Mathematical and empirical evaluation of accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings

Bandpay, M. Gorji; Ameri, Farhad; Ansari, Keivan; Moradian, Siamak

doi:10.1007/s11998-018-0056-5

Cited by 16 publications

(4 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, leaf greens cannot be reproduced well with only these two pigments. According to K–M theory, the reflectance properties of various pigments can be used to obtain a simplified formula between the coating reflectance R and the coating absorption coefficient K and scattering coefficient S. 15 The spectral reflectance properties of chrome yellow and iron oxide red are utterly different from those of cobalt blue and chromium oxide green. The four-color pastes can be mixed in different proportions to modulate the spectral reflectance of the ink.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

Multi-response mixture design applied for the formulation of a textile green camouflage ink with reproduction of a leaf green

Xiao

et al. 2023

Textile Research Journal

View full text Add to dashboard Cite

This study establishes a proportioning model of green camouflage ink for textile screen printing to reproduce a leaf green using four high-performance inorganic pigment pastes: cobalt blue, chrome oxide green, chrome yellow, and iron red. In order to study the influence of four-color paste formulations on the camouflage performance of ink, a multi-response quadratic Scheffe mathematical model was established, and a total of 20 runs of color paste formulations were designed. Blending mixed color paste with water-based pure acrylic lotion, drying retarder, and thickener, the ink was then printed to the surface of the khaki camouflage decorative textile through screen printing. The spectral reflectance of the ink film was measured at 380∼1100 nm, and the response values were calculated. The regression model of each response was fitted using the least squares method. The model and verification experiments show that when the color paste formulation is 45.08% cobalt blue, 10.00% chrome green, 40.53% chrome yellow, and 4.39% iron red, the green camouflage ink match the leaf green well. The color difference between the green camouflage ink and the leaf green is less than 3, the reflectance ratio in the near-infrared and infrared bands is not less than 5, and the near-infrared brightness contrast with the leaf green is not more than 0.2. In addition, the green camouflage ink’s reflectivity is located in the leaf green hyperspectral channel.

show abstract

Section: Experimental Results and Analysismentioning

confidence: 99%

Multi-response mixture design applied for the formulation of a textile green camouflage ink with reproduction of a leaf green

Xiao

et al. 2023

Textile Research Journal

View full text Add to dashboard Cite

show abstract

“…Computer color matching provides a large number of shades combining a small number of colorants [3]. Therefore, it has been emphasized that in the manufacturing of plastics, printing, textiles, and paintings, predicting the color by a color matching system is a tool that has solved the problem of chromatic variations that arise between production batches [1,4]. In other words, the computer colorant formulation can be an asset to any dyer.…”

Section: Introductionmentioning

confidence: 99%

Determination of suitable wavelengths in dye concentration estimation by spectral analysis of K/S’s scalability

Safi¹,

Ameri²,

Ansari³

2021

Phys. Scr.

View full text Add to dashboard Cite

K/S and reflectance graphs are essential tools in characterizing the dyeing behavior. In textile coloration, estimating the dye concentration is poor using the Kubelka-Munk model due to its low scalability and deviation of the reflectance function from linearity after low dye concentrations, particularly in the wavelengths where the gradient of K/S against dye concentration is noticeable. This paper focused on extending the validity of the Kubelka-Munk function, which originates from the linearity of reflectance function against higher dye concentration. A data set of dyed polyester specimens with three disperse dyes in a dye concentration range was prepared. At the present work, K/S was analyzed by describing the scalability property, and the suitable wavelengths in the visible spectrum where K/S benefits from minor deviation from linearity were also discussed. It was observed that the K/S function is not always scalable and deviates in λ max after a specific dye concentration for K/S > 17. Accordingly, the wavelengths other than λ max were found that could be as important as λ max. For the K/S values > 25, no practical region was achieved.

show abstract

“…15,16 However, the medium described by the L-B law is expected to be transparent and uniform due to it ignoring scattered and reflected light. 17,18 Therefore, the poor prediction accuracy of the L-B law was commonly observed in fiber assemblies in the textile industry as the fibers are not fully opaque or transparent. 19 Alternatively, the Kubelka-Munk (K-M) two-flux theory describes the propagation law of light in turbid media by taking both scattered and reflected light into consideration, 20,21 which makes the K-M theory suitable to be applied in various scenarios, such as textile color prediction, 22,23 soil moisture inversion, 24,25 and food quality testing.…”

mentioning

confidence: 99%

Modified addition theorem on Kubelka-Munk transmission law for mass prediction of each primary in two-mixed cotton fiber blends

Wu,

Lu,

et al. 2024

Textile Research Journal

View full text Add to dashboard Cite

Unclear light propagation in mixed fibers has resulted in unachievable masses of primary fibers, in particular thin two-mixed fiber assemblies for decades. Hereby, a modified mixed medium addition theorem of the Kubelka-Munk transmission model is proposed to address this issue. This theorem was constructed by introducing a transfer function in the common ones on scattering coefficients, and such a transfer function takes both the mass proportion of each component and the reflectivity of mixed material into consideration. This opens up a new avenue for understanding the possible light mechanism of color mixed fiber assemblies. The proposed method demonstrated excellent accuracy in determining the primary masses of 48 specimens, with an average mean absolute error of only 2.23 mg. In comparison, the Lambert-Beer law yielded a much higher average mean absolute error of 8.66 for all types of blended samples. Such superiority was particularly obvious in white-black mixed samples, probably due to its comprised reflectance. In brief, this proposed theorem shows a high-quality prediction accuracy level in fiber mass and can be expanded to detect and control mixed fibers, as well as fiber length and uniformity detection through further study.

show abstract

Mathematical and empirical evaluation of accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings

Cited by 16 publications

References 69 publications

Multi-response mixture design applied for the formulation of a textile green camouflage ink with reproduction of a leaf green

Multi-response mixture design applied for the formulation of a textile green camouflage ink with reproduction of a leaf green

Determination of suitable wavelengths in dye concentration estimation by spectral analysis of K/S’s scalability

Modified addition theorem on Kubelka-Munk transmission law for mass prediction of each primary in two-mixed cotton fiber blends

Contact Info

Product

Resources

About