Study on the Piecewise Inverse Model of Accumulated Temperature Based on Skewness-Distribution Parameters of Canopy Images in Pepper

Abstract

The crop leaf color is tightly connected with its meteorological environment. Color gradation skewness-distribution (CGSD) parameters can describe the information of leaf color more accurately, systematically, and comprehensively from five dimensions. We took photographs of pepper growing in the greenhouse at a fixed time every day and observed the meteorological factors. The results showed that the CGSD parameters were significantly correlated with meteorological factors, especially with the accumulated temperature, which showed the strongest correlation. Since the relationship between canopy leaf color and accumulated temperature is nonlinear, the piecewise inversion models were constructed by taking the stationary point of the high-order response model of G_skewness to accumulated temperature as the point of demarcation. The rate of outliers had decreased by 57.72%; moreover, the overall inversion accuracy had increased by 3.31% compared with the linear model directly constructed by the stepwise regression. It was observed that the pepper in the greenhouse had a different response to the same meteorological environmental stimulus before and after the stationary point. This study will provide a new method for constructing crop growth models in future research.

1. Introduction

Meteorological conditions are crucial factors that determine crop growth and leaf development [1,2]. Agrometeorologists are very concerned about the impact of meteorological environment on the growth of crops [3,4] and try to build various evaluation indexes to monitor the growth of crops [5], evaluate the agrometeorological conditions, and even predict the yield of crops [6,7]. Recently, more and more qualitative and quantitative descriptions of plant phenotype based on digital imaging technology have been studied [8]; the deepening research on the phenotype of crop for building intelligent agriculture, in particular, is growing vigorously. The progress that builds quantitative analysis of genotype-by-environment interactions by obtaining high-quality and massive visual feature data is an important aspect of plant phenotype research [9].

Crop leaf is a vital vegetative organ, while leaf color is a typical phenotypic characteristic of crop that is affected by meteorological conditions and can help to understand crop growth status [10,11,12]. This can assist in monitoring the growth of crops and evaluating the agrometeorological conditions, and eventually in conducting corresponding management for crops. Therefore, understanding the influence of meteorological conditions on leaf color and simulation of plant leaf color is very important for the crop production.

The RGB model is the most commonly used color representation for digital images [13]. It is widely used to determine the chlorophyll content of potato, rice, wheat, cauliflower, cabbage, barley, tomato, quinoa, and amaranth [14,15,16,17,18]. Since the nutritional status of plants can also be reflected in their leaf color [19], the RGB model is also used to assess whether plants lack certain nutrients [20]. This is simpler and more efficient than laboratory leaf analyses or even chlorophyll meter (SPAD) and nitrogen prediction [10]. In addition, the RGB model of digital color images has also been used to determine plant adaptability and degree of damage under biological or abiotic stresses [21]. Particularly when plant leaves display obvious senescence and color change after a long period of severe adversity and climate change, the RGB model is used to analyze the color depth of leaves and area size of different colors, as well as their proportion [22].

Plants cannot move freely like animals to avoid the coercion of severe environments, so they have evolved a complete set of self-regulation and adaptive mechanisms for alternatives in the environment [23]. Changes in the environment around plants tend to be cyclical and relatively moderate, without causing stress to the plants, such as changes in meteorological factors of temperature, humidity, and atmospheric pressure, from morning to night in the greenhouse. These factors cause a series of physiological and biochemical reactions within the plant [24,25], such as the leaf adjustment of stomatal movement [26], changes in chloroplast arrangement [27], and regulation of photosynthetic intensity [28,29], which can cause changes in plant color under visible light [30].

However, there is not enough research on the leaf color caused by these environmental changes especially in the stable microclimate environment of a greenhouse in visible light imaging. One reason is that these moderate changes do not significantly change the content of chlorophyll. Another important reason is that the traditional RGB model has few image parameters, so it can only describe the color depth of leaves [31] but not describe the small changes in leaf color more accurately. In our previous study, we found that the distribution of leaf color gradation follows a skewed distribution and extended the RGB model parameters from 4 to 20, and we established a method to describe the distribution of leaf color [32]. These color gradation skewness-distribution (CGSD) parameters can describe leaf color information more accurately and comprehensively [32,33]. This made it possible to study the relationship between the stable environment of a greenhouse and moderate changes in leaf color, which will fill the research gap on the leaf color caused by external meteorological changes.

In order to study whether the multi-dimensional characteristics of skewed parameters are also suitable for the studies of externally complex meteorological factors, we found images of peppers in the greenhouse and correspondent meteorological data from the microclimate observation database constructed by the Jiangsu Provincial Meteorological Bureau. We analyzed the relationship between color changes in images of pepper canopy and meteorological factors in the environment. Also, we used skewed parameters and meteorological factors such as temperature, humidity, and air pressure to construct the leaf color response model and the meteorological factor inversion model. Our study provides new ideas and methods for building the correlation model between meteorological factors and the internal physiological state of plants via leaf color as a bridge. If there is a quantitative mathematical relationship between CGSD parameters of leaves and the external environmental factors, even crop modeling will be improved.

2. Materials and Methods

2.1. Plant Material and Growth Conditions

The pepper was planted in the greenhouse located at the institute of vegetable crops, Jiangsu academy of agricultural sciences, Nanjing City, Jiangsu Province, China (25°5′ N, 116°58′ E) in 2021. The pepper was planted with a total nutrient matrix which was in the proportion of N: P₂O₅: K₂O in a 100 g matrix at 20:10:20; trace elements included Cu, Fe, Zn, Mn, B, Mo ≥1%, and pH 5.85. Moreover, the matrix contained an active accelerator and sustained release agent of poly-fertilizer. Four plots were set up for repeated treatment (Figure 1).

2.2. Meteorological Data Acquisition

Meteorological data were obtained from the agricultural meteorological observation station (DZZ4, Jiangsu Provincial Radio Science Research Institute Co., LTD., Wuxi, China) in the facility. The observed meteorological elements included daily meteorological elements, such as the daily mean temperature (T_m), daily maximum temperature (T_max), daily minimum temperature (T_min), daily air pressure (P_m), daily maximum air pressure (P_max), daily minimum air pressure (P_min), daily mean relative humidity (RH_m), daily minimum relative humidity (RH_min), daily mean dew point temperature (TD_m), daily mean water pressure (e_m), daily mean carbon dioxide concentration (C_m), daily maximum carbon dioxide concentration (C_max), and daily minimum carbon dioxide concentration (C_min). The accumulated temperature (AT) was calculated from T_m.

$$\mathit{AT}={\displaystyle \sum T_{\mathit{dm}}}$$

(1)

2.3. Pepper Image Collection in the Greenhouse

The monitoring camera used for image acquisition (model: DH-SD-65F630U-HN-Q; manufacturer: Zhejiang Dahua Technology Co., Ltd., Hangzhou, China) had an image resolution of 1920 × 1080, and the surveillance camera was installed 360 cm high. Additionally, the study used fixed focal length shooting and automatic white balance. Each camera took a photo once at each interval from 7:00 to 18:00, and the resulting digital photo size was 2560 × 2592. The digital images of pepper canopy at 18:00 were collected for analysis.

2.4. Extraction of Canopy Leaf Color Gradation Skewed-Distribution (CGSD) Characteristics of Pepper Image

We refer to Chen’s method for processing and collecting information of the image [32]. After cutting, denoising, and collecting information of the image, a color gradation cumulative histogram of the image was constructed. Then, the mean, median, mode, skewness, and kurtosis functions were used to analyze the canopy leaf color gradation skewed-distribution characteristics, respectively. Twenty CGSD parameters were then obtained, including R_Mean, R_Median, R_Mode, R_Skewness, R_Kurtosis, G_Mean, G_Median, G_Mode, G_Skewness, G_Kurtosis, B_Mean, B_Median, B_Mode, B_Skewness, B_Kurtosis, Y_Mean, Y_Median, Y_Mode, Y_Skewness, and Y_Kurtosis. Finally, the CGSD parameters tables of color gradation distribution of RGB images were formed.

2.5. Data Analysis

2.5.1. Correlation Analysis of 20 CGSD Parameters to Meteorological Factors

A correlation analysis with SPSS was used to analyze the relationship between 20 CGSD parameters of leaf RGB images collected each day, and the corresponding meteorological factors with double tail inspection were collected for examination of significance.

2.5.2. Construction of Response and Inversion Liner Models

By using SPSS, the linear response models of 20 CGSD parameters of leaf RGB images were established by a regression approach based on the least-square method, with daily meteorological factors as the independent variables. Correspondingly, the linear inversion models of meteorological factors based on 20 CGSD parameters were also established by a stepwise regression on the least-square method.

2.5.3. Construction of Curve Models and Determination of Stationary Point of Models

The main canopy leaf color factors of the inversion models built in Section 2.5.2 were selected to construct the conic and cubic model of canopy leaf color to accumulated temperature by using the curve estimation method in SPSS.

The first derivatives of the conic and cubic models were obtained by using the calculus method. According to the monotonicity theorem of the function, the corresponding × value (accumulated temperature value) when the first derivative of the two model equations is 0 was obtained, which is the stationary point of the function.

2.5.4. Construction of Piecewise Models

Taking the stationary point of the accumulated temperature obtained in Section 2.5.3 as the bound, the samples in the modeling group which were less than or equal to the stationary point were taken as the piecewise model modeling group I, and the samples greater than the boundary value were taken as group II. Then, the inversion models of canopy leaf color to accumulated temperature of these two groups were constructed, respectively, by using the method in Section 2.5.2.

2.5.5. Accuracy Analysis of Models

The piecewise inversion model was used to fit with the modeling samples and three groups of testing samples, and the fitting accuracy of each group of samples was calculated using the equation as shown in (2):

$$IA=(1-\left|\frac{A{T}_{\mathrm{P}}-AT}{AT}\right|)\times 100\%$$

(2)

IA is the inversion accuracy, %; AT_P is the fitted value of the accumulated temperature, °C·d; AT is the measured value of the accumulated temperature, °C·d. Samples with inversion accuracy outside the interval range of [0.100%] were marked as outliers. The outliers were not counted in the calculation of the average simulation of inversion accuracy.

3. Results

3.1. Skew Analysis of the Distribution of Canopy Leaf Color Gradation of the RGB Images

In previous studies, we had found the relationship between meteorological factors with CSGD parameters in Begonia fimnristipula grown in a greenhouse [34]. In this study, we found that the cumulative distribution of color gradation of pepper leaves during different growth periods in a glass greenhouse also conformed to the skew distribution and that the distribution also exhibited different distribution characteristics (Figure 2).

3.2. Correlation Analysis, Multiple Linear Relationships of Microclimate Factors in a Glasshouse, and Population Canopy CGSD Parameters

The correlation analysis with SPSS shows that among 14 meteorological factors, the daily average water pressure was significantly or extremely significantly correlated with 18 CSCD parameters, respectively. Meanwhile, the accumulated temperature, maximum value of daily CO₂ concentration, as well as the daily minimum temperature, were significantly or extremely significantly correlated with 17 CGSD parameters, respectively. However, the daily maximum temperature was not correlated with any CGSD parameter (Figure 3).

R_Mean, R_Median, R_Kurtosis, G_Mean, G_Mode, G_Kurtosis, B_Mean, B_Median, B_Skewness, B_Kurtosis, Y_Mean, Y_Median, and Y_Kurtosis were significantly and extremely significantly correlated with 13 meteorological factors, and G_Median and Y_Moed were significantly and extremely significantly correlated with 12 and 10 meteorological factors. R_Skewness, G_Skewness, and B_Mode were related to less than half of the meteorological factors, while R_Mode and Y_Skewness were only correlated with the daily maximum temperature.

3.3. Construction of the Canopy Leaf Color Response Regression Model

Table 1. Canopy leaf color response regression models of pepper and their goodness of fit.

Models		R-Square	Adjusted R-Square	RMSE	F Value	Significance F
RMean	Y1 = −1137.831 + 0.019 AT + 2.774 Pmax − 1.629 Pmin	0.508	0.493	10.672	33.374	0.000
RMedian	Y2 = −1186.280 + 0.018 AT + 2.960 Pmax − 1.769 Pmin	0.458	0.441	11.246	27.340	0.000
RMode	Y3 = −1054.301 + 2.880 Pmax + 0.016 Cmax − 1.821 Pmin	0.172	0.146	17.325	6.710	0.000
RSkewness	Y4 = −0.174 − 0.002 Cmin + 0.029 RHm − 0.030 em	0.193	0.168	0.421	7.717	0.000
RKurtosis	Y5 = 120.664 − 0.002 AT − 0.113 Pmax	0.280	0.265	1.901	19.026	0.000
GMean	Y6 = −1030.263 + 0.015 AT + 2.477 Pmax − 1.399 Pmin + 0.014 Cm	0.458	0.436	10.805	20.320	0.000
GMedian	Y7 = −1174.908 + 0.015 AT + 2.840 Pmax − 1.620 Pmin + 0.017 Cm	0.420	0.396	12.335	17.367	0.000
GMode	Y8 = −1397.657 + 0.024 AT + 3.486 Pmax − 2.043 Pmin	0.357	0.337	18.080	17.932	0.000
GSkewness	Y9 = 22.809 − 0.069 Pmax + 0.047 Pmin − 0.001 Cmin	0.264	0.241	0.299	11.601	0.000
GKurtosis	Y10 = 22.211 + 0.0004 AT − 0.032 em − 0.018 Pmin	0.627	0.616	0.350	54.394	0.000
BMean	Y11 = −783.168 + 0.025 AT + 0.785 Pmax + 0.007 Cmax	0.884	0.880	6.752	245.771	0.000
BMedian	Y12 = −809.815 + 0.026 AT + 0.807 Pmax + 0.007 Cmax	0.878	0.874	7.186	232.068	0.000
BMode	Y13 = −14.306 + 1.457 Tmin	0.078	0.069	17.553	8.370	0.000
BSkewness	Y14 = 1.500 − 0.001 AT	0.565	0.560	0.395	128.410	0.000
BKurtosis	Y15 = 20.585 − 0.001 AT − 0.539 Tm − 0.005 Cmin	0.430	0.412	2.357	24.352	0.000
YMean	Y16 = −965.515 + 0.018 AT + 2.523 Pmax − 1.525 Pmin	0.524	0.509	10.168	35.587	0.000
YMedian	Y17 = −1099.405 + 0.017 AT + 2.301 Pmax − 1.155 Pmin + 0.032 Cm − 0.384 RHm	0.522	0.497	10.981	20.775	0.000
YMode	Y18 = 74.780 + 0.024 Cmax + 0.017 AT − 2.193 TDm	0.286	0.264	19.612	12.958	0.000
YSkewness	Y19 = 21.832 − 0.063 Pmax − 0.001 Cmin + 0.042 Pmin	0.212	0.187	0.341	8.692	0.000
YKurtosis	Y20 = 5.158 − 0.001 AT − 0.049 em	0.465	0.454	0.765	42.565	0.000

showed that 20 models of canopy color to meteorological factors could be constructed, even the significance was extremely significant. In these models, the primary determinant of 14 CGSD response models, such as the mean, median, and kurtosis of R, G, B channels and gray image, as well as G_mode and B_skewness, was accumulated temperature. R² of the 14 models were also generally close or more than 0.5. This indicated that accumulated temperature plays a decisive role in the canopy leaf color state formation.

3.4. Construction Inversion Models of Accumulated Temperature Based on CSCD Parameters and Analysis of Inversion Accuracy of the Models

Based on the results of 3.2 and 3.3, we used CGSD parameters as the independent variable to build an inversion model of accumulated temperature, which is the decisive factor of the canopy leaf color state formation. The model was as follows:

AT: Y21 = 48.020 B_Mean + 374.594 G_Skewness − 15.344 R_Median − 3.303 B_Mode − 91.688

Furthermore, by verifying the inversion accuracy of the model, it was found that Y21 had a high inversion accuracy of 87.87% for the samples of group 2 from same planting row, while under the same environment, Y21 had a decreased accuracy, even at the lowest level reaching 76.78% for the samples (group 3 and group 4) from different planting rows (

Table 2. Analytical results of inversion accuracy of the inversion model of Y21 for the samples of four groups.

Index	Modeling Group (Group 1)	Group 2 from Same Planting Row	Group 3 from Different Planting Row	Group 4 from Different Planting Row
Sample number	101	101	101	101
Outlier number	7	9	8	11
Outlier ratio	6.93%	8.91%	7.92%	10.89%
Inversion accuracy	88.62%	87.87%	80.37%	76.78%

). Meanwhile, the inversion model had a large number of outliers, especially the proportion of outlier points for group 4, which out of the modeling samples had reached more than 10%, indicating that the inversion model was inappropriate.

Further research revealed that the appearance of outliers related to the plant age, which all appeared in the samples from the first 25 days of growth (Figure 4). This indicated the inversion method was not suitable for the accumulated temperature of the whole growth cycle of pepper, especially in the early growth period.

3.5. Outlier Analysis

In order to find the cause of the outliers, we took the modeling group (group 1) as samples to draw a scatter plot (Figure 5, Figure 6 and Figure 7). The accumulated temperature had a stable growth with the increase of leaf age, even without fluctuations. The CGSD parameters of pepper canopy showed an obviously monotonic change between the leaf age of 20 to 40. A monotonic decrease of B_Means was observed in the first half of the leaf age, and a monotonic increase was observed in the last half. Meanwhile, the G_Skewness showed a reverse monotonical change.

Because CGSD parameters did not simply vary linearly, it was inappropriate to use a single linear model to build the inversion mode of canopy leaf color to accumulated temperature. The segmented linear model, with the stagnation point as the boundary, should be used to build the inversion model.

3.6. Determination of Point of Demarcation of Piecewise Function Model

The turning point (i.e., stationary point), which was between the different trends in the change process of canopy leaf color with accumulated temperature, would be taken as the point of demarcation of the piecewise function model. In order to identify the turning point, we respectively fitted the B_Mean and G_Skewness, which had the highest correlation coefficient with accumulated temperature to the response model, by using the univariate quadratic and cubic equations (

Table 3. The univariate quadratic and cubic equation models of B_mean and G_skewness to accumulated temperature.

Models	R-Square	Adjusted R-Square	RMSE	F Value	Significance F
BMean Y22 = 0.0000070982 AT2 + 0.0038009585 AT + 23.89	0.897	0.895	6.326	426.329	0.000
BMeanY23 = −0.0000000132 AT 3 + 0.0000604278 AT 2 − 0.0534623558 AT + 36.65	0.962	0.961	3.847	824.278	0.000
GSkewnessY24 = −0.0000003471 AT 2 + 0.0010537988 AT − 0.65	0.391	0.378	0.270	31.433	0.000
GSkewnessY25 = 0.0000000004 AT 3 − 0.0000020405 AT 2 + 0.0028721223 AT − 1.05	0.604	0.592	0.219	49.345	0.000

). It was shown that the cubic curve model could better characterize the relationship between B_Mean, G_Skewness, and accumulated temperature. Therefore, the first derivatives of the two ternary equations (Y23 and Y25) were calculated, and the corresponding values of accumulated temperature were the stationary points (

Table 4. The first derivative equation models of B_mean and G_skewness to accumulated temperature.

Model	First Derivative Equation	x1	x2
Y23	Y23′ = 0.0000000396 AT 2 + 0.0001208546 AT − 0.0534623558	536.78	2515.14
Y25	Y25′ = 0.0000000012 AT 2 − 0.0000080810 AT + 0.0028721223	994.74	2406.09

). Combined with the scatter plots, we defined that the points of demarcation of two piecewise function models of B_Mean and G_Skewness to accumulated temperature were 537 and 995, respectively.

3.7. Determination and Prediction of Piecewise Function Model

Based on the points of demarcation, we constructed the piecewise inversion model of accumulated temperature to canopy color, respectively (

Table 5. The piecewise inversion model of accumulated temperature to canopy color based on the points of demarcation.

Models		R-Square	Adjusted R-Square	RMSE	F Value	Significance F
Tt = 1–537	Y26-1 = 728.655 − 10.377 RMode	0.849	0.841	63.410	112.130	0.000
Tt > 537	Y26-2 = 33.381 + 33.397 BMean − 3.705 RMode	0.963	0.962	123.844	991.054	0.000
Tt = 1–995	Y27-1 = 1978.483 − 14.777 GMode − 175.613 BSkewness	0.849	0.841	114.955	104.333	0.000
Tt > 995	Y27-2 = −790.630 + 43.366 BMean + 562.171 BSkewness − 2.945 RMean	0.953	0.950	111.400	383.353	0.000

), and then calculated the fitting accuracy of these piecewise functions (

Table 6. Comparison of inversion effects of the piecewise inversion models of Y26 and Y27 to Y21.

		Modeling Group (Group 1)	Group 2 from Same Planting Row	Group 3 from Different Planting Row	Group 4 from Different Planting Row	Summarized Result
Sample number		101	101	101	101	404
Y21	Outlier number	7	9	8	11	35
	Outlier ratio	6.93%	8.91%	7.92%	10.89%	8.66%
	Inversion accuracy	88.62%	87.87%	80.37%	76.78%	83.41%
Y26	Outlier number	2	4	4	2	12
	Outlier ratio	1.98%	3.96%	3.96%	1.98%	2.97%
	Inversion accuracy	90.48%	88.63%	80.24%	78.33%	84.42%
Y27	Outlier number	4	4	5	3	16
	Outlier ratio	3.96%	3.96%	4.95%	2.97%	3.96%
	Inversion accuracy	88.76%	85.37%	86.45%	84.10%	86.17%

, Figure 8 and Figure 9).

By using the piecewise inversion model, the rate of the outliers decreased by more than 50%. In the piecewise inversion model Y26, as the point of demarcation was calculated from the cubic curve model of B_Mean to accumulated temperature, the number of outliers decreased by 23; in fact, the rate of the outliers decreased by 65.70% compared with Y21. Furthermore, in the piecewise inversion model Y27, as the point of demarcation was calculated from the cubic curve model of G_Skewness to accumulated temperature, the number of outliers decreased by 19, and the rate of outliers had decreased by 57.72% compared with Y21. The above results showed that the model Y26 was dominant in reducing the outliers. In addition, by using these piecewise inversion models, the overall fitting accuracy of Y26 and Y27 also increased by 1.21% and 3.31% compared with Y21, respectively. Y26 performed best in the modeling group (group 1) and group 2, while Y27 increased by 8.53% compared with Y21 in group 3 and group 4 of different planting rows. In conclusion, Y27, which used the point of demarcation calculated from the cubic curve model of G_Skewness to accumulated temperature, had the best comprehensive effect.

4. Discussion

The research on the coupling effect between the environmental meteorological factors and crop growth is the basis of building collaborative environmental regulation models for a greenhouse. This has great significance to realize the precise regulation of a greenhouse environment and to promote the high-quality, high-quantity, and efficient production of greenhouse crops and even to reduce the costs.

Digital color images can reflect the growing state of plants [12], which provides a new method for research on crop growth. Based on our previous research, the traditional method, which used normal distribution and the corresponding parameter system for estimating canopy leaf color, was corrected. In fact, the color gradation of leaves follows skew distribution, and 20 CGSD parameters were established in our study [32,33,34]. CGSD parameters can describe the information of leaf color more accurately, systematically, and comprehensively from five dimensions, in which the mean value represents the mean color gradation of each pixel, the median value represents the median value of the percentile distribution of color gradation of pixels, and the mode value represents the color gradation with the largest proportion of the same color frequency of pixels. In addition, based on matrix and high-order statistics, skewness and kurtosis could quantitatively descript the bias and concentration of color gradation distribution.

The crop leaf color is tightly connected with its meteorological environment [35,36,37]. Our work indicated that the CGSD parameters of canopy leaf color are correlated with meteorological factors significantly, especially with the accumulated temperature, which shows the strongest correlation. Therefore, not only can environmental factors be used to simulate canopy leaf color changes (response model of canopy leaf color), but conversely, canopy leaf color can also be used to characterize the changes in meteorological factors (inversion model of canopy leaf color). Furthermore, parametric models could be established to characterize this relationship quantitatively. The stepwise regression is widely used because of its simple principle and convenience. However, the stepwise regression only could express the linear relationship between independent variables and dependent variables, that is, the monotonic function. If the relationship between independent variables and dependent variables is nonlinear, a large number of outliers will appear when using the monotonic function, which would affect the usability and accuracy of the model.

In this study, there were a lot of outliers in the response model of canopy leaf color to accumulated temperature, mainly due to the two main factors, B_Mean and G_Skewness, showing the nonlinear characteristics. That is to say, the relationship between canopy leaf color and accumulated temperature is nonlinear. In the previous study of Begonia fimnristipula, even though we had built the inverse model to the accumulated temperature by using spatial high-order and the prediction accuracy had been improved [34], there were still too many outliers. Therefore, a piecewise function was used to express the relationship between canopy leaf color and accumulated temperature more accurately. Taking the stationary point of the high-order response model of the two main factors as the bound, the piecewise inversion models of canopy leaf color to accumulated temperature were constructed by using the stepwise regression method in sequence.

By comparing the inversion accuracy of these models based on the stationary point of different parameters, we found that the piecewise models constructed by taking the stationary point of the cubic curve model of G_Skewness to accumulated temperature as the point of demarcation had the best effects, and the rate of outliers had decreased by 57.72%; moreover, the overall inversion accuracy had increased by 3.31% compared with the linear model constructed directly by the stepwise regression. It was shown that the pepper in greenhouse had a different response to the same meteorological environmental stimulus before and after the stationary point. That should be due to the accumulation of small meteorological environment changes leading to the qualitative changes of plants. We expect to further explore whether the stationary point can be used as a dividing marker of plant growth and a development cut-off point in subsequent studies.

5. Conclusions

The CGSD parameters of canopy leaf color of pepper were significantly correlated with meteorological factors in a greenhouse, especially with the accumulated temperature. Since the relationship between canopy leaf color and accumulated temperature is nonlinear, the piecewise inversion models, which had higher inversion accuracy and less outliers, were constructed by taking the stationary point of the high-order response model of G_Skewness to accumulated temperature as the point of demarcation.

In conclusion, exploring and building the relationship between CGSD parameters of leaves and the internal development of plants, as well as the external environmental factors, makes it possible that canopy leaf color information could be taken as a bridge to the associated models of the internal physiological state of plants and the external environment, especially for quickly but moderately environmental changing. It will provide a new method for constructing crop growth models in future studies.