Study on the kinetics of shrinkage and color changes of chrysanthemum based on image processing

doi:10.12398/j.issn.2096-7217.2024.04.002

Abstract

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

CLC Number:

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.

Figures/Tables 29

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

Figure 1 Flow of calculating chrysanthemum shrinkage using image processing

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

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

Figure 4 Drying curves of chrysanthemums at different drying temperatures

Figure 5 Drying rate curves of chrysanthemums at different drying temperatures

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

Figure 6 Chrysanthemum images collected during drying

Figure 7 Variation curve of shrinkage rate of chrysanthemums during drying

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

Figure 8 Fit of experimental and predicted values of shrinkage rate

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

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

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

Figure 10 Fit of experimental and predicted values of L*

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

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

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

Figure 12 Fit of experimental and predicted values of a*

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

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

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

Figure 14 Fit of experimental and predicted values of b*

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

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

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

Figure 16 Fit of experimental and predicted values of L*

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

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

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

Figure 18 Fit of experimental and predicted values of a*

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

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

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

Figure 20 Fit of experimental and predicted values of b*

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