2.1. Constructing Datasets

Owing to the lack of datasets documenting plant growth processes, we constructed an RGB image dataset covering the complete growth stages of pak choi. The experiments were conducted in a controlled environmental chamber. To accurately simulate the typical growth conditions of a greenhouse, the environmental parameters of the chamber were regulated according to the settings listed in Table 1.

A camera with a resolution of \(1920 \times 1080\) pixels was used to record the complete growth cycle of the pak choi. As shown in Fig. 1(a), the camera was fixed in the middle position above the incubator, one at the front and one at the back, and the lens was shot at a perpendicular distance of 1.2 m from the target leaves, skewed downward by 45°. The photographing interval was 4 h ⁹.

An image of the pak choi growth process is shown in Fig. 1(b). First, the top view was restored by perspective transformation, and an image was obtained, as shown in Fig. 1(c), which was used to produce the growth stage dataset of pak choi (GS-PC). Based on experimental requirements and the standardized BBCH scale, we categorized the pak choi growth process into three primary stages: germination, seedling, and vigorous growth ^10,11. The germination stage is characterized by a field emergence rate exceeding 10% and the full expansion of cotyledons. The seedling stage was identified by the presence of at least one true leaf, along with a plant height below 7 cm or a total leaf number no greater than nine. Progression into the vigorous growth stage was defined as an average leaf count exceeding nine leaves, accompanied by a marked increase in above-ground dry matter accumulation. This classification scheme provides a clear basis for subsequent quantitative observations and experiments on pak choi growth.

The statistical profiles of the datasets are listed in Table 2. To improve the efficiency of the model training and ensure the accuracy of the training results, the pixel size of the images was uniformly compressed to \(640 \times 640\) pixels.

Owing to the limited and uneven number of collected images of pak choi, as well as the uniform lighting and background, data augmentation processing was performed on the growth images of pak choi to improve model accuracy and robustness. We used a random mixture of techniques such as brightness adjustment (\(\pm10\)%), flipping, angle rotation (\(\pm15{°}\)), and image scaling (up to 15%). The image obtained after data enhancement is shown in Fig. 2. Additionally, the YOLOv5 model utilizes mosaic data enhancement ¹², which splices four input images into a single large mosaic image. This approach can effectively simulate the interrelationships and interactions between the backgrounds of pak choi planting in a real scene.

2.2. Feature Selection

To investigate the relationship between the morphological traits and total fresh weight of pak choi, a series of experiments was designed to collect quantitative measurements of chlorophyll content, maximum leaf length, maximum leaf width, average leaf thickness, and total leaf surface area. Pearson correlation analysis was conducted to evaluate the contribution of each morphological feature to the prediction of total fresh weight, as listed in Table 3.

The results showed strong positive correlations (\(p < 0.01\)) between total fresh weight and maximum leaf length (\(r = 0.898\)), maximum leaf width (\(r = 0.813\)), and leaf surface area (\(r = 0.860\)). In contrast, total fresh weight was not significantly correlated with leaf thickness (\(p > 0.05\)). However, further assessment identified strong multicollinearity among the leaf surface area, maximum leaf length, and maximum leaf width. The simultaneous inclusion of these three variables in a regression model results in severe multicollinearity, compromising the stability and interpretability of the regression coefficients. Consequently, leaf surface area was chosen as a representative morphological variable for subsequent modeling.

Chlorophyll content was incorporated as a key predictor. Although chlorophyll content demonstrated a comparatively weaker correlation with total fresh weight, it served as an indicator of photosynthetic capacity and physiological activity, thereby contributing a distinct functional perspective to biomass estimation. This selection effectively avoids multicollinearity when introducing complementary information. The resulting model, which combines leaf surface area and chlorophyll content, integrates both structural and functional traits, and enhances its stability and physiological relevance for predicting the total fresh weight of pak choi.

3.1. Total Fresh Weight Estimation Model for Pak Choi

This study proposed a quantitative calculation model for the growth status of pak choi, as shown in Fig. 3. A depth camera was used to capture the RGB images and 3D point cloud data of the target scene simultaneously. As a single image contains multiple plants, we used an improved YOLOv5 model based on the ASPP module and Ghost convolution in the first stage to locate individual pak choi plants and identify their growth stages (germination, seedling, and vigorous growth). Based on the localization results, images of individual plants were cropped, as shown in Fig. 1(c). Subsequently, a method based on the HSV color space was used to segment the leaves.

In the second stage, the growth parameters of the pak choi were calculated. Based on the leaf area obtained through segmentation, the corresponding 3D point cloud data, which included the spatial coordinates \((x, y)\) and depth information \(z\), were extracted. After applying SOR filtering to the extracted point cloud, the convex hull algorithm was used to construct a continuous triangular mesh surface from a discrete point cloud. The leaf surface area (\(A_{l}\)) was calculated using the triangular element accumulation method. Simultaneously, the chlorophyll content (\(C_{\mathit{chl}}\)) was predicted from the RGB image of the leaf region using a stacking ensemble model developed for chlorophyll estimation. Considering the issue of leaf occlusion, we added the ratio of image pixels occupied by the leaf surface (\(R_{l}\)) to the independent variables and used multiple linear regression to calculate the total fresh weight of the pak choi.

\(R_{l}\) represents the probability of unidentified leaf presence, derived from the HSV color space-based leaf segmentation. For pak choi at the germination stage (Index1), the ratio was set to 0 due to minimal leaf occlusion. The ratio was calculated based only on the leaf pixel occupancy rate when the growth stage recognition model predicted the seedling (Index2) or vigorous growth (Index3) stages. Let the width of the single pak choi image be \(w\), height be \(h\), and leaf segmentation area region be \(C\). If the growth stage recognition results in \(x\), the formula for the independent variable of the image pixel ratio occupied by the leaf surface is shown in Eq. \(\eqref{eq:Equation1}\).

Finally, we obtained an equation for calculating the total fresh weight of a single pak choi using multivariate linear fitting, as shown in Eq. \(\eqref{eq:Equation2}\).

3.2. Lightweight YOLOv5 Model Based on ASPP Module and Ghost Convolution

Substantial morphological variations during the growth cycle of pak choi, combined with frequent inter-plant occlusion under high-density planting conditions, significantly degrade the detection performance of conventional YOLOv5. Furthermore, the computational constraints of devices in agricultural settings require lightweight architectures for real-time inference. Therefore, this study incorporates Ghost convolutions and ASPP modules into YOLOv5’s Backbone and Neck networks. The proposed modifications enhance multi-scale recognition accuracy while reducing the parameter count and improving computational efficiency ^13,14,15.

The improved YOLOv5 network architecture is shown in Fig. 4(a), and the specific improvements are divided into the following two parts:

1. (1)

   The second C3 module in the Backbone is replaced with the Ghost-ASPP module, as shown in Fig. 4(b). This module first uses GhostConv to reduce the number of channels, and then employs parallel deep separable convolutions with different dilation rates (dilation rates \(=\) 1, 2) to capture local details and global contextual information, respectively. Finally, the spatial features of different scales are fused through concatenation and GhostConv. This module enhanced the robustness of the model, enabling the effective identification of pak choi at different growth stages.

2. (2)

   In the Neck, GhostConv was introduced to replace part of the standard convolution, as shown in Fig. 4(c), which uses linear convolution to reduce the number of model parameters. The Ghost module adopts a dual-path feature generation mechanism. The main path generates a basic feature map through a standard convolution (\(1 \times 1\)), and the number of output channels is compressed to half of the original size. The secondary path applies a \(5 \times 5\) depth-separable convolution to the main path output to generate the remaining channels through an inexpensive linear computation.

3.3. Leaf Segmentation Method Based on HSV Color Space

Leaf image segmentation affects the quality of the subsequent 3D point cloud selection and the accuracy of the total fresh weight calculations. Traditional segmentation methods in the RGB color space are highly susceptible to changes in the light intensity and color temperature ^16,17,18. In natural agricultural settings, the chromatic characteristics of leaves exhibit significant variability owing to fluctuating environmental conditions including illumination changes, weather variations, and heterogeneous soil backgrounds. We propose a lightweight leaf segmentation method based on the HSV color space, which improves segmentation quality and robustness while meeting the real-time requirements of monitoring systems.

A flowchart of the leaf segmentation process image is shown in Fig. 5. First, a bilateral filter is applied to the cropped image to smooth textures and suppress noise, thereby enhancing the subsequent color segmentation. The image is then converted from RGB space to HSV space, and a binary image (mask) is generated by segmenting it according to the green range. The green part is the white pixel and the other colors are black pixels. Next, the segmented binary image is subjected to a closed operation to bridge the narrower discontinuities and fill the breaks in the contour lines making the contours smoother. Subsequently, the processed image was subjected to an open operation to eliminate the white noise and fine parts. Although a more completely segmented image was obtained at this stage, some larger black noise spots remained. Considering the morphological characteristics of pak choi with larger leaves and coarser rhizomes in the late stages of growth, we identified the outline of the plant and filled it internally. Finally, the leaf regions are segmented and isolated from the image.

3.4. Chlorophyll Content Prediction Model with Stacking Ensemble Learning

Based on the methodology of Zhang et al. ¹⁹, six color indices (\(B\), GI, GLA, \(g\), \(g - b\), and CIVE) are extracted from the RGB images of segmented leaf regions and selected as feature variables to estimate chlorophyll content, whose definitions are provided in Eqs. \(\eqref{eq:gi}\) to \(\eqref{eq:cive}\). Among these, the \(B\) channel reflects chlorophyll absorption characteristics in the blue spectrum. The GI and CIVE indices enhanced the distinction between vegetation and background, whereas GLA and \(g\) intensified the leaf greenness from different perspectives. The \(g - b\) index highlights chlorophyll-sensitive responses by leveraging the spectral difference between green and blue bands.

Based on the selected features, a stacking ensemble modeling strategy was implemented. At the first level, three base learners, multiple linear regression (MLR), support vector regression (SVR), and random forest (RF), were employed to generate preliminary predictions of chlorophyll content, capturing both linear and non-linear relationships among the multidimensional vegetation indices. At the second level, ridge regression was utilized as the meta-learner, integrating the base learners’ predictions through regularized linear weighting. This design mitigates multicollinearity among the base predictions, resulting in a more stable and robust model for estimating chlorophyll content in pak choi. The ensemble model achieved a coefficient of determination (\(R^2\)) of 0.713 and a root mean square error (RMSE) of 3.094 on the test set, demonstrating strong predictive performance.

3.5. Leaf Surface Area Computation Based on Triangular Mesh Reconstruction

Common surface area calculation methods include planar projection, voxelization, unstructured point cloud integration, and triangular mesh techniques ^20,21,22. Because of the curling and wrinkling of leaves, which creates uneven structures, we used the triangular meshing method to construct a continuous surface model using the convex hull algorithm. This can help fully retain the topological structural characteristics of the leaves and reduce surface area calculation errors.

The point cloud extracted from the leaf section was filtered using SOR filtering, followed by surface reconstruction using the convex hull algorithm. The pseudocode for triangular mesh generation is provided in Algorithm 1. Tetrahedra were initially constructed as the basic structure of the convex hull, and the remaining point cloud data were then inserted point by point. For each point to be inserted, the half-edge data structure is iteratively updated through visible face detection. After removing all the visible faces from the current convex hull, a new point was connected to the boundary edges of the visible faces to generate new triangular faces, thereby expanding the convex hull shell. The final convex hull was used to calculate the surface area of the leaves.

After completing the triangular meshing, the surface area of the leaves was calculated by summing the areas of all triangular elements. Specifically, for each triangular element \(\triangle ABC_{i}\), we first calculated the two edge vectors based on the coordinates of the three vertices \(A_{i}(x_{i1}, y_{i1}, z_{i1})\), \(B_{i}(x_{i2}, y_{i2}, z_{i2})\), and \(C_{i}(x_{i3}, y_{i3}, z_{i3})\). The area of a single element is then calculated using the formula for the magnitude of the cross product of the vectors \(S_{\triangle ABC_{i}}\), as follows:

Through Eq. \(\eqref{eq:Equation5}\), the total surface area of the leaves was obtained by accumulating the areas of the triangles.

4.1. Evaluation Metrics

This study evaluated the detection results of the improved YOLOv5 model using commonly used target detection evaluation criteria, including precision (P), recall (R), precision–recall curve (PR curve), mean average precision (mAP) for all classes, and the comprehensive evaluation index F1 value. We also evaluated the computational efficiency of the model using frames per second (fps) and related parameters ^23,24.

Precision measures the proportion of correctly predicted positive instances among all model-predicted positives, whereas recall indicates the fraction of actual positives correctly identified by the model. Here, \(\mathit{TP}\) denotes correctly detected bounding boxes with an IoU exceeding a specified threshold, \(\mathit{FP}\) represents incorrect positive predictions, and \(\mathit{FN}\) represents undetected ground-truth instances.

A PR curve can be plotted using recall as the \(x\)-axis and precision as the \(y\)-axis. The area under the PR curve was defined as the AP, which was calculated using interpolation, as shown in Eq. \(\eqref{eq:Equation8}\). Calculate the AP for all categories and calculate the average to obtain the mAP, as shown in Eq. \(\eqref{eq:Equation9}\). Assuming that \(K\) categories exist.

The F1 score is a metric for multi-class classification problems that considers precision and recall as equally important. The formula used is as follows:

The evaluation criteria for the multiple linear regression included model fit, regression significance, residual normality, independence, and variance homogeneity. In this study, we used the coefficient of determination, regression significance test (F-test), and Durbin–Watson test (DW test) to evaluate the fitting effect ^25,26,27,28.

The coefficient of determination \(R^2\) represents the percentage of variation in the dependent variable, which can be explained by the independent variable, and reflects the accuracy of the regression equation fit. Adjusted \(R^2\) is commonly used in multiple linear regression to offset the impact of sample size. The calculation formula is as follows:

The numerator in Eq. \(\eqref{eq:Equation11}\) represents the sum of the squared differences between the predicted and true values, whereas the denominator denotes the sum of the squared differences between the mean and true values. As expressed in Eq. \(\eqref{eq:Equation12}\), \(n\) is the sample size and \(p\) is the number of features. An increasing magnitude of \(R^{2}\mathrm{{\_}adjusted}\) indicates an improved goodness-of-fit for the regression model.

The F-test is a test of the overall significance for regression models that tests whether the combined effect of all explanatory variables on an explained variable is significant. According to the principles of hypothesis testing, the null and alternative hypotheses were as follows:

The DW test was used to test the independence of residuals in the regression analysis. The residuals \(e\) are the differences between the predicted and actual values in the population. The correlation equation for each residual is \(e_{t} = \rho e_{t-1} + v_{t}\), the null hypothesis \(H_0\) is \(\rho = 0\), and the statistical formula is given by Eq. \(\eqref{eq:Equation15}\).

As \(d \approx 2(1-\rho)\), \(d\) closer to 2 indicates better residuals. Generally, \(d\) between 1 and 3 indicates that the regression meets the residual independence test.

4.2. Training Details

In this study, YOLOv5 was used for localization and growth stage identification of pak choi. The hyperparameters and hyperparameter fine-tuning methods that we set during the model training are listed in Table 4. The learning rate is adjusted through LambdaLR, as shown in Fig. 6. The initial learning rate of the bias layer is 0.1 to ensure faster adjustment. Here, we used a warm-up learning strategy in which the learning rate increased linearly from a smaller value to the initial learning rate within the warm-up phase, and then decayed linearly.

This study was conducted on a computing platform equipped with an Intel Xeon Platinum 8352V CPU and an NVIDIA RTX 4090 GPU. The environment was built on Ubuntu 20.04, and PyTorch 1.11.0 was utilized for deep neural network implementation, with the detection environment including CUDA 11.3 and Python 3.8 (see Table 5).

4.3. Analysis of improved YOLOv5

To validate the effectiveness of the model improvements, we conducted ablation experiments on the improved parts and compared the experimental results, as listed in Table 6. The same hyperparameters and preprocessing operations were used in the experiments to ensure methodological rigor and reproducibility.

The ablation experiment results showed that compared with the baseline model YOLOv5s, introducing the Ghost-ASPP module alone resulted in a slight improvement in P (0.9%) and R (0.9%), with the mAP and F1-score increasing by 1.8% and 1.98%, respectively, and a slight improvement in inference speed. This indicates that the Ghost-ASPP module enhances the feature extraction capabilities while reducing the number of computational parameters and improving the computational efficiency. When only the GhostConv module was used to replace standard convolutions, compared to the baseline model, YOLOv5+GhostConv achieved improvements of 3.4%, 2.5%, 3%, and 3.57% in P, R, mAP, and F1-score, respectively, with a slight increase in inference speed to 120.62 fps. The number of parameters is reduced by 300,416, indicating that the GhostConv module effectively reduces the feature map redundancy and improves the detection accuracy.

The joint model combining the Ghost-ASPP and GhostConv modules achieved the best performance, with P, mAP, and F1-score reaching the highest values, representing increases of 5.9%, 3.5%, and 4.66%, respectively, compared to YOLOv5s. It also maintained a high recall rate. Owing to the parallel structure of the Ghost-ASPP module and the inexpensive linear operations of the GhostConv module, the computational load of the model was significantly reduced, achieving a real-time inference speed of 121.54 fps, an increase of 2.31 compared to the baseline model.

It can be observed that there is a synergistic effect between the Ghost-ASPP and GhostConv modules. Ghost-ASPP enhances multi-scale feature representation capabilities, whereas GhostConv optimizes computational efficiency by reducing redundant features. Both improve the accuracy of identifying the growth stages of pak choi while reducing the number of model parameters and improving computational efficiency.

To fully illustrate the applicability of the proposed model, Fig. 7 shows the recognition results of the baseline model YOLOv 5s and the improved model. It can be observed that the improved model has a higher recognition accuracy for pak choi at different growth stages.

4.4. Results from Fitting the Total Fresh Weight Equation

This study conducted fitting experiments using two variables (\(A_{l}\), \(C_{\mathit{chl}}\)) and three variables (\(A_{l}\), \(C_{\mathit{chl}}\), \(R_{l}\)), and the fitting performances are listed in Table 7. The results indicated that incorporating \(R_{l}\) as an additional independent variable improved the overall model fit, reducing the mean relative error to 12.16%. In this case, the coefficient of determination (\(R^2\)) reached 0.790, suggesting that the predictors collectively explained 79% of the variation in total fresh weight, which aligned with our expectations. The DW test result was \(d = 1.742\), which fell between 1 and 3, indicating that the independence of the fitting residuals was satisfied.

The residuals were then tested. As shown in Fig. 8(a), the mean of the standardized residuals is \(\mbox{$-$1.98E-15} \approx 0\), and the standard deviation is 0.96, which is close to 1. The residuals follow a normal distribution, meeting the normality condition for linear regression. The normal probability plot (P-P plot) of the standardized residuals, shown in Fig. 8(b), is approximately a straight line, indicating conformity with a normal distribution. The standardized residual plot shown in Fig. 8(c) indicates that the residual scatter points were distributed around zero, maintaining an approximately symmetrical distribution without significant changes as the predicted values increased. This indicated that the residuals of the linear regression model for total fresh weight of pak choi met the conditions of homoscedasticity and independence.

The results of the analysis of variance showed that when \(\mathrm{F} = 42.601\), \(p < 0.001\). This indicates that at least one independent variable affects the dependent variable, thereby increasing the regression variance and reducing the residual variance; the model passes the overall significance test.

The regression coefficients were calculated, and significance and multicollinearity tests were performed, as listed in Table 8. It can be observed that the independent variables \(A_{l}\) (\(t = 7.648\), \(p < 0.001\)) and \(C_{\mathit{chl}}\) (\(t = 2.394\), \(p = 0.022\)) have statistically significant effects on the total fresh weight of pak choi, which aligns with practical expectations. Although \(R_{l}\) was not statistically significant, its inclusion in the model, as listed in Table 7, contributed to a reduction in the prediction error and an overall improvement in the model performance. This suggests that \(R_{l}\) provides meaningful information for estimating the total fresh weight of pak choi. The collinearity statistics included two indicators: the variance inflation factor (VIF) and tolerance. Table 8 shows that all variables have \(\textrm{VIF} < 10\) (\(\textrm{tolerance} > 0.1\)), indicating no significant multicollinearity among the independent variables. Therefore, the linear regression model was valid.

The final fitted equation for calculating the total fresh weight of pak choi is expressed in Eq. \(\eqref{eq:Equation2}\).