基于图像处理的菊花收缩率及色泽变化研究

doi:10.12398/j.issn.2096-7217.2024.04.002

摘要/Abstract

摘要：

外观品质是评价干燥花质量的重要指标。为了实现对干燥过程中菊花外观品质的快速无损检测，本研究将计算机视觉技术应用于菊花的红外辅助热风干燥过程中，基于Python语言开发了一种图像处理算法来获取在不同温度下（35 ℃，50 ℃和65 ℃）的干燥过程中菊花花瓣和花蕊表面收缩率和色泽参数的变化信息，并作为外观品质的评价指标，以此实现对干燥过程的精准控制。干燥动力学研究表明：菊花的干燥过程中始终处于降速干燥阶段，且干燥温度的升高导致了干燥时间的显著（p<0.05）缩短和干燥速率的显著升高。基于平方确定系数（R²）、残差平方和（RSS）、均方误差（MSE）值评估了常用的薄层干燥数学模型与试验数据的拟合程度，发现Henderson and Pabis模型、Page模型、Lewis模型与试验数据拟合度更高，能更好地描述菊花的干燥过程。此外，基于图像处理获取的不同干燥阶段菊花的表面收缩率及亮度值（L*）、红/绿值（a*）和黄/蓝值（b*）发现菊花形态和色泽的变化取决于干燥温度和干燥时间的共同作用，更低的干燥温度和更短的干燥时间更有利于抑制菊花在干燥过程的外观品质的劣变。进一步对零阶、一阶和一阶分数模型预测的收缩率和色泽（L*、a*和b*）值与试验数据进行线性回归分析，发现一阶分数模型能更为精准地预测菊花在干燥过程中收缩率以及色泽的变化规律。

关键词: 菊花, 图像处理, 干燥动力学, 收缩率, 色泽, 预测模型

Abstract:

Appearance quality is an important indicator in assessing the quality of dried chrysanthemums. To achieve rapid and non-destructive detection of the appearance quality of chrysanthemums during drying， this study applied computer vision technology in the infrared-assisted hot air drying of chrysanthemums and developed a Python-based image processing algorithm to acquire information on the changes in the shrinkage and color of petals and stamens of chrysanthemums at different temperatures （35 ℃， 50 ℃， and 65 ℃）. These parameters serve as evaluation indices for the appearance quality and facilitat precise control of the drying process. The kinetic analysis showed that the drying of chrysanthemums had a consistently decreasing drying rate. High drying temperatures significantly reduced drying time and increased drying rates （p<0.05）. Evaluation of the fit of mathematical models for thin-layer drying， including the Henderson and Pabis model， the Page model， and the Lewis model， showed that these models were in better agreement with the experimental data and thus more accurately described the drying process of chrysanthemums. Furthermore， changes in shrinkage rate and lightness （L*）， red/green （a*）， and yellow/blue （b*） values during drying showed that the morphological and color of chrysanthemums depended on drying temperature and time. Lower temperatures and shorter drying times were favorable for maintaining the appearance quality of the chrysanthemums. Linear regression analysis using zero-order， first-order， and first-order fractional models showed that the first-order fractional model provided more accurate predictions of shrinkage and color changes during the drying process of chrysanthemums.

Key words: chrysanthemum, image processing, drying kinetics, shrinkage, color, prediction model

中图分类号:

徐辉煌, 吴敏, 王梦露. 基于图像处理的菊花收缩率及色泽变化研究[J]. 智能化农业装备学报（中英文）, 2024, 5(4): 24-38.

XU Huihuang, WU Min, WANG Menglu. Study on the kinetics of shrinkage and color changes of chrysanthemum based on image processing[J]. Journal of Intelligent Agricultural Mechanization, 2024, 5(4): 24-38.

图/表 29

表1 四种常用的农产品干燥模型

Table 1 Four commonly used mathematical models for drying agricultural products

模型名称	表达式
Lewis model	MR=exp(-kt)
Page model	MR=exp(-ktⁿ )
Henderson and Pabis model	MR=aexp(-kt)
Wang and Singh model	MR=1+at+bt²

图1 使用图像处理计算菊花收缩率的流程

Figure 1 Flow of calculating chrysanthemum shrinkage using image processing

图2 使用图像处理获取菊花花瓣色泽参数的流程

Figure 2 Flow of obtaining color parameters of chrysanthemum petals using image processing

图3 使用图像处理获取菊花花蕊色泽参数的流程

Figure 3 Flow of obtaining color parameters of chrysanthemum stamens using image processing

图4 不同温度下菊花的干燥曲线

Figure 4 Drying curves of chrysanthemums at different drying temperatures

图5 不同干燥温度下菊花的干燥速率曲线

Figure 5 Drying rate curves of chrysanthemums at different drying temperatures

表2 不同干燥温度的试验数据与数学模型拟合及相关性检验结果

Table 2 Experimental data of different drying temperatures and mathematical model fitting and correlation test results

模型名称	干燥温度/℃	模型参数	RSS	MSE	R²
Lewis MR=exp(-kt)	35	k=0.001 3	8.06×10^-3	1.42×10^-4	0.998
	50	k=0.007 3	1.30×10^-2	7.23×10^-4	0.992 7
	65	k=0.012 7	3.33×10^-3	2.78×10^-4	0.997 1
Page MR=exp(-ktⁿ )	35	k=0.001 5，n=0.972 2	7.00×10^-3	1.25×10^-4	0.998 2
	50	k=0.006 5，n=1.023 4	1.27×10^-2	7.48×10^-4	0.992 5
	65	k=0.011 7，n=1.018 5	3.21×10^-3	2.92×10^-4	0.996 9
Henderson and Pabis MR=aexp(-kt)	35	k=0.001 2，a=0.985 6	6.11×10^-3	1.09×10^-4	0.998 5
	50	k=0.007 6，a=1.029 1	1.11×10^-2	6.52×10^-4	0.993 4
	65	k=0.012 7，a=1.002 5	3.32×10^-3	3.02×10^-4	0.996 8
Wang and Singh MR=1+at+bt²	35	a=-0.001 1，b=3.51×10^-7	2.08×10^-2	3.71×10^-4	0.994 8
	50	a=-0.005 6，b=8.25×10^-6	4.57×10^-2	2.69×10^-3	0.972 8
	65	a=-0.009 5，b=2.33×10^-5	2.07×10^-2	1.88×10^-3	0.980 1

图6 干燥过程中采集的菊花图像

Figure 6 Chrysanthemum images collected during drying

图7 干燥过程中菊花收缩率的变化曲线

Figure 7 Variation curve of shrinkage rate of chrysanthemums during drying

表3 零阶、一阶模型与不同干燥温度下收缩率值的拟合结果

Table 3 Fitting of zero-order and first-order models to shrinkage rate values at different drying temperatures

干燥温度/℃	模型	P₀	k	R²
35	P=P_o + kt	0.07	0.000 3	0.937 5
35	P=P_o exp (-kt)	0.10	0.028 9	0.868 9
50	P=P_o + kt	0.19	0.001 2	0.757 1
50	P=P_oexp (-kt)	0.25	0.002 4	0.635 4
65	P=P_o + kt	0.17	0.001 7	0.772 5
65	P=P_o exp (-kt)	0.21	0.003 7	0.754 5

图8 收缩率试验值与预测值拟合

Figure 8 Fit of experimental and predicted values of shrinkage rate

图9 花瓣L*值在干燥过程中的变化曲线

Figure 9 Change curves of L* values of petals during drying

表4 零阶、一阶和一阶分数模型与不同干燥温度下L*值的拟合结果

Table 4 Fitting of zore-order， first-order and first-order fraction models to L* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	C=C_o+kt	58.31	-	-0.000 8	0.91
	C=C_oexp(-kt)	58.31	-	0.000 01	0.909 9
	$C - C f C 0 - C f = e x p (- k t)$	58.31	168.31	0.000 003 6	0.908 3
50	C=C_o+kt	56.94	-	-0.006 8	0.956 2
	C=C_oexp(-kt)	56.95	-	0.000 1	0.957
	$C - C f C 0 - C f = e x p (- k t)$	54.41	49.62	0.001 1	0.957 7
65	C=C_o+kt	57.05	-	-0.015 3	0.880 4
	C=C_oexp(-kt)	57.07	-	0.000 2	0.885 7
	$C - C f C 0 - C f = e x p (- k t)$	53.77	53.27	0.008 2	0.953 6

表4 零阶、一阶和一阶分数模型与不同干燥温度下L*值的拟合结果

Table 4 Fitting of zore-order， first-order and first-order fraction models to L* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	C=C_o+kt	58.31	-	-0.000 8	0.91
	C=C_oexp(-kt)	58.31	-	0.000 01	0.909 9
	$C - C f C 0 - C f = e x p (- k t)$	58.31	168.31	0.000 003 6	0.908 3
50	C=C_o+kt	56.94	-	-0.006 8	0.956 2
	C=C_oexp(-kt)	56.95	-	0.000 1	0.957
	$C - C f C 0 - C f = e x p (- k t)$	54.41	49.62	0.001 1	0.957 7
65	C=C_o+kt	57.05	-	-0.015 3	0.880 4
	C=C_oexp(-kt)	57.07	-	0.000 2	0.885 7
	$C - C f C 0 - C f = e x p (- k t)$	53.77	53.27	0.008 2	0.953 6

图10 L*试验值与预测值拟合

Figure 10 Fit of experimental and predicted values of L*

图11 花瓣a*值在干燥过程中的变化曲线

Figure 11 Change curves of a* values of petals during drying

表5 零阶、一阶和一阶分数模型与不同干燥温度下a*值的拟合结果

Table 5 Fitting of zero-order， first-order and first-order fraction models to a* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	-0.14	-	0.000 1	0.716 9
	$C = C 0 e x p (- k t)$	-0.14	-	0.000 5	0.712 4
	$C - C f C 0 - C f = e x p (- k t)$	-0.14	0.89	0.000 1	0.711 8
50	$C = C 0 + k t$	-0.17	-	0.000 6	0.957 8
	$C = C 0 e x p (- k t)$	0.000 000 32	-	-0.030 6	0.531 7
	$C - C f C 0 - C f = e x p (- k t)$	-0.16	-0.65	-0.001	0.952 7
65	$C = C 0 + k t$	-0.01	-	0.001 6	0.910 1
	$C = C 0 e x p (- k t)$	0.06	-	-0.007 9	0.803 9
	$C - C f C 0 - C f = e x p (- k t)$	-0.01	-61.24	-0.000 03	0.901

表5 零阶、一阶和一阶分数模型与不同干燥温度下a*值的拟合结果

Table 5 Fitting of zero-order， first-order and first-order fraction models to a* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	-0.14	-	0.000 1	0.716 9
	$C = C 0 e x p (- k t)$	-0.14	-	0.000 5	0.712 4
	$C - C f C 0 - C f = e x p (- k t)$	-0.14	0.89	0.000 1	0.711 8
50	$C = C 0 + k t$	-0.17	-	0.000 6	0.957 8
	$C = C 0 e x p (- k t)$	0.000 000 32	-	-0.030 6	0.531 7
	$C - C f C 0 - C f = e x p (- k t)$	-0.16	-0.65	-0.001	0.952 7
65	$C = C 0 + k t$	-0.01	-	0.001 6	0.910 1
	$C = C 0 e x p (- k t)$	0.06	-	-0.007 9	0.803 9
	$C - C f C 0 - C f = e x p (- k t)$	-0.01	-61.24	-0.000 03	0.901

图12 a*试验值与预测值拟合

Figure 12 Fit of experimental and predicted values of a*

图13 花瓣b*值在干燥过程中的变化曲线

Figure 13 Change curves of b* values of petals during drying

表6 零阶、一阶和一阶分数模型与不同干燥温度下b*值的拟合结果

Table 6 Fitting of zero-order， first-order and first-order fraction models to b* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	2.40	-	0.001 2	0.936 5
	$C = C 0 e x p (- k t)$	2.46	-	-0.000 4	0.943 5
	$C - C f C 0 - C f = e x p (- k t)$	2.47	0.07	-0.000 4	0.942 5
50	$C = C 0 + k t$	3.30	-	0.004 2	0.632 9
	$C = C 0 e x p (- k t)$	3.39	-	-0.000 9	0.585 6
	$C - C f C 0 - C f = e x p (- k t)$	2.32	4.61	0.014 4	0.989 2
65	$C = C 0 + k t$	3.84	-	0.009 7	0.699
	$C = C 0 e x p (- k t)$	3.98	-	-0.001 8	0.640 6
	$C - C f C 0 - C f = e x p (- k t)$	2.86	5.62	0.019 4	0.997 4

表6 零阶、一阶和一阶分数模型与不同干燥温度下b*值的拟合结果

Table 6 Fitting of zero-order， first-order and first-order fraction models to b* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	2.40	-	0.001 2	0.936 5
	$C = C 0 e x p (- k t)$	2.46	-	-0.000 4	0.943 5
	$C - C f C 0 - C f = e x p (- k t)$	2.47	0.07	-0.000 4	0.942 5
50	$C = C 0 + k t$	3.30	-	0.004 2	0.632 9
	$C = C 0 e x p (- k t)$	3.39	-	-0.000 9	0.585 6
	$C - C f C 0 - C f = e x p (- k t)$	2.32	4.61	0.014 4	0.989 2
65	$C = C 0 + k t$	3.84	-	0.009 7	0.699
	$C = C 0 e x p (- k t)$	3.98	-	-0.001 8	0.640 6
	$C - C f C 0 - C f = e x p (- k t)$	2.86	5.62	0.019 4	0.997 4

图14 b*试验值与预测值拟合

Figure 14 Fit of experimental and predicted values of b*

图15 花蕊L*值在干燥过程中的变化曲线

Figure 15 Change curves of L* values of stamens during drying

表7 零阶、一阶和一阶分数模型与不同干燥温度下L*值的拟合结果

Table 7 Fitting of zero-order， first-order and first-order fractional models to L* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	36.63	-	0.005	0.974 7
	$C = C 0 e x p (- k t)$	36.78	-	0.000 2	0.982 4
	$C - C f C 0 - C f = e x p (- k t)$	37.26	25.46	0.000 7	0.993 9
50	$C = C 0 + k t$	34.26	-	0.033	0.871 9
	$C = C 0 e x p (- k t)$	35.01	-	0.001 3	0.913 2
	$C - C f C 0 - C f = e x p (- k t)$	37.19	21.40	0.006 2	0.983
65	$C = C 0 + k t$	35.29	-	0.059 9	0.834 1
	$C = C 0 e x p (- k t)$	36.18	-	0.002 3	0.884 3
	$C - C f C 0 - C f = e x p (- k t)$	38.34	21.72	0.010 2	0.958 9

表7 零阶、一阶和一阶分数模型与不同干燥温度下L*值的拟合结果

Table 7 Fitting of zero-order， first-order and first-order fractional models to L* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	36.63	-	0.005	0.974 7
	$C = C 0 e x p (- k t)$	36.78	-	0.000 2	0.982 4
	$C - C f C 0 - C f = e x p (- k t)$	37.26	25.46	0.000 7	0.993 9
50	$C = C 0 + k t$	34.26	-	0.033	0.871 9
	$C = C 0 e x p (- k t)$	35.01	-	0.001 3	0.913 2
	$C - C f C 0 - C f = e x p (- k t)$	37.19	21.40	0.006 2	0.983
65	$C = C 0 + k t$	35.29	-	0.059 9	0.834 1
	$C = C 0 e x p (- k t)$	36.18	-	0.002 3	0.884 3
	$C - C f C 0 - C f = e x p (- k t)$	38.34	21.72	0.010 2	0.958 9

图16 L*试验值与预测值拟合

Figure 16 Fit of experimental and predicted values of L*

图17 花蕊a*值在干燥过程中的变化曲线

Figure 17 Change curves of a* values of stamens during drying

表8 零阶、一阶和一阶分数模型与不同干燥温度下a*值的拟合结果

Table 8 Fitting of 0th-order， first-order and first-order fractional models to a* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	-3.39	-	0.000 7	0.971
	$C = C 0 e x p (- k t)$	-3.42	-	0.000 2	0.967 6
	$C - C f C 0 - C f = e x p (- k t)$	-3.39	149.03	0.000 004 4	0.970 4
50	$C = C 0 + k t$	-3.43	-	0.012 4	0.935 6
	$C = C 0 e x p (- k t)$	-4.23	-	0.009	0.808 7
	$C - C f C 0 - C f = e x p (- k t)$	5.03	3.61	0.002 8	0.961 9
65	$C = C 0 + k t$	-3.44	-	0.021 3	0.866 5
	$C = C 0 e x p (- k t)$	-4.26	-	0.014 9	0.783 1
	$C - C f C 0 - C f = e x p (- k t)$	4.74	2.87	0.005 8	0.906 4

表8 零阶、一阶和一阶分数模型与不同干燥温度下a*值的拟合结果

Table 8 Fitting of 0th-order， first-order and first-order fractional models to a* values at different drying temperatures

干燥温度/℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	-3.39	-	0.000 7	0.971
	$C = C 0 e x p (- k t)$	-3.42	-	0.000 2	0.967 6
	$C - C f C 0 - C f = e x p (- k t)$	-3.39	149.03	0.000 004 4	0.970 4
50	$C = C 0 + k t$	-3.43	-	0.012 4	0.935 6
	$C = C 0 e x p (- k t)$	-4.23	-	0.009	0.808 7
	$C - C f C 0 - C f = e x p (- k t)$	5.03	3.61	0.002 8	0.961 9
65	$C = C 0 + k t$	-3.44	-	0.021 3	0.866 5
	$C = C 0 e x p (- k t)$	-4.26	-	0.014 9	0.783 1
	$C - C f C 0 - C f = e x p (- k t)$	4.74	2.87	0.005 8	0.906 4

图18 a*试验值与预测值拟合

Figure 18 Fit of experimental and predicted values of a*

图19 花蕊b*值在干燥过程中的变化曲线

Figure 19 Change curves of b* values of stamens during drying

表9 零阶、一阶和一阶分数模型与不同干燥温度下b*值的拟合结果

Table 9 Fitting of zero-order， first-order and first-order fractional models to b* values at different drying temperatures

干燥温度 /℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	11.03	-	-0.001 4	0.951 7
	$C = C 0 e x p (- k t)$	11.07	-	0.000 1	0.958 3
	$C - C f C 0 - C f = e x p (- k t)$	8.38	8.09	0.000 8	0.970 5
50	$C = C 0 + k t$	10.55	-	-0.016 1	0.897 7
	$C = C 0 e x p (- k t)$	11.15	-	0.002 4	0.951 5
	$C - C f C 0 - C f = e x p (- k t)$	4.19	3.47	0.004 6	0.966 2
65	$C = C 0 + k t$	10.66	-	0.030 3	0.889 3
	$C = C 0 e x p (- k t)$	11.37	-	0.004 5	0.942 9
	$C - C f C 0 - C f = e x p (- k t)$	3.87	2.21	0.006 5	0.943 5

表9 零阶、一阶和一阶分数模型与不同干燥温度下b*值的拟合结果

Table 9 Fitting of zero-order， first-order and first-order fractional models to b* values at different drying temperatures

干燥温度 /℃	模型	C₀	C_f	k	R²
35	$C = C 0 + k t$	11.03	-	-0.001 4	0.951 7
	$C = C 0 e x p (- k t)$	11.07	-	0.000 1	0.958 3
	$C - C f C 0 - C f = e x p (- k t)$	8.38	8.09	0.000 8	0.970 5
50	$C = C 0 + k t$	10.55	-	-0.016 1	0.897 7
	$C = C 0 e x p (- k t)$	11.15	-	0.002 4	0.951 5
	$C - C f C 0 - C f = e x p (- k t)$	4.19	3.47	0.004 6	0.966 2
65	$C = C 0 + k t$	10.66	-	0.030 3	0.889 3
	$C = C 0 e x p (- k t)$	11.37	-	0.004 5	0.942 9
	$C - C f C 0 - C f = e x p (- k t)$	3.87	2.21	0.006 5	0.943 5

图20 b*试验值与预测值拟合

Figure 20 Fit of experimental and predicted values of b*

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