Using the Single-Constant Kubelka–Munk Model for Surface Color Prediction of Pre-Colored Fiber Blends

Abstract

This paper is committed to improving surface color prediction accuracy of the single-constant Kubelka–Munk (KM) model for pre-colored fiber blends without increasing the model complexity. The single-constant KM model is only applicable to certain media with a constant scattering coefficient. However, the scattered lights in pre-colored fiber blends are intertwined with a great deal of fiber surface reflections, making it impossible to obtain the true KM scattering coefficient. To solve this problem, we analyzed the propagation behavior of light beams within the pre-colored fiber blends, and proposed a light scattering correction equation to remove the effects of fiber surface reflections on the scattered lights. Then, an improved single-constant KM model was established based on the corrected spectral data. Pre-colored cotton fiber blended samples were prepared to assess the color prediction accuracy. The results show the improved model, with coefficients k1 = 0.9477 and k2 = 0.0523, achieved superior performance compared to the original single-constant KM model and the two-constant KM model. The average color difference (ΔE2000) of the improved model is 1.20, while the average ΔE2000 of the original single-constant KM model is 6.37, and that of the two-constant KM model is 1.58. Importantly, the improved model has not added complexity to the single-constant KM model since the light scattering correction equation is essentially used to pre-process the spectral data. It can be concluded that the improved model is beneficial and practical.