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; This function written in Racket 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. #lang racket ; 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. (define ciede_2000(lambda (l_1 a_1 b_1 l_2 a_2 b_2) ; Working in Racket 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... (define pi 3.14159265358979323846264338328) (define k_l 1.0) (define k_c 1.0) (define k_h 1.0) (define n (* 0.5 (+ (sqrt (+ (* a_1 a_1) (* b_1 b_1))) (sqrt (+ (* a_2 a_2) (* b_2 b_2)))))) (set! 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. (set! n (+ 1.0 (* 0.5 (- 1.0 (sqrt (/ n (+ n 6103515625.0))))))) ; Application of the chroma correction factor. (define c_1 (sqrt (+ (* a_1 a_1 n n) (* b_1 b_1)))) (define 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. (define h_1 (if (and (= b_1 0) (= a_1 0)) 0 (atan b_1 (* a_1 n)))) (define h_2 (if (and (= b_2 0) (= a_2 0)) 0 (atan b_2 (* a_2 n)))) (if (< h_1 0.0) (set! h_1 (+ h_1 pi pi)) empty) (if (< h_2 0.0) (set! h_2 (+ h_2 pi pi)) empty) (set! n (abs (- h_2 h_1))) ; Cross-implementation consistent rounding. (if (and (< (- pi 1E-14) n) (< n (+ pi 1E-14))) (set! n pi) empty) ; 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. (define h_m (* 0.5 (+ h_1 h_2))) (define h_d (* 0.5 (- h_2 h_1))) (if (< pi n) (begin (set! 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. (set! h_m (+ h_m pi))) ; (if (< h_m pi) (set! h_m (+ h_m pi)) (set! h_m (- h_m pi)))) empty ) (define p (- (* 36.0 h_m) (* 55.0 pi))) (set! n (* 0.5 (+ c_1 c_2))) (set! 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. (define r_t (* -2.0 (sqrt (/ n (+ n 6103515625.0))) (sin (* (/ pi 3.0) (exp (/ (* p p) (* -25.0 pi pi))))))) (set! n (* 0.5 (+ l_1 l_2))) (set! n (* (- n 50.0) (- n 50.0))) ; Lightness. (define 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. (define 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))))))) (set! n (+ c_1 c_2)) ; Hue. (define h (/ (* 2.0 (sqrt (* c_1 c_2)) (sin h_d)) (* k_h (+ 1.0 (* 0.0075 n t))))) ; Chroma. (define 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. (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 = 93.4 a1 = 18.3 b1 = 5.4 ; L2 = 92.2 a2 = 13.1 b2 = -3.3 ; CIE ΔE00 = 7.0238296967 (Bruce Lindbloom, Netflix’s VMAF, ...) ; CIE ΔE00 = 7.0238434958 (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.