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-- This function written in Haskell 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.
import System.Environment (getArgs)
import System.Random
import Text.Printf (printf)
-- 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.
ciede_2000 :: Double -> Double -> Double -> Double -> Double -> Double -> Double
ciede_2000 l_1 a_1 b_1 l_2 a_2 b_2 =
-- Working in Haskell 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...
let
k_l = 1.0
k_c = 1.0
k_h = 1.0
n = (\() ->
let
x = (sqrt(a_1 * a_1 + b_1 * b_1) + sqrt(a_2 * a_2 + b_2 * b_2)) * 0.5
-- A factor involving chroma raised to the power of 7 designed to make
-- the influence of chroma on the total color difference more accurate.
y = x * x * x * x * x * x * x
in 1.0 + 0.5 * (1.0 - sqrt(y / (y + 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 = (\() -> let x = atan2 b_1 (a_1 * n) in if x < 0.0 then x + 2.0 * pi else x)()
h_2 = (\() -> let x = atan2 b_2 (a_2 * n) in if x < 0.0 then x + 2.0 * pi else x)()
-- Cross-implementation consistent rounding.
n_0 = (\() -> let x = abs(h_2 - h_1) in if pi - 1E-14 < x && x < pi + 1E-14 then pi else x)()
-- 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 = (\() ->
let
x = (h_1 + h_2) * 0.5
-- 📜 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.
in if pi < n_0 then x + pi else x
-- in if pi < n_0 then if x < pi then x + pi else x - pi else x
)()
h_d = (\() ->
let
x = (h_2 - h_1) * 0.5
in if pi < n_0 then x + pi else x
)()
p = 36.0 * h_m - 55.0 * pi
n_2 = (\() -> let x = (c_1 + c_2) * 0.5 in x * x * x * x * x * x * x)()
-- 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_2 / (n_2 + 6103515625.0))
* sin(pi / 3.0 * exp(p * p / (-25.0 * pi * pi)))
n_3 = (\() -> let x = (l_1 + l_2) * 0.5 in (x - 50.0) * (x - 50.0))()
-- Lightness.
l = (l_2 - l_1) / (k_l * (1.0 + 0.015 * n_3 / sqrt(20.0 + n_3)))
-- 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_4 = c_1 + c_2
-- Hue.
h = 2.0 * sqrt(c_1 * c_2) * sin(h_d) / (k_h * (1.0 + 0.0075 * n_4 * t))
-- Chroma.
c = (c_2 - c_1) / (k_c * (1.0 + 0.0225 * n_4))
-- Returning the square root ensures that dE00 accurately reflects the
-- geometric distance in color space, which can range from 0 to around 185.
in 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 = 12.1 a1 = 32.6 b1 = -4.0
-- L2 = 13.7 a2 = 27.0 b2 = 4.7
-- CIE ΔE00 = 6.0199657517 (Bruce Lindbloom, Netflix’s VMAF, ...)
-- CIE ΔE00 = 6.0199522437 (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.
-----------------------------------------------
-----------------------------------------------
------- -------
------- CIEDE 2000 -------
------- Testing Random Colors -------
------- -------
-----------------------------------------------
-----------------------------------------------
-- This Haskell 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
roundTo :: Int -> Double -> Double
roundTo 0 x = fromIntegral (round x :: Int)
roundTo _ x = fromIntegral (round (x * 10) :: Int) / 10
randomRound :: StdGen -> (Int, StdGen)
randomRound gen = randomR (0, 1) gen
randomInRange :: (Double, Double) -> StdGen -> (Double, StdGen)
randomInRange (low, high) gen = randomR (low, high) gen
randomRoundedInRange :: (Double, Double) -> StdGen -> (Double, StdGen)
randomRoundedInRange range gen0 =
let (x, gen1) = randomInRange range gen0
(n, gen2) = randomRound gen1
y = roundTo n x
in (y, gen2)
main :: IO ()
main = do
args <- getArgs
let nIterations = case args of
(x:_) -> case reads x :: [(Int,String)] of
[(v,"")] | v > 0 -> v
_ -> 10000
_ -> 10000
gen0 <- newStdGen
let loop 0 _ = return ()
loop n gen = do
let (l1, gen1) = randomRoundedInRange (0, 100) gen
(a1, gen2) = randomRoundedInRange (-128, 128) gen1
(b1, gen3) = randomRoundedInRange (-128, 128) gen2
(l2, gen4) = randomRoundedInRange (0, 100) gen3
(a2, gen5) = randomRoundedInRange (-128, 128) gen4
(b2, gen6) = randomRoundedInRange (-128, 128) gen5
dE = ciede_2000 l1 a1 b1 l2 a2 b2
putStrLn $ printf "%g,%g,%g,%g,%g,%g,%.17g" l1 a1 b1 l2 a2 b2 dE
loop (n-1) gen6
loop nIterations gen0