Quantitative Detection of Water Content of Winter Jujubes Based on Spectral Morphological Features

Abstract

The spectral information extracted from hyperspectral images is characterized by redundancy and complexity, while the spectral morphological features extracted from the spectral information help to simplify the data and provide rich information about the material composition. This study is based on using spectral morphological features to quantitatively detect the water content of winter jujubes, and it extends the research scope to the composite effect of spectral morphological features on the basis of previous research. Firstly, a multiple linear regression analysis was carried out on different characteristic bands. Secondly, the multiple regression terms with high significance levels were used as the characteristic variables to be fused with the extracted characteristic wavelength variables for the data fusion. Finally, a partial least squares model was established for the water content of the winter jujubes. The results of the study show that a quantitative relationship can be established between the spectral morphology characteristics and the water content of winter jujubes. The coefficients of determination of the regression equations under the characteristic bands with center wavelengths of 1024 nm, 1146 nm, 1348 nm, and 1405 nm were 0.8449, 0.7944, 0.7479, and 0.9477, respectively. After fusing the spectral morphological features, the partial least squares modeling effects were all improved. The optimal model was the fusion model at a center wavelength of 1146 nm with a correlation coefficient of 0.9942 for the calibration set and 0.8698 for the prediction set. The overall results showed that the wave valley is more reflective of the fruit quality, and the morphological characteristics of the wave valley are more suitable than those of the wave peak for the quantitative detection of the moisture content of winter jujubes.

1. Introduction

The water content of winter jujubes is an important indicator of the taste [1]. Especially after picking fresh winter jujubes, their texture will change, they will gradually lose water, and their internal tissue will become soft. An excessive moisture content may also cause dates to become stickier during transportation, leading to the growth of mold and bacteria, while too low of a moisture content may cause the fruit to dry out. Therefore, it is particularly important to carry out different methods of storage and transportation for winter jujubes with different moisture contents. The traditional method of determining the moisture content of winter jujubes is the drying weight loss method. This method is more accurate, but it is time-consuming and labor-intensive, which cannot meet the requirements of rapid detection. The near-infrared hyperspectral detection of fruit quality has been a new idea in recent years [2,3]. Hongjuan Chang [4] et al. conducted a study on the detection of the soluble solids content of mangos with hyperspectral imaging. They found that the use of the interval variable iterative space contraction algorithm, combined with the back propagation neural network model, can better predict the soluble solids content of mangos. The model had a prediction set coefficient of determination of 0.86 and a prediction set root mean square error of 0.392. Jiaojiao Lin [5] et al. chose Guifei fruit and Tainong No. 1 fruit as the research objects and achieved the non-destructive detection of the fruits’ soluble solids content by using hyperspectral imaging technology. The prediction set coefficient of determination of the established model was 0.88, and the root mean square error of the prediction set was 0.64. P Mishra [6] et al. predicted the moisture content of pears based on near-infrared spectroscopy with variable selection and model updating. They found that model updating using only a small number of new samples reduced the deviation of the moisture content model from 1.31% to 0.19% and the root mean square error of the prediction set from 1.44% to 0.58%. It is thus feasible to establish a correlation between moisture content and hyperspectral features by determining the spectral absorption intensity of the moisture [7,8]. It has the advantage of being real-time and non-destructive compared to traditional methods. The problem of having too many redundant variables in the spectral information extracted using hyperspectral imaging has prompted researchers to continuously optimize the feature wavelength extraction methods and deep learning models. The disadvantage of such methods is that they inevitably lead to the loss of information related to the target component [9,10,11]. For example, when exploring the water content model of jujubes at different polarizations, Datao Lei [12] et al. selected 38 from 254 wavelength variables. They subsequently needed to evaluate the model’s performance through cross-validation and other methods to ensure the adequacy of the wavelength variables.

Spectral morphology features can reflect the absorption and reflection characteristics of the spectra of the samples to be measured, and they contain rich information that can be directly related to the molecular structure and chemical composition of the samples to be measured [13]. Considering the limitations of statistical empirical models, the introduction of spectral morphology features as additional variable information can compensate for the problem of insufficient detection accuracy due to the loss of variables. Dongsheng Wang et al. [14] extracted spectral features using the near-infrared spectra of sandstone. They subsequently used a BP neural net classifier to invert the water content of sandstone; the accuracy of the sandstone water content inversion model established was 90.3% in the training set, and the accuracy of the test set was 83.9%. Haoling Liu et al. [15] proposed a modeling method of apple mildew heart disease discrimination by fusing spectral morphological features. They found that the support vector model established by using the normalized intensity difference and feature spectral fusion to establish the support vector machine model provided the best effect. Its training set accuracy reached 98.1%, and the test set accuracy reached 96.3%. Hongyang Liu et al. [16] established a model for the detection of soluble solids content of jujube by data fusion of spectral morphological features with high correlation and characteristic wavelengths. The prediction set correlation coefficient of the model was 0.9, and the root mean square error of the prediction set was reduced to 0.792%. All of the above studies only considered the individual effects of spectral morphological features on the detection targets, neglecting the compound effects among the different morphological features.

This manuscript takes winter jujubes as the research object and carries out quantitative detection research on the water content of the winter jujubes based on their spectral morphological features. On the basis of the previous research, the research scope is extended to the compound effect of spectral morphological features. The quantitative relationship between the spectral morphological features and the water content is explored through multiple linear regression. The subsequent fusion of spectral morphological features and characteristic wavelengths is compared and analyzed in the water content detection model of winter jujubes. In this way, it provides a certain theoretical basis and reference value for the application of spectral morphological features to the quality detection of winter jujubes and other fruits.

2. Materials and Methods

2.1. Samples and Instruments

The experimental winter jujube samples were all collected on the same day from Alar City, the First Division of Xinjiang Production and Construction Corps (latitude 40°35′10″ N, longitude 81°18′12″ E). The 120 ripe winter jujubes used for the experiment had no obvious differences in shape and size, and there was no damage visible to the naked eye on the surface. The spectra were collected with a lmage-λ-N17E-N3 enhanced near-infrared hyperspectral camera from Sichuan Shuangliu Spectrum Technology Co. (Chengdu, China). The hyperspectral camera operates within a range of 900 to 1750 nm, with 254 wavelength variables and a spectral res-olution of 5 nm at the center. It has a spatial resolution of 320 × 256 and uses a pendulum-sweep mechanism, which re-sults in mirrored images. Spectral calibration was carried out using a HSIA-CT-150∗150 standard white plate manufactured by Sichuan Shuangliu Spectrum Technology Co. The test samples were transferred to the laboratory for water determination immediately after the experiment. The moisture of the samples was determined by using an A2003 electronic balance made by Mettler-Toledo Instruments Co. (Columbus, OH, USA) and a GZX-9140-MBE electric blast drying oven made by Shanghai Boxun Medical and Biological Instruments Co. (Shanghai, China).

2.2. Spectral Acquisition Method

The spectra were collected under clear weather. The winter jujube samples were placed on the experimental frame in order, with the darker side of the winter jujube facing outward to ensure that the shadow would not block the other samples. Two standard whiteboards were placed in different positions for calibration, as shown in Figure 1. The hyperspectral camera was adjusted to the same height as the test frame and placed in front of the test frame at 1.5 m for wiring and debugging. The integration time of the detector element, InGaAs, was 1 ms at this time, the measured outdoor temperature was 21 °C, the air humidity was 55%, and the east wind was level 2. A hyperspectral camera was used to scan the fruits and whiteboards on the test frame. The solar incident zenith angle of 52.51°, the detector detection zenith angle of 91.91°, and the relative azimuth angle of 29.99° were measured during the scanning.

After the spectral acquisition was completed, the spectra were flat-field corrected using the ENVI 5.3 software. The spectral data were extracted using the ENVI software, with the region of interest size of 3 pi × 3 pi selected. The spectra were processed by removing the envelope to highlight the spectral features.

2.3. Spectral Data Processing Methods

Raw spectra will inevitably be affected by external environmental interference and the random noise of the instrument itself. The raw spectra not only contain useful information related to the physical and chemical information of the target but also a substantial amount of noise and redundant information. The data processing of spectra can effectively separate the noise, improve the signal-to-noise ratio, and achieve the purpose of improving the accuracy of the model.

Locally Estimated Scatterplot Smoothing (LOESS), also called Locally Weighted Scatterplot Smoothing (LOWESS), is a non-parametric regression technique. LOESS works by fitting a weighted least squares regression to a subset of the data points around each point to be smoothed, with the weights decreasing as the distance from the point increases. This helps preserve local trends in the data while reducing noise. LOESS is particularly useful for capturing local trends in the data, as it smooths based on the local structure of the dataset rather than imposing a global fit like a polynomial or a moving average. The smoothing window set in this manuscript is 10% of the data points (i.e., 10 points).

First derivative processing (FDP) removes low-frequency background fluctuations (e.g., baseline drift, gradual trend) from the spectrum by calculating the rate of change of the spectrum. FDP enhances the high-frequency detail information and variations in the spectrum, thus making the spectral data clearer and easier to analyze. Figure 2 shows the spectral preprocessing results.

Competitive Adaptive Reweighted Sampling (CARS) focuses on feature selection by retaining the wavelength variables with large absolute values of weights in a partial least squares regression [17]. CARS first calculates the regression weights using partial least squares and then removes wavelengths with lower weights by normalizing the regression weights to select useful information. In order to ensure the stability of the extracted feature variables, the cycle of extracting feature wavelengths is set at 50 times, and the partial least squares method is used to establish a prediction model after each extraction [18,19]. The group with the best prediction effect is selected as the final selected feature variable. Figure 3 shows the use of CARS to extract the characteristic wavelengths of the water content of winter jujubes.

The Variable Importance in Projection (VIP) analysis is a method for assessing the contribution of independent variables (features) to the predictive power of a model. VIP values can help identify which features are the most important for the model interpretation and prediction, and, thus, for the feature selection or interpretation of the model results.

The VIP value measures the importance of each independent variable in the PLS model and is calculated based on the projection weights of the independent variables on the latent variables (LVs). A VIP value >1 indicates that the independent variable is important; a VIP value <1 indicates that the independent variable is likely to be unimportant; and a VIP value of ≈1 indicates that the independent variable needs to be analyzed in conjunction with the other metrics. Figure 4 shows the extraction of characteristic wavelength variables using the VIP analysis. The red dots in the Figure 4 represent the screened significant wavelength variables. The blue points in the Figure 4 represent unimportant wavelength variables.

2.4. Water Content Collection Method

After the spectral acquisition was completed, the samples were immediately transferred to the laboratory for the determination of their water content index to avoid a loss of water that would lead to data distortion. According to the drying and mass reduction method of the national standard (GB/T 5009.3-2016) [20], each winter jujube sample was put into an electric blast drying oven for drying at a temperature of 75 °C for 36 h.

$w={\displaystyle \frac{\left(m_1-m_2\right)}{m_1}}\times 100\%$

In the formula, $\mathrm{w}$ is the moisture content of the sample; ${\mathrm{m}}_1$ is the mass of the sample before drying; and ${\mathrm{m}}_2$ is the mass of the sample after drying.

2.5. Sample Set Partitioning Method

In this study, sample set partitioning based on the joint x–y distance (SPXY) is used to divide the sample set, and the ratio of training set and prediction set is 3:1, as shown in Table 1. In general, the data range of the prediction set of water content is included in the training set, which is helpful in the establishment of the model.

2.6. Model Evaluation Methods

In order to evaluate the performance of the model, the Ratio of Performance to Interquartile Range (RPIQ), R-squared (${\mathrm{R}}^2$), Correlation Coefficient of Calibration (Rc), Root Mean Square Errors of Calibration (RMSEC), Correlation Coefficients of Prediction (Rp), and Root Mean Square Errors of Prediction (RMSEP) were selected to evaluate the accuracy and predictive ability of the model. When RPIQ ≥ 2, the model has good predictive ability; when 1.4 ≤ RPIQ < 2.0, the model can make rough estimations of the samples; and when RPIQ < 1.4, the model is unreliable. The closer the coefficient of determination and the correlation coefficient are to 1, the better the model’s linearity. The smaller the root mean square error, the better the predictive performance of the model.

$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^N{(y_i-\widehat{y})}^2}{{\sum }_{i=1}^N{\left(y_i-\overline{y}\right)}^2}}$

$R={\displaystyle \frac{{\sum }_{i=1}^N\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}{\sqrt{{\sum }_{i=1}^N\left(x_i-\overline{x}\right)}\ast \sqrt{{\sum }_{i=1}^N\left(y_i-\overline{y}\right)}}}$

$RMSE=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{(y_i-\widehat{y})}^2}$

$RPIQ={\displaystyle \frac{IQR}{RMSEP}}$

In the formula, N is the number of samples, $\overline{\mathrm{x}}$ and $\overline{\mathrm{y}}$ are the mean values of the corresponding variables, ${\mathrm{x}}_{\mathrm{i}}$ and ${\mathrm{y}}_{\mathrm{i}}$ are the actual values of the corresponding variables, and $\hat{\mathrm{y}}$ is the predicted value of the corresponding variable. IQR is the interquartile range.

3. Results and Discussion

3.1. Spectral Morphology Feature Extraction

The original hyperspectral curve of the winter jujube is extracted after FDP [21], and its morphological characteristic parameters are illustrated in Figure 5. These parameters are Peak Height, Full Width at Half Maximum, Left Slope, Right Slope, Left Shoulder Width, Right Shoulder Width, and Peak Area, totaling seven morphological characteristic parameters. These seven morphological features are denoted by the letters A, B, C, D, E, F, and G in the following text. Specifically, Peak Height refers to the maximum value at the peak of the spectrum. Peak Area refers to the area of integration of the half-height width with the spectral curve, i.e., the area of the region in the figure where the rectangle intersects the curve. Full Width at Half Maximum refers to the width of the peak at half the height of the peak of the spectrum. Left Slope of the half-height width refers to the spectral slope at the left edge of the half-height width. Right Slope of the half-height width refers to the spectral slope at the right edge of the half-height width. Left Shoulder Width refers to the distance between the left edge (where the first derivative is 0) and the center of the half-height width. Right Shoulder Width refers to the distance between the right edge (where the first derivative is 0) and the center of the half-height width. The spectral morphology characteristics of the wave valley are symmetrical with the wave peak.

From the first derivative curve of the winter jujube spectrum, this manuscript selected four characteristic bands that satisfied the conditions [22], including two wave peaks and two wave valleys. They are labeled, in order, as wave peak R1, wave valley R2, wave peak R3, and wave valley R4, and the specific information regarding the characteristic bands is shown in Table 2.

Among the seven spectral morphology features, there are different magnitudes and thresholds, but this scale difference does not affect the model’s predictions because, in the analysis of linear regression, the data is not calculated by distance or gradient descent. In the modeling of water content detection, characteristic wavelengths and morphological parameters are combined using partial least squares (PLS). An analytical solution is used to solve the coefficients of the linear regression. The data is not normalized, which only affects the computational efficiency [23]. Figure 6 shows the data box lines of the spectral morphology parameters for the different characteristic bands.

3.2. Multiple Linear Regression Modeling of Spectral Morphology Parameters in Different Characteristic Bands

The hyperspectral response to water is mainly due to the absorption characteristics of water. Water has obvious absorption characteristics in a specific wavelength range, so the use of hyperspectral curves can respond to the water content of the fruit, while the spectral morphological features describe the spectral characteristic bands, and the morphological features of different characteristic bands and the water content of the fitted multivariate linear regression equations (MLRs) can be realized to quantitatively detect the water content of the fruit [24,25].

The center wavelengths of the four characteristic bands R1, R2, R3, and R4 are 1024 nm, 1146 nm, 1348 nm, and 1405 nm, respectively, which contain 34, 44, 17, and 46 wavelength variables. The absorption peak of water is subject to deviations due to temperature, instrument accuracy, sample condition, etc. The four selected characteristic center wavelengths are within the reasonable deviation range of the known strong absorption peaks of water (970 nm, 1200 nm, and 1450 nm), so the use of these hyperspectral data can also provide effective information about the water content of winter jujubes. MLR was performed using the spectral morphology characteristics of the winter jujubes and moisture content, and four regression equations were obtained for the different characteristic bands:

$\begin{array}{cc}{Y}_1=& 1.73-0.3604\ast A-0.0078\ast B+0.1734\ast C+0.0206\ast D+0.1186\ast E+0.0342\ast F+0.2767\ast G\hfill \\ & - 1.09\ast AB+0.9084\ast AC+0.1508\ast AD+0.0241\ast AE+0.3102\ast AF+7.63\ast AG\hfill \\ & + 0.2514\ast BC-0.0385\ast BD+0.1467\ast BE+0.1065\ast BF+0.8681\ast BG+0.2112\ast CD\hfill \\ & + 0.0935\ast CE-0.1381\ast CF-0.7491\ast CG+0.3036\ast DE+0.2171\ast DF-0.611\ast DG\hfill \\ & - 0.1088\ast EF+0.1787\ast EG-0.079\ast FG-4.22\ast A^2-1.06\ast B^2+0.0131\ast C^2-0.2602\hfill \\ & \ast D^2+0.0206\ast E^2-0.0692\ast F^2-3.67\ast G^2\hfill \end{array}$

$\begin{array}{cc}{Y}_2=& -10.9-0.0894\ast A+0.2759\ast B-0.7037\ast C+1.2\ast D+0.057\ast E+0.1789\ast F-0.9571\ast G+0.652\hfill \\ & \ast AB-1.12\ast AC-0.3956\ast AD-0.552\ast AE+0.2185\ast AF+0.5726\ast AG-1.61\ast BC\hfill \\ & + 2.08\ast BD+0.2092\ast BE-141.56\ast BF-2.9\ast BG-2.62\ast CD-0.3656\ast CE+0.9215\hfill \\ & \ast CF+3.85\ast CG-0.3905\ast DE-0.3601\ast DF-2.03\ast DG-0.3112\ast EF+0.3796\ast EG\hfill \\ & + 0.2243\ast FG-0.4813\ast A^2+47.69\ast B^2+0.6098\ast C^2+1.6\ast D^2+0.1859\ast E^2+105.71\hfill \\ & \ast F^2+1.41\ast G^2\hfill \end{array}$

$\begin{array}{cc}{Y}_3=& 0.9295-1.04\ast A-0.4272\ast B+1.24\ast C+0.9067\ast D+0.1034\ast E+0.9886\ast G+11.78\ast AC\hfill \\ & + 10.35\ast AD+1.35\ast AE+0.2154\ast AG-0.7939\ast CD-0.0837\ast CE-13.9\ast CG\hfill \\ & - 0.2292\ast DE-11.18\ast DG-1.78\ast EG\hfill \end{array}$

$\begin{array}{cc}{Y}_4=\hfill & 1.51+3.91\ast A+1.18\ast B+1.29\ast C-0.7819\ast D-0.0366\ast E-0.3339\ast F\\ & - 1.76\ast G+2.23\ast AB+1.51\ast AC+1.17\ast AD-0.2918\ast AE\hfill \\ & - 4.27AF-0.3521\ast AG+0.4871\ast BC-0.076\ast BD-1.89\ast BF\hfill \\ & - 2.08\ast BG-0.5448\ast CD-2.03\ast CF-1.38\ast CG+0.4537\ast DF\hfill \\ & - 1.28\ast DG+2.02FG\hfill \end{array}$

In the above equation, ${\mathrm{Y}}_1$ represents the multiple regression equation for band R1. ${\mathrm{Y}}_2$ represents the multiple regression equation for band R2. ${\mathrm{Y}}_3$ represents the multiple regression equation for band R3. ${\mathrm{Y}}_4$ represents the multiple regression equation for band R4. ‘AB’ stands for “A∗B”, as do the other symbols.

The regression polynomials for the water content of the winter jujubes fitted by R1 (1024 nm) and R2 (1146 nm) both consist of 35 terms. The R-squared (${\mathrm{R}}^2$) values for these models are 0.8449 and 0.7944, respectively, with standard deviation (Std. Dev.) values of 0.0175 and 0.0198, coefficient of variation (C.V.) values of 2.61% and 2.94%, and adequate precision (AP) values of 10.5817 and 8.1083. In contrast, the regression polynomial fitted by R3 (1348 nm) has 16 terms, with an ${\mathrm{R}}^2$ of 0.7479, a Std. Dev. of 0.0242, a C.V. of 3.57%, and an AP of 6.3668. The regression polynomial fitted by R4 (1405 nm) has 23 terms, with an ${\mathrm{R}}^2$ of 0.9477, a Std. Dev. of 0.0162, a C.V. of 2.4%, and an AP of 9.2541.

Figure 7 presents the residual normality plots for the different characteristic bands, while Figure 8 compares the actual and predicted values for these bands. Different colored points in the graph represent different sample values. The coefficient of variation (C.V.), defined as the ratio of the standard deviation to the mean, is considered low if C.V. ≤ 10%, indicating the minimal dispersion of spectral morphology features and data points clustered closely around the mean. The adequate precision (AP), the ratio of the effective signal to the noise, is deemed acceptable if it is greater than 4. The AP values for all four bands confirm sufficient signal strength. These results demonstrate that the four multivariate regression equations exhibit strong fitting performances and are capable of accurately predicting the water content of winter jujubes.

An Analysis of Variance (ANOVA) is a statistical method used to compare the means of two or more groups of data. In this study, an ANOVA was employed to evaluate the significant differences between the terms of the different multivariate regression models. The ANOVA results for the four polynomial models are presented in Table 3, Table 4, Table 5 and Table 6. Due to space limitations, only the F-values and p-values are provided in the tables. The F-value represents the ratio of between-group variation to within-group variation and is used to test the significance of differences between groups. The p-value indicates the probability that the observed differences are due to random error. In this analysis, the significance level (α) was set at 0.05, meaning that differences were considered statistically significant when the p-value was less than 0.05.

The ANOVA results reveal that 10 terms in the R1 (1024 nm) polynomial—C, E, AB, AG, BC, BE, BG, DE, $A^2$, and $G^2$—have p-values < 0.05, indicating their significance in the regression model. For the R2 (1146 nm) polynomial, only three terms (CD, CF, and $E^2$) have p-values < 0.1, which are considered “marginally significant”, although the null hypothesis cannot be strictly rejected. In contrast, the R3 (1348 nm) polynomial includes nine terms (A, B, C, AC, AD, AE, CG, DG, and EG) with p-values < 0.01, approaching a highly significant level. Similarly, the R4 (1405 nm) polynomial has nine terms (AB, AC, AD, AG, BC, BG, CF, CG, and DG) with p-values < 0.05, and the BC term has a p-value < 0.01 (0.0035), nearing a highly significant level.

Overall, the R1 (1024 nm), R2 (1146 nm), and R4 (1405 nm) models exhibit significant overall p-values, while the R3 (1348 nm) model has an overall p-value > 0.05, despite most of its terms approaching a highly significant level. This suggests that the polynomial regression may exhibit a high degree of linearity, making coefficient estimation challenging. To address this, the model complexity can be reduced using techniques such as the variance inflation factor (VIF) [26] and stepwise regression [27]. Additionally, increasing the number of test samples in future studies could help comprehensively calibrate the significance levels and regression polynomial coefficients.

3.3. Quantitative Detection of Water Content in Winter Jujubes by Integrating Characteristic Wavelength and Spectral Morphological Features

To further analyze the impact of the spectral morphological features on modeling the water content of winter jujubes, the highly significant multiple regression terms from different characteristic bands were extracted and fused with the feature wavelength data obtained through CARS. PLS models were then constructed to enhance the models’ robustness and detection accuracy. The highly significant multiple regression terms indicate a statistically significant influence on the water content of winter jujubes. Therefore, incorporating these terms as features in the PLS model can improve its explanatory power and prediction accuracy [28,29]. This approach is particularly beneficial when the original feature dimensions are high, as selecting highly significant terms can reduce redundancy and enhance the training efficiency of the PLS model. The specific details of the highly significant multiple regression terms are provided in Table 7.

The spectral characteristic wavelengths were extracted using CARS. As shown in Figure 5, as the number of iterations increased, the interactive validation root mean square error reached the minimum at the 14th iteration, and 70 feature wavelength variable data were finally selected.

The correlation coefficient, root mean square error, and residual value were used as evaluation indexes to compare the model performance differences of the water content of winter jujubes under different modeling data. The manuscript is modeled using the full spectrum, the full spectrum after FDP, and the VIP values as well, and this is done to increase the contrast. In this study, cross-validation was used to optimize the PLS model. A 10-fold cross-validation was performed with the maximum number of principal components set to 30. The optimal number of latent variables for the models was determined to be 9, 16, 5, 25, 27, 28, 29, and 27, respectively. The comparison results are shown in Table 8, and Figure 9 shows the scatter plot of the water content of winter jujubes fused with the spectral morphological features by CARS.

As shown in Table 8, the modeling performance using CARS improved after integrating the spectral morphological features. For the model incorporating R1 (1024 nm), the Rc increased from 0.9892 to 0.9927, and the RMSEC decreased from 0.4994% to 0.409%. The model incorporating R2 (1146 nm) exhibited the best performance, with the Rc improving to 0.9942, the Rp increasing to 0.8698, and the RPIQ rising to 3.0515. For the model incorporating R3 (1348 nm), the performance improvement was primarily observed in the calibration set, while its effect on the prediction set was moderate, with an RPIQ of only 1.9279, below the threshold for excellent models. The model incorporating R4 (1405 nm) also showed better performance, with the Rc increasing by 0.0012, the Rp improving by 0.0047, the RMSEC decreasing to 0.4637%, and the RPIQ rising to 2.4089.

Overall, the models incorporating the two valley morphological features performed better. This is because the data distribution in the valley region is smoother, with less noise and lower feature correlations, enabling the PLS model to extract latent variables more effectively and improve modeling accuracy. In contrast, the peak region may contain more outliers or noise [30] and exhibit stronger feature correlations, making it challenging for the PLS model to extract useful information, thereby affecting the model’s predictive performance.

4. Conclusions

To investigate the influence of the spectral morphological features on the modeling of water content in winter jujubes, this study first performed smoothing and first derivative preprocessing on the hyperspectral data of the winter jujubes. Based on this, the spectral morphological features of different bands were extracted and subjected to multiple linear regression with the water content of the winter jujubes to establish the quantitative detection regression equations. Subsequently, considering the combined effects of the spectral morphological features, all highly significant multiple regression terms from each characteristic band were used as feature variables and fused with the feature wavelength variables extracted using the CARS algorithm. The PLS models for the winter jujubes’ water content were then constructed for comparative analysis. The specific conclusions are as follows:

(1) Spectral morphological characteristics can establish a quantitative relationship with the water content of winter jujubes. In this study, multiple linear regression fitting was performed using R1 (1024 nm), R2 (1146 nm), R3 (1348 nm), and R4 (1405 nm). The R² values for the regression equations were 0.8449, 0.7944, 0.7479, and 0.9477, respectively. The overall model evaluation indicated that all models, except for R3 (1348 nm), were statistically significant. Specifically, the p-value for R3 (1348 nm) was 0.058, which is close to the significance level, while the other three models demonstrated significant results.

(2) The integration of spectral morphological features as feature variables with feature wavelength data to construct a water content PLS model significantly enhanced the accuracy of the detection model. Notably, the fusion of the R2 (1146 nm) model demonstrated exceptional performance, achieving the Rc of 0.9942, the Rp of 0.8698, the RMSEC of 0.3594%, the RMSEP of 1.3352%, and the RPIQ of 3.0515. This model effectively enables the non-destructive testing of water content in winter jujubes.

(3) Whether using multiple linear regression analysis or partial least squares regression analysis, the spectral morphological features of the valley demonstrated a strong performance in the quantitative detection of water content in winter jujubes. This indicates that spectral morphological features can be effectively utilized for water content detection in winter jujubes, with the valley features exhibiting a particularly stable and reliable performance. This also supports the fact that the wave valley correlates with the fruit quality.

This study focused on the quantitative detection of water content in winter jujubes. While achieving certain results, it also has some limitations:

(1) Detection Model: There is a nonlinear relationship between the quality of winter jujubes and their spectral data. However, the study only constructed PLS detection models. Future research should explore other models more suitable for describing nonlinear relationships, such as support vector machines (SVMs), random forests, and neural networks, to further improve the accuracy of winter jujube quality detection.

(2) Experimental Conditions: The spectral data were collected only during a specific period, without considering the impact of environmental factors such as weather and time on the spectral data. Additionally, the samples were limited to winter jujubes from Alar City, Xinjiang, resulting in a relatively narrow source of samples. The stability and generalizability of the model need improvement. Future experiments should involve changing the background materials, performing a background correction, and optimizing the experimental design to reduce external interference and enhance model accuracy.

Author Contributions

Conceptualization, Y.D., H.L. (Huaping Luo) and H.L. (Hongyang Liu); Methodology, Y.D., H.L. (Huaping Luo) and H.L. (Hongyang Liu); Software, Y.D. and H.L. (Hongyang Liu); Validation, Y.D., H.L. (Huaiyu Liu), L.K. and Y.T.; Investigation, H.L. (Huaiyu Liu), L.K. and Y.T.; Data curation, Y.D.; Writing—original draft, Y.D.; Writing—review & editing, Y.D.; Supervision, H.L. (Huaping Luo); Project administration, H.L. (Huaping Luo); Funding acquisition, H.L. (Huaping Luo). All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data will be made available on request.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this manuscript.

Footnotes

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Figures and Tables

Figure 1. Outdoor sample placement.

Figure 2. Spectral preprocessing results. (a) Original NIR hyperspectral curve; (b) NIR hyperspectral curve after LOESS; (c) NIR hyperspectral curve after FDP.

Figure 3. CARS selected characteristic wavelengths of water content of winter jujubes.

Figure 4. VIP analysis of extracted characteristic wavelength variables.

Figure 5. Schematic diagram of spectral morphology feature extraction.

Figure 6. Box plots of spectral morphological features in different bands. (a) Box plot of morphology features for band R1; (b) box plot of morphology features for band R2; (c) box plot of morphology features for band R3; (d) box plot of morphology features for band R4.

Figure 7. Normal plots of residuals for different characteristic bands. (a) Normal plot of residuals for R1; (b) normal plot of residuals for R2; (c) normal plot of residuals for R3; (d) normal plot of residuals for R4.

Figure 8. Plots of actual vs. predicted for different characteristic bands. (a) Plot of actual vs. predicted for R1; (b) plot of actual vs. predicted for R2; (c) plot of actual vs. predicted for R3; (d) plot of actual vs. predicted for R4.

Figure 9. Scatter plots of water content of winter jujubes with CARS fusion spectral morphological features. (a) Scatter plot of CARS fusion R1; (b) scatter plot of CARS fusion R2; (c) scatter plot of CARS fusion R3; (d) scatter plot of CARS fusion R4.

Table 1

Results of calibration set and prediction set division of winter jujube samples.

Index	Sample Set	Data Range	Average Value	Interquartile Range	Standard Deviation	Coefficient of Variation
Water content (%)	calibration set	59.32–75.35	67.28	4.5211	3.43	5.10
	prediction set	61.98–70.72	66.50	2.9871	2.21	3.31

Table 2

Results of characteristic band extraction.

Characteristic Band	Central Wavelength /nm	Band Range/nm	Wavelength Ordinal Number
wave peak R1	1024	980–1085	24–57
wave valley R2	1146	1069–1208	52–95
wave peak R3	1348	1321–1375	129–145
wave valley R4	1405	1368–1522	143–188

Table 3

Multiple linear regression ANOVA table for R1.

Source	F-Value	p-Value	Source	F-Value	p-Value	Source	F-Value	p-Value
Model	3.74	0.0006	AF	0.7411	0.3978	DF	2.19	0.1519
A-A	2.81	0.1065	AG	6.05	0.0215	DG	0.8585	0.3634
B-B	0.0168	0.8980	BC	7.28	0.0126	EF	3.71	0.0660
C-C	6.85	0.0151	BD	0.0804	0.7792	EG	0.5801	0.4537
D-D	0.0586	0.8108	BE	4.43	0.0459	FG	0.0559	0.8151
E-E	4.41	0.0465	BF	2.56	0.1229	A 2	6.86	0.0150
F-F	0.6496	0.4282	BG	6.48	0.0177	B 2	0.0688	0.7954
G-G	1.90	0.1807	CD	1.58	0.2206	C 2	0.0565	0.8142
AB	8.97	0.0063	CE	1.24	0.2757	D 2	2.97	0.0979
AC	2.76	0.1095	CF	3.29	0.0822	E 2	0.5661	0.4591
AD	0.0420	0.8394	CG	2.13	0.1572	F 2	2.17	0.1541
AE	0.0073	0.9328	DE	6.22	0.0199	G 2	5.91	0.0229

Table 4

Multiple linear regression ANOVA table for R2.

Source	F-Value	p-Value	Source	F-Value	p-Value	Source	F-Value	p-Value
Model	2.76	0.005	AF	0.1643	0.6887	DF	1.51	0.2308
A-A	0.0512	0.8229	AG	0.0708	0.7923	DG	0.4112	0.5272
B-B	0.1863	0.6697	BC	2.17	0.1532	EF	0.6418	0.4306
C-C	2.77	0.1085	BD	1.23	0.2786	EG	0.2282	0.637
D-D	2.56	0.1219	BE	0.1933	0.664	FG	0.087	0.7705
E-E	0.1937	0.6636	BF	1.56	0.2238	A 2	0.5733	0.456
F-F	0.3143	0.58	BG	0.8136	0.3757	B 2	1.62	0.2142
G-G	1.14	0.295	CD	3.19	0.0862	C 2	2.52	0.1247
AB	0.2983	0.5898	CE	0.8306	0.3708	D 2	1.54	0.2256
AC	0.999	0.3271	CF	3.3	0.0815	E 2	3.16	0.0878
AD	0.129	0.7225	CG	2.12	0.1576	F 2	1.54	0.2255
AE	1.55	0.225	DE	0.8024	0.3789	G 2	0.2763	0.6037

Table 5

Multiple linear regression ANOVA table for R3.

Source	F-Value	p-Value	Source	F-Value	p-Value	Source	F-Value	p-Value
Model	2.41	0.058	G-G	8.3	0.0129	CE	0.4122	0.532
A-A	13.18	0.0031	AC	15.91	0.0015	CG	19.35	0.0007
B-B	12.8	0.0034	AD	15.9	0.0015	DE	6.9	0.0209
C-C	11.82	0.0044	AE	12.86	0.0033	DG	13.17	0.0031
D-D	8.84	0.0108	AG	0.127	0.7273	EG	15.29	0.0018
E-E	4.55	0.0525	CD	2.18	0.1634

Table 6

Multiple linear regression ANOVA table for R4.

Source	F-Value	p-Value	Source	F-Value	p-Value	Source	F-Value	p-Value
Model	4.73	0.0306	AB	13.03	0.0112	BF	1.15	0.3253
A-A	0.5155	0.4998	AC	11.3	0.0152	BG	12.72	0.0118
B-B	0.8232	0.3992	AD	10.82	0.0166	CD	1.34	0.2913
C-C	2.94	0.1371	AE	2.16	0.1924	CF	4.03	0.0916
D-D	0.2345	0.6454	AF	0.3897	0.5554	CG	9.46	0.0218
E-E	0.1124	0.7488	AG	9.65	0.021	DF	0.0393	0.8494
F-F	0.1127	0.7486	BC	21.54	0.0035	DG	12.36	0.0126
G-G	0.1385	0.7226	BD	0.1049	0.7571	FG	0.1109	0.7504

Table 7

Statistics of highly significant multiple regression terms in different characteristic bands.

Characteristic Band	Highly Significant Multiple Regression Terms	Number of Variables
R1	C, E, AB, AG, BC, BE, BG, DE, $A^2, G^2$	10
R2	CD, CF, $E^2$	3
R3	A, B, C, D, G, AC, AD, AE, CG, DE, DG, EG	12
R4	AB, AC, AD, AG, BC, BG, CF, CG, DG	9

Table 8

PLS model results of water content of winter jujubes with different modeling data.

Selection of Variables	Number of Variables	Calibration Set		Prediction Set
		Rc	RMSEC	Rp	RMSEP	RPIQ
Full	254	0.9079	1.4195	0.7909	1.2443	2.4006
FDP	254	0.9660	0.8589	0.7414	1.9451	2.0461
VIP	63	0.7856	2.0939	0.5659	2.0210	1.7493
CARS	70	0.9892	0.4994	0.8534	1.2187	2.3837
CARS + R1	80	0.9927	0.4090	0.8023	1.4333	2.5446
CARS + R2	73	0.9942	0.3594	0.8698	1.3352	3.0515
CARS + R3	82	0.9943	0.3640	0.7518	1.6859	1.9279
CARS + R4	79	0.9904	0.4637	0.8581	1.2964	2.4089

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