2.1.

Hyperspectral Imaging System

The hyperspectral imaging system used in the proposed method consists of four main components: (1) a bottom horizontal support plate, linked to a stepper motor (Leashine, 20CM003, $100\mathrm{r}/\min$), which can be moved horizontally; (2) a camera mount for fixing and changing the vertical position of the camera (the vertical distance between the camera and the platform is 50 cm); (3) hyperspectral cameras (Specim FX10-CHINA, Specim FX17-CHINA); and (4) a dual illumination system. The hyper-spectral imaging system is shown in Fig. 1.

Fig. 1

Schematic diagram of the hyperspectral imaging system.

The obtained hyperspectral images comprise hundreds of sequential bands of tomato leaves and stems. White and black references were used to correct the hyperspectral images.¹⁸ $R$ represents a ratio comparing the images with a white background; 100 represents having the same reflectivity as a white background, and 0 represents having the same reflectivity as a black background. The value is calculated as:

2.2.

Spectrophotometer

The absorbance at 450 nm is measured using a spectrophotometer (UV3600_UV-Vis-NIR dual-beam spectrophotometer-OPTOSKY-CHINA).

Reflectance spectral data of tomato plants were collected using a hyperspectral system with a wavelength range of 370 to 1715 nm and a spectral resolution of 1 nm. Tomato leaf and stem samples were collected at different growth stages (1 to 8 weeks) and under the same treatments. The contents of $\alpha$-AMS, POD, and PAL were determined by traditional chemical methods.¹⁹ Hyperspectral-based prediction models for $\alpha$-AMS, POD, and PAL content in the tomato plants were then developed using various modeling techniques. The study compared and analyzed the prediction accuracies to obtain relatively good detection models. Figure 2 shows the flowchart of this study.

Fig. 2

Research flowchart.

2.3.

Gold-Standard Detection of Enzyme Concentration

In this paper, the chemically detected enzyme activity was used as the gold standard for comparative analysis.

The three enzyme activities were calculated by determining the enzyme concentration in the sample through a linear regression equation and then multiplying by the dilution factor to obtain the actual concentration of the sample. The specific equations are as follows:

All three equations indicate that the change in absorbance per minute per gram of fresh weight (FW) sample at either 470 or 450 nm is its POD activity unit (U). Statistical analyses of the chemical assays for the three enzyme activities are presented in Table 1.

Table 1

Descriptive statistical analysis of enzyme concentration detected by chemistry.

2.4.

Spectral Selection

Spectral selection is a technique used to extract effective wavelength variables from high-dimensional spectral data. This method reduces redundancy and noise in the data, leading to improved accuracy and stability of the model.²⁰ This study employed two spectral selection algorithms, namely GA and SPA, which were combined with PLS. A spectral prediction model was developed for predicting enzyme activities in tomato plants.

GA and SPA are two very effective methods in the field of spectral selection. The advantage of GA lies in its global search capability, which can simulate the natural selection and genetic mechanism in the process of biological evolution and find the optimal wavelength combinations through crossover, mutation, and selection operations of populations. This method not only is capable of handling large-scale datasets but also can effectively avoid falling into local optimal solutions, thus improving the generalization ability of the model.¹⁴

On the other hand, SPA, as a forward variable selection method, selects wavelengths by minimizing the covariance between variables. It is computationally efficient, easy to implement, and particularly suitable for dealing with spectral data with a high degree of covariance. SPA selects the variables step by step by successive projections, which reduces the complexity of the model while maintaining its stability and prediction accuracy.²¹

Spectral selection allows the analyst to select specific spectral regions to observe, allowing for more accurate identification and quantification of components in a sample. It allows for increasing the sensitivity; by selecting specific spectral lines, the sensitivity to detect specific elements or compounds can be increased. It reduces interference; good selectivity enables the determination of elements and compounds with similar chemical properties, reducing spectral interference from other elements. Finally, it improves the analysis speed; spectral selection can quickly locate the spectral region of interest, speeding up the analysis process.

The following equation was used for modeling using a chemical detection algorithm as the gold standard assay to predict enzyme activity in tomatoes:

GA is a global optimization algorithm that simulates the processes of natural selection, crossover, and mutation to gradually improve the fitness of the population. A GA was used to select the best subset of wavelengths as input variables for the PLS regression. Each wavelength variable is regarded as a gene, each wavelength subset is regarded as a chromosome, and the prediction error is taken as the fitness function.²²

SPA is a spectral selection algorithm based on orthogonal projection. It constructs a subset of wavelengths that is minimally redundant and maximally correlated with the target variable by progressively selecting the most correlated wavelength variable.²³

PLS is a multivariate statistical data analysis method that enables regression modeling (multivariate linear regression), data structure simplification (principal component analysis), and correlation analysis (typical correlation analysis) between two sets of variables to be performed simultaneously under a single algorithm. The PLS method is used to obtain mutually orthogonal eigenvectors for the independent variables and the dependent variable, respectively, by projecting their high-dimensional data spaces into the corresponding low-dimensional spaces. The mutually orthogonal eigenvectors of the independent variable and the dependent variable are obtained, and then the one-way linear regression relationship between the eigenvectors of the independent variable and the dependent variable is established. Not only can it overcome the problem of covariance, but it also emphasizes the explanatory and predictive roles of the independent variables on the dependent variable when selecting the feature vectors and removes the influence of unhelpful noise on the regression, resulting in the model containing a minimum number of variables.

SVM is a supervised learning model mainly used for classification and regression analysis. The basic idea is to maximize the spacing between different classes of data points by finding an optimal hyperplane (or hypersurface). This optimal hyperplane, called the maximum spacing hyperplane, maximizes the separation of data points of different categories and thus achieves good classification results.²⁴

The PSO-BP neural network is an algorithm that combines PSO and the BP neural network and is mainly used for nonlinear function fitting and regression problems. The basic idea is to use the PSO algorithm to optimize the weights and thresholds of the BP neural network to improve the performance and convergence speed of the BP neural network. PSO is a heuristic algorithm that simulates the foraging behavior of a flock of birds for searching, and it is able to achieve the search of the global optimal solution.²⁵

RF is an integrated learning method that is defined as a linear classifier with maximum intervals on the feature space. RF constructs multiple decision trees during training and outputs classes as patterns of classes (classification) or average predictions (regression). The learning strategy of RF is interval maximization, which can be formalized as solving a convex quadratic programming, which is also equivalent to minimizing a regularized hinge loss function.²⁶

The average coefficient of determination for the three enzymes and the average root mean square error of the three enzymes of the two spectral selection algorithms mentioned above are used to measure the degree of model fit to the data and the prediction error, respectively. The larger the average coefficient of determination is and the smaller the average root mean square error is, the better the predictive performance of the model is. These two metrics are used to compare the advantages and disadvantages of the GA and SPA algorithms and choose the better algorithm. Then, the better algorithm in combination with PLS, SVM, PSO-BP, and RF is used to observe the prediction results.

The establishment of predictive models is a key step in spectral analysis, which allows for the use of spectral data to predict the nature or composition of a target substance. Using spectra selected by GA as inputs, four predictive models were built: GA-PLS, GA-SVM, GA-PSO-BP, and GA-RF; they are based on PLS regression, SVM, particle swarm optimization-backpropagation neural network (PSO-BP), and RF algorithms, respectively.

3.1.

Extraction of Hyperspectral Image Data From Leaves and Stems of Tomato Samples

This paper focuses on the spectral characteristics of tomato plants, specifically their leaves and stems. To observe these characteristics, a hyperspectral imaging system was used to photograph the plants, resulting in a clear image (Fig. 3). The image allows for the distinction of different colors and shapes of the tomato leaves and stems. To analyze the spectral information, the image was processed using ENVI software. This produced a spectral plot of the average of the spectra of each point of all leaves in different wavelength ranges. Figures 4 and 5 show the results, with the horizontal axis representing the wavelength and the vertical axis representing the intensity of light received by the detector. Upon comparison of these graphs, it is evident that they share similar trends in their spectral curves, which are linked to their physiological and chemical properties.

Fig. 3

Photos of tomato plants in the NIR and VIS bands: (a) photos of tomato plants in the NIR band and (b) photos of tomato plants in the VIS light band.

Fig. 4

Reflectance of tomato stems and leaves in the NIR spectrum: (a) reflectance spectra of tomato stems in the NIR band and (b) reflectance spectra of tomato leaves in the NIR band.

Fig. 5

Reflectance of tomato stems and leaves in the VIS spectrum: (a) reflectance spectra of tomato stems in the VIS band and (b) reflectance spectra of tomato stems in the NIR band.

However, it is evident in Figs. 4 and 5 that there is also some noise in the raw image and spectral data, which may affect the analysis results. Therefore, some preprocessing of the data is needed to remove or reduce the effect of noise before proceeding to subsequent studies. In the lower spectral range of 370 to 430 nm and in the higher spectral ranges of 880 to 940 nm and 1640 to 1715 nm, the noise is high and shows high-frequency features. These noises may come from the instrument, the environment, or the sample itself. To prevent these noises from interfering with the study, it was decided to exclude these bands in the preprocessing stage and keep only the low spectral range 430 to 880 nm and the high spectral range 940 to 1640 nm.

3.2.

Preprocessing of Data

Data preprocessing is an important step in spectral analysis as it eliminates noise, baseline drift, scattering effects, and other interfering factors in the spectral data. This improves the quality and comparability of spectral signals, enhancing the correlation between the spectra and the target substances. This, in turn, provides more accurate and effective data for subsequent model building and analysis.²⁷ Three data preprocessing methods were used: variable normalization, truncation operations, and removal of outliers.

Variable standardization is a frequently used data preprocessing technique. It removes differences in magnitude and scale between variables, resulting in each variable having a mean of 0 and a standard deviation of 1.²⁸ This approach prevents the model from being influenced by variables that are too large or too small and enhances the stability and generalization of the model. The reflectance at each wavelength was normalized based on the variables to enable comparison at the same scale. The truncation operation selects a suitable wavelength range by removing irrelevant or redundant information, reducing data dimension and computational complexity. The above two data preprocessing methods were used to obtain clearer and more concise spectral data, laying the foundation for subsequent spectral analyses.

These remove noise and interference and improve the quality and credibility of the data.²⁹ After preprocessing, two spectral graphs are obtained, as shown in Fig. 6; these represent the reflectance of tomato leaves at different wavelengths.

Fig. 6

Spectral information of unpretreated and pretreated tomato stems: (a) spectral information of unpretreated tomato stems in the NIR light band and (b) spectral information of pretreated tomato stems in the NIR band.

3.3.

Spectral Band Selection

Parameters such as population size, crossover probability, and mutation probability were set, and several iterations were run to finally obtain an optimal solution for a leaf and stem variable containing 31 and 26 wavelengths in the VIS range and 35 and 28 wavelengths in the NIR band range.

The SPA was used to select the best subset of wavelengths to be used as input variables for the PLS regression. The number of wavelengths to be selected was set, and the SPA algorithm was run; the result was an optimal solution containing 27 and 20 wavelength variables in the VIS range and 25 and 19 wavelength variables in the NIR range for both leaf and stem.

The relationship between the variable importance and the variable index was obtained as follows.

The importance of each band of the leaf of tomato plants in the NIR band was obtained by the GA model, as shown in Fig. 7, and the screened spectral bands were determined based on the order of importance as well as the cumulative contribution, which was taken as the 179th (1460 nm)-214th (1574 nm), totaling 35 bands. Similarly, the bands screened under the other seven models can be obtained. The calibration and validation sets are first assigned based on the available data.

Fig. 7

Significance of each band of leaves in the NIR range under the GA model.

Significance refers to the degree of contribution of each NIR band to the enzyme activity in the GA model. To reduce the dimensionality of the data analysis and to improve the analytical relevance of the characteristic spectra, the variables with more than 80% importance were taken for the analysis in this paper, i.e., the bands from 179 to 214.

3.4.

Allocation of Calibration and Validation Sets

Allocation was done by the random division method, i.e., the dataset was randomly divided into the test set and validation set in the ratio of 11:3, with the validation set being used to verify the accuracy of the constructed model. All 100 tomato plants used in this experiment were examined by spectral analysis and then sent for chemical examination. 21 were used as the validation set and the remaining 79 were used as the test set.

This paper combines GA and SPA with the PLS, SVM, PSO-BP, and RF algorithms and conducts a comparative analysis on different parts of tomatoes (leaves and stems) and different spectral bands (VIS and NIR bands), respectively. Table 2 shows an example with GA-PLS and SPA-PLS. Here, LEAF-NIR represents the average determination coefficient and average root mean square error of the analysis of leaves under NIR, LEAF-VIS represents the average determination coefficient and average root mean square error of the analysis of leaves under VIS light, STEM-NIR represents the average determination coefficient and average root mean square error of the analysis of stems under NIR, and STEM-VIS represents the average determination coefficient and average root mean square error of the analysis of stems under VIS light.

Table 2

Comparison of the accuracy of the GA and SPA spectral selection methods.

To compare the effectiveness of the two spectral selection algorithms, GA and SPA, two spectral prediction models were developed by combining them with PLS regression, respectively, to predict the prediction accuracies of the three enzymes in the VIS and NIR ranges for tomato leaves and stems. The average root mean square error ($\overline{\mathrm{RMSEP}}$) and the average coefficient of determination (${\bar{R}}_p$) for the three enzymes were used as evaluation metrics. The results showed that the validation set’s $\overline{\mathrm{RMSEP}}$ and ${\bar{R}}_p$ of the GA-PLS model for tomato leaves were 1.659 and 0.815 in the NIR and 1.754 and 0.783 in the VIS range, respectively. The validation set’s $\overline{\mathrm{RMSEP}}$ and ${\overline{R}}_p$ for tomato stems in the NIR band were 1.986 and 0.787, respectively, and in the VIS range were 2.113 and 0.711, respectively. By contrast, the validation set of SPA-PLS model for tomato leaves and stems had a higher $\overline{\mathrm{RMSEP}}$ and lower ${\bar{R}}_p$ compared with the GA-PLS model, which indicates that the GA-PLS model has a higher prediction accuracy and stability than the SPA-PLS model.

In summary, two spectrum selection algorithms, GA and SPA, were used and combined with PLS regression to build a spectrum prediction model. The results show that the GA-PLS model is better than the SPA-PLS model, so GA is chosen as the spectrum selection algorithm.

3.5.

Prediction Results

Four prediction models, GA-PLS, GA-SVM, GA-PSO-BP, and GA-RF, were developed to predict the enzyme activities of stems and leaves of the tomato plant in the NIR and VIS wavelengths, respectively.

The average root means square error of the three enzymes and average coefficient of determination for the three enzymes were used as evaluation metrics. The results obtained are presented in Table 3.

Table 3

Comparison of the accuracy of the four prediction models.

To visualize the prediction of tomato enzyme concentration, GA-PLS-LEAF-NIR was used as an example. The statistical analysis of the predicted and chemically detected values is presented in Table 4.

Table 4

Descriptive statistical analysis of the prediction of the three enzymes by the GA-PLS-LEAF-NIR model.

3.6.

Validation of a Predictive Model for Tomato Enzyme Content

The samples not involved in the modeling were randomly selected as the validation set, and the three enzyme contents of 21 samples were predicted by the GA-PLS-LEAF-NIR model. The scatter plots of the predicted and measured values are shown in Fig. 8, where real value represents the chemically detected enzyme activity and predicted value represents the enzyme activity predicted by the GA-PLS-LEAF-NIR model.

Fig. 8

Prediction effect of the validation set of the three enzymes: (a) comparison chart of POD enzyme content validation set data, (b) comparison chart of PAL enzyme content validation set data, and (c) comparison chart of $\alpha$-AMS enzyme content validation set data.

The ${\bar{R}}_p$ of GA-PLS in the NIR leaf model was 0.815 and $\overline{\mathrm{RMSEP}}$ was 1.659, which had good fit and prediction and helped to improve the model accuracy.

To compare the effectiveness of the four prediction models, they were applied to the problem of enzyme content prediction in tomato plants. The results showed that the GA-PLS model has the best prediction effect overall. Moreover, the effect of leaf prediction is better than that of stem for the prediction of enzyme content in tomato plants, and the effect of prediction in the NIR band is better than that in the VIS range. This also indicates that the GA-PLS model has a higher prediction accuracy and stability than the other three models.