基于纽介堡方程的色纺织物颜色预测

doi:10.13475/j.fzxb.20220603301

纺织学报 ›› 2024, Vol. 45 ›› Issue (01): 83-89.doi: 10.13475/j.fzxb.20220603301

基于纽介堡方程的色纺织物颜色预测

杨柳¹^,², 李羽佳¹^,², 俞琰¹^,², 马磊³, 张瑞云¹^,²^,⁴()

1.东华大学纺织学院, 上海 201620
2.东华大学纺织面料技术教育部重点实验室, 上海 201620
3.中国纺织信息中心, 北京 100010
4.上海市纺织智能制造与工程一带一路国际联合实验室, 上海 200051

收稿日期:2022-06-13 修回日期:2023-08-11 出版日期:2024-01-15 发布日期:2024-03-14
通讯作者: 张瑞云(1969—),女,教授,博士。主要研究方向为新型功能纤维与数字化纺织技术。E-mail:ryzhang@dhu.edu.cn。
作者简介:杨柳(1992—),女,博士生。主要研究方向为色纺织物计算机测配色。
基金资助:
上海市科学技术委员会“科技创新行动计划”“一带一路”国际合作项目(21130750100);中央高校基本科研业务费专项资金资助项目(CUSF-DH-D-2018038);中国留学基金委资助项目(201806630110)

Color prediction of fiber-colored fabrics based on Neugebauer equation

YANG Liu¹^,², LI Yujia¹^,², YU Yan¹^,², MA Lei³, ZHANG Ruiyun¹^,²^,⁴()

1. College of Textiles, Donghua University, Shanghai 201620, China
2. Key Laboratory of Textile Science & Technology, Ministry of Education, Donghua University, Shanghai 201620, China
3. China Textile Information Center, Beijing 100010, China
4. Shanghai Belt and Road Joint Laboratory of Textile Intelligent Manufacturing, Shanghai 200051, China

Received:2022-06-13 Revised:2023-08-11 Published:2024-01-15 Online:2024-03-14

摘要/Abstract

摘要：

色纺织物由多种色纤维混合织造,其颜色预测过程复杂,基于格拉斯曼色光混合理论和印刷网点的纽介堡方程,建立了便于计算的颜色预测模型。预测过程分2种情况讨论,一种是取决于表面一层色纤维,另一种是取决于最上面2层纤维相互作用。当考虑最上面2层纤维相互叠加时,相互堆叠简化为与同色堆叠或与两色堆叠。根据不同方式各自建立颜色预测模型,选出预测色差最小的模型并对其优化。结果表明:当以色纺织物最上面2层纤维堆叠组成的色元对混色织物颜色预测时,2层纤维组分不同,认为堆叠顺序对该色元颜色值无影响建立的模型预测色差最小,且对该模型中各色元占比面积系数进行一阶线性回归修正后能较好地用于色纺织物表面颜色值的预测。

关键词: 格拉斯曼色光混合理论, 色纺织物, 纽介堡方程, 颜色预测, 色差

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

中图分类号:

TS181.8

杨柳, 李羽佳, 俞琰, 马磊, 张瑞云. 基于纽介堡方程的色纺织物颜色预测[J]. 纺织学报, 2024, 45(01): 83-89.

YANG Liu, LI Yujia, YU Yan, MA Lei, ZHANG Ruiyun. Color prediction of fiber-colored fabrics based on Neugebauer equation[J]. Journal of Textile Research, 2024, 45(01): 83-89.

图/表 7

表1

表2

表3

预测模型2#中三色纤维混合参数"

色元数量i	基本色元	色元占比f_i	色元三刺激值
1	A+A	a²	$X 1 Y 1 Z 1$
2	B+B	b²	$X 2 Y 2 Z 2$
3	C+C	c²	$X 3 Y 3 Z 3$
4	A+B/B+A	2ab	$X 4 Y 4 Z 4$
5	A+C/C+A	2ac	$X 5 Y 5 Z 5$
6	B+C/C+B	2bc	$X 6 Y 6 Z 6$

表3

图1

表4

表5

一次线性回归系数"

色元数量i	$U i$	$V i$	$W i$
1	19.69	12.33	7.61
2	33.93	31.08	5.15
3	13.78	12.19	23.75
4	22.24	13.18	4.93
5	0.26	2.46	12.01
6	4.07	4.15	5.52

表5

图2

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纤维颜色	X	Y	Z
红	21.03	12.29	7.68
黄	46.26	41.65	4.40
蓝	8.26	8.86	26.41

混色织物	色差	模型1#	模型2#	模型3#
红+黄	最大值	11.93	7.41	9.23
	最小值	3.19	0.36	1.57
	均值	8.72	4.73	6.65
红+蓝	最大值	9.45	5.54	6.60
	最小值	3.69	0.70	1.94
	均值	6.81	3.89	5.05
黄+蓝	最大值	28.38	17.99	21.16
	最小值	11.04	4.77	6.34
	均值	20.22	12.14	14.66
三彩色混	最大值	26.46	16.46	20.03
	最小值	5.67	3.98	4.52
	均值	12.75	8.51	10.01
	总均值	12.39	7.83	9.49

基于纽介堡方程的色纺织物颜色预测

Color prediction of fiber-colored fabrics based on Neugebauer equation

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试样编号	色纤维占比/%
试样编号	红	黄	蓝
1	10	10	80
2	10	20	70
…	…	…	…
9	20	10	70
…	…	…	…
36	80	10	10

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