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// This function written in Pascal 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.
program ciede2000;
uses
SysUtils, 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.
function ciede_2000(l_1, a_1, b_1, l_2, a_2, b_2: Double): Double;
var
k_l, k_c, k_h, n, c_1, c_2, h_1, h_2, h_m, h_d, p, r_t, l, t, h, c: Double;
begin
// Working in Pascal 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 * 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.
c_1 := sqrt(a_1 * a_1 * n * n + b_1 * b_1);
c_2 := 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 := arctan2(b_1, a_1 * n);
h_2 := arctan2(b_2, a_2 * n);
if h_1 < 0.0 then h_1 := h_1 + 2.0 * Pi;
if h_2 < 0.0 then h_2 := h_2 + 2.0 * Pi;
n := abs(h_2 - h_1);
// Cross-implementation consistent rounding.
if abs(Pi - n) < 1E-14 then n := 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 Pi < n then
begin
h_d := h_d + 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 := h_m + Pi;
// if h_m < Pi then h_m := h_m + Pi else h_m := h_m - Pi;
end;
p := 36.0 * h_m - 55.0 * 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 * 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 / 2.0)
+ 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.
Exit(sqrt(l * l + h * h + c * c + c * h * r_t));
end;
// GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
// Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
// L1 = 19.8 a1 = 60.4 b1 = -2.5
// L2 = 19.4 a2 = 54.3 b2 = 2.6
// CIE ΔE00 = 2.9493283636 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 2.9493152754 (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 Pascal 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
function RoundToDecimals(Value: Double; Decimals: Integer): Double;
var
Factor: Double;
begin
Factor := Power(10.0, Decimals);
Exit(Round(Value * Factor) / Factor);
end;
function MyRound(Value: Double): Double;
begin
if Random(2) = 0.0 then
Exit(RoundToDecimals(Value, 0))
else
Exit(RoundToDecimals(Value, 1));
end;
function Uniform(MinVal, MaxVal: Double): Double;
begin
Exit(MinVal + (MaxVal - MinVal) * Random);
end;
var
nIterations, i: LongInt;
l1, a1, b1, l2, a2, b2, deltaE: Double;
begin
Randomize;
if ParamCount >= 1 then
nIterations := StrToInt(ParamStr(1))
else
nIterations := 10000;
for i := 1 to nIterations do
begin
l1 := Uniform(0.0, 100.0);
a1 := Uniform(-128.0, 128.0);
b1 := Uniform(-128.0, 128.0);
l2 := Uniform(0.0, 100.0);
a2 := Uniform(-128.0, 128.0);
b2 := Uniform(-128.0, 128.0);
l1 := MyRound(l1);
a1 := MyRound(a1);
b1 := MyRound(b1);
l2 := MyRound(l2);
a2 := MyRound(a2);
b2 := MyRound(b2);
deltaE := ciede_2000(l1, a1, b1, l2, a2, b2);
WriteLn(Format('%.1f,%.1f,%.1f,%.1f,%.1f,%.1f,%.17f',
[l1, a1, b1, l2, a2, b2, deltaE]));
end;
end.