;

	// Hue difference, getting the sign correct
	let hdiff = h2 - h1;
	let hsum = h1 + h2;
	let habs = Math.abs(hdiff);
	let Δh;

	if (Cdash1 * Cdash2 === 0) {
		Δh = 0;
	}
	else if (habs <= 180) {
		Δh = hdiff;
	}
	else if (hdiff > 180) {
		Δh = hdiff - 360;
	}
	else if (hdiff < -180) {
		Δh = hdiff + 360;
	}
	else {
		console.log("the unthinkable has happened");
	}

	// weighted Hue difference, more for larger Chroma
	let ΔH = 2 * Math.sqrt(Cdash2 * Cdash1) * Math.sin(Δh * d2r / 2);

	// calculate mean Lightness and Chroma
	let Ldash = (L1 + L2)/2;
	let Cdash = (Cdash1 + Cdash2)/2;
	let Cdash7 = Math.pow(Cdash, 7);

	// Compensate for non-linearity in the blue region of Lab.
	// Four possibilities for hue weighting factor,
	// depending on the angles, to get the correct sign
	let hdash;
	if (Cdash1 * Cdash2 === 0) {
		hdash = hsum;   // which should be zero
	}
	else if (habs <= 180) {
		hdash = hsum / 2;
	}
	else if (hsum < 360) {
		hdash = (hsum + 360) / 2;
	}
	else {
		hdash = (hsum - 360) / 2;
	}

	// positional corrections to the lack of uniformity of CIELAB
	// These are all trying to make JND ellipsoids more like spheres

	// SL Lightness crispening factor
	// a background with L=50 is assumed
	let lsq = (Ldash - 50) ** 2;
	let SL = 1 + ((0.015 * lsq) / Math.sqrt(20 + lsq));

	// SC Chroma factor, similar to those in CMC and deltaE 94 formulae
	let SC = 1 + 0.045 * Cdash;

	// Cross term T for blue non-linearity
	let T = 1;
	T -= (0.17 * Math.cos((     hdash - 30)  * d2r));
	T += (0.24 * Math.cos(  2 * hdash        * d2r));
	T += (0.32 * Math.cos(((3 * hdash) + 6)  * d2r));
	T -= (0.20 * Math.cos(((4 * hdash) - 63) * d2r));

	// SH Hue factor depends on Chroma,
	// as well as adjusted hue angle like deltaE94.
	let SH = 1 + 0.015 * Cdash * T;

	// RT Hue rotation term compensates for rotation of JND ellipses
	// and Munsell constant hue lines
	// in the medium-high Chroma blue region
	// (Hue 225 to 315)
	let Δθ = 30 * Math.exp(-1 * (((hdash - 275)/25) ** 2));
	let RC = 2 * Math.sqrt(Cdash7/(Cdash7 + Gfactor));
	let RT = -1 * Math.sin(2 * Δθ * d2r) * RC;

	// Finally calculate the deltaE, term by term as root sume of squares
	let dE = (ΔL / (kL * SL)) ** 2;
	dE += (ΔC / (kC * SC)) ** 2;
	dE += (ΔH / (kH * SH)) ** 2;
	dE += RT * (ΔC / (kC * SC)) * (ΔH / (kH * SH));
	return Math.sqrt(dE);
	// Yay!!!
};