Abstract:

Objective Fiber-colored fabrics are woven from a variety of colored fibers, and the fabric color prediction is complicated. According to the stacking of color fibers and the interaction between fiber and incident light, color prediction models convenient for color calculation were established based on the Glassmann' color mixing theory and Neugebauer Equation, and the model was further optimized to predict the color of fabrics for accuracy and efficiency.

Method Color prediction was discussed in two cases: one was depended on the surface layer of colored fibers, and the other was depended on the interaction of the top two-layer fibers. When considering the top two layers of fibers that were superimposed on each other, the mutual stacking was simplified as stacking with the same color or stacking with another color regardless of the number of primary fibers in the fabric. Color prediction models were established according to different calculation methods, and the model with the minimum color difference was selected and optimized.

Results According to different calculation methods, three color prediction models were set up. When the color of fiber-colored fabrics was depended on the surface layer of colored fibers, model 1 was used based on the mixing primary faber colors and the average color difference for all the fabrics was 12.39. When the color of fiber-colored fabrics was depended on the interaction of the top two-layer fibers, models 2 and 3 were used. In this case, considering that the top two layers of fibers were superimposed on each other, the mutual stacking was simplified as stacking with the same color or stacking with another color, regardless of the number of primary fibers in the fabric. The color of fiber-colored fabrics was mixed by 6 primary units in model 2, and its average color difference for all the fabrics was 7.83. The color of fiber-colored fabrics was mixed by 9 primary units in model 3, where unit A+B is different from the unit B+A, but is the same as A+C and B+C. The average color difference using model 3 for all the fabrics was 9.49. Model 2 achieved the smallest average color difference, meaning that when the color of fiber-colored fabrics was depended on the interaction of the top two-layer fibers, the stacking sequence has no effect on the color value of the primary units. This model was optimized by linear regression and the proportion coefficient of each primary unit in the model can be better adopted to predict the color value of fiber-colored fabrics. The new model was named model 4, and its average color difference for all the fabrics was 3.38. The new model 4 was proven to be convenient for prediction of the surface color of fiber-colored fabrics, and could be used as a reference for predicting the color of two-color or three-color mixed fabrics.

Conclusion Based on the Glassmann' color mixing theory and Neugebauer equation, three color prediction models were set up. Model 2 is associated to the smallest average color difference and is further optimized by linear regression. The new model 4 is convenient for predicting the surface color of fiber-colored fabrics, and can be used as a reference for predicting the color of two-color or three-color mixed fabrics. The De Mitchell equation was dupted to calculate the proportion coefficient of the primary units in the Neugebauer equation, and it was found difficult to calculate and required assumptions, resulting in theoretical errors. In this research, the primary units was simplified according to different assumptions, also generated theoretical errors, resulting in model 4 predicting higher color difference than the 1 color difference unit. The primary units of the fiber-colored fabrics is expected to be optimized in future research, fully considering the theoretical error when calculating the primary units proportion.

Key words: Glassmann's theory of color light mixing, fiber-colored fabrics, Neugebauer equation, color prediction, color difference