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' This function written in VBA 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. ' Prevents errors due to typos or undeclared variables. Option Explicit ' 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. Public Function ciede_2000(l_1 As Double, a_1 As Double, b_1 As Double, l_2 As Double, a_2 As Double, b_2 As Double) As Double ' Working in VBA 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... Const M_PI = 3.14159265358979323846264338328, k_l = 1.0, k_c = 1.0, k_h = 1.0 Dim n As Double, c_1 As Double, c_2 As Double, h_1 As Double, h_2 As Double Dim h_m As Double, h_d As Double, p As Double, r_t As Double, l As Double Dim t As Double, h As Double, c As Double n = (Sqr(a_1 * a_1 + b_1 * b_1) + Sqr(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 - Sqr(n / (n + 6103515625.0))) ' Application of the chroma correction factor. c_1 = Sqr(a_1 * a_1 * n * n + b_1 * b_1) c_2 = Sqr(a_2 * a_2 * n * n + b_2 * b_2) ' Using 14 lines to simulate atan2, as VBA does not have this built-in. If 0.0 < a_1 Then h_1 = Atn(b_1 / (a_1 * n)) - (b_1 < 0.0) * 2.0 * M_PI ElseIf a_1 < 0.0 Then h_1 = Atn(b_1 / (a_1 * n)) + M_PI Else h_1 = M_PI + ((0.0 < b_1) - (b_1 < 0.0)) * 0.5 * M_PI End If If 0.0 < a_2 Then h_2 = Atn(b_2 / (a_2 * n)) - (b_2 < 0.0) * 2.0 * M_PI ElseIf a_2 < 0.0 Then h_2 = Atn(b_2 / (a_2 * n)) + M_PI Else h_2 = M_PI + ((0.0 < b_2) - (b_2 < 0.0)) * 0.5 * M_PI End If ' The atan2 polyfill (customized) is complete. n = Abs(h_2 - h_1) ' Cross-implementation consistent rounding. If M_PI - 1E-14 < n And n < M_PI + 1E-14 Then n = M_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 M_PI < n Then h_d = h_d + M_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 + M_PI ' If h_m < M_PI Then h_m = h_m + M_PI Else h_m = h_m - M_PI End If p = 36.0 * h_m - 55.0 * M_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 * Sqr(n / (n + 6103515625.0)) _ * Sin(M_PI / 3.0 * Exp(p * p / (-25.0 * M_PI * M_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 / Sqr(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 + M_PI * 0.5) _ + 0.32 * Sin(3.0 * h_m + 8.0 * M_PI / 15.0) _ - 0.17 * Sin(h_m + M_PI / 3.0) _ - 0.2 * Sin(4.0 * h_m + 3.0 * M_PI / 20.0) n = c_1 + c_2 ' Hue. h = 2.0 * Sqr(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. ciede_2000 = Sqr(l * l + h * h + c * c + c * h * r_t) End Function ' GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching ' Online Tests : https://michel-leonard.github.io/ciede2000-color-matching ' L1 = 85.3 a1 = 21.6 b1 = 3.9 ' L2 = 87.7 a2 = 27.3 b2 = -4.2 ' CIE ΔE00 = 6.1457265560 (Bruce Lindbloom, Netflix’s VMAF, ...) ' CIE ΔE00 = 6.1457093985 (Gaurav Sharma, OpenJDK, ...) ' Deviation between implementations ≈ 1.7e-5 ' See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.