This is a 4,377-byte text/plain file, placed in the public domain, which has been consulted 96 times since the year 2026.
-- This function written in SQL 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. CREATE OR REPLACE FUNCTION ciede_2000( l_1 DOUBLE PRECISION, a_1 DOUBLE PRECISION, b_1 DOUBLE PRECISION, l_2 DOUBLE PRECISION, a_2 DOUBLE PRECISION, b_2 DOUBLE PRECISION ) RETURNS DOUBLE PRECISION LANGUAGE plpgsql IMMUTABLE AS $$ DECLARE -- Working in PostgreSQL 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 DOUBLE PRECISION := 1.0; k_c DOUBLE PRECISION := 1.0; k_h DOUBLE PRECISION := 1.0; n DOUBLE PRECISION; c_1 DOUBLE PRECISION; c_2 DOUBLE PRECISION; h_1 DOUBLE PRECISION; h_2 DOUBLE PRECISION; h_m DOUBLE PRECISION; h_d DOUBLE PRECISION; r_t DOUBLE PRECISION; p DOUBLE PRECISION; t DOUBLE PRECISION; l DOUBLE PRECISION; c DOUBLE PRECISION; h DOUBLE PRECISION; BEGIN 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 := COALESCE(ATAN2(b_1, a_1 * n), 0); h_2 := COALESCE(ATAN2(b_2, a_2 * n), 0); IF h_1 < 0 THEN h_1 := h_1 + 2 * PI(); END IF; IF h_2 < 0 THEN h_2 := h_2 + 2 * PI(); END IF; n := ABS(h_2 - h_1); -- Cross-implementation consistent rounding. IF PI() - 1E-14 < n AND n < PI() + 1E-14 THEN n := PI(); END IF; -- 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 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(); -- h_m := h_m + CASE WHEN h_m < PI() THEN PI() ELSE -PI() END; END IF; 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() * 0.5) + 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. RETURN 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 = 33.5 a1 = 17.2 b1 = 4.9 -- L2 = 33.0 a2 = 11.1 b2 = -2.9 -- CIE ΔE00 = 7.1051316240 (Bruce Lindbloom, Netflix’s VMAF, ...) -- CIE ΔE00 = 7.1051454450 (Gaurav Sharma, OpenJDK, ...) -- Deviation between implementations ≈ 1.4e-5 -- See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.