Potato trials were conducted at the National Precision Agriculture Experimental Base in Changping District, Beijing, China ( Figure 1 ). Two early-maturing potato varieties, Zhongshu 3 (Z3) and Zhongshu 5 (Z5), were planted. To increase the spatial variability of LAI, three treatments were performed, including different planting densities, nitrogen gradients, and potassium gradients. Planting density was categorized into three levels: 60,000 (P1), 72,000 (P2), and 84,000 (P3) tubers/hm². Nitrogen treatments were categorized into four levels: 0 (N0), 112.5 (N1), 225 (N2), and 337.5 (N3) kg/hm² of pure nitrogen. Potash treatments were categorized into three levels: 0 (K0), 495 (K1, applied to the planting density and nitrogen test areas), and 990 (K2) kg/hm² of K₂O. In this experiment, each plot size of 32.5 m² was applied with 90 kg/hm2 P2O5 and each treatment was replicated three times, totalling 48 plots. Field management practices, including weeding, fertilization, and irrigation, were consistent with local agricultural conditions. To calibrate the UAV hyperspectral images acquired during the study, 11 ground control points were evenly distributed around the experimental field. The spatial locations of these points were determined using the Qianxun SR2 high-precision RTK measurement system.

In 2019, UAV hyperspectral images were acquired during three critical stages of potato development: tuber formation (28 May), tuber growth (10 June), and starch accumulation (20 June). These stages correspond to BBCH codes 41, 44, and 47 (referred to as BBCH41, BBCH44, and BBCH47), respectively. The images were captured using an M600 UAV (SZ DJI Technology Co., Ltd., Shenzhen, China) equipped with a UHD 185-Firefly imaging spectrometer (Cubert GmbH, Ulm, Germany). The UHD185 has 125 spectral channels covering a wavelength range of 450–950 nm, with a sampling interval of 4 nm. The UAV followed identical flight paths across all three growth stages, maintaining consistent take-off positions. The image acquisition was conducted under clear, cloudless, and windless conditions, between 11:30 am and 13:30 pm, when direct sunlight reached the ground. Flights were carried out at an altitude of 20 meters, resulting in a spatial resolution of 1.43 cm, with a flight speed of 1.5 m/s. To facilitate the efficient stitching of orthophotos, the heading and sidelap overlaps were manually set to 85% and 93%, respectively. Given the small size of the field, each hyperspectral image acquisition took approximately 12 minutes. Before each take-off, dark current and radiometric calibration were performed on the ground using a black-and-white calibration plate.

The processing of UAV hyperspectral images involves several key steps: panchromatic image stitching, fusion of panchromatic and hyperspectral images, and extraction of canopy spectral reflectance. First, Agisoft PhotoScan software (Agisoft LLC, St. Petersburg, Russia) was used to correct the topography of the panchromatic images by integrating the positional data from the ground control points. Next, the panchromatic images were mosaicked using the structure-from-motion algorithm, and orthophotos of the test field were generated. The panchromatic orthophoto was then fused with the hyperspectral image using Cube-Pilot software (Cubert GmbH, Ulm, Germany) to create a new hyperspectral image. Finally, the average spectral reflectance of the potato canopy was extracted from the vector files of the 48 plots using ENVI software, and this data was used for subsequent analysis.

To obtain LAI data, three uniformly growing plants were destructively sampled at each growth stage of tuber formation, tuber growth, and starch accumulation. Plants were transported quickly to the laboratory to prevent water loss leading to leaf curling. After manual separation of the stems and leaves, 60 leaf discs were punched out with a 0.8 cm diameter punch and their wet weights were measured using a high-precision balance (W1). The remaining leaves of the three plants were also measured for their wet weight (W2). Finally, the LAI of each plot was calculated using the weight ratio and planting density. The formula for LAI was as follows:

Where WI and W2 were the wet weight of 60 leaf discs and the remaining leaves of three plants respectively. S was the area of leaf discs. M was the number of potato plants per unit area.

The spectral information extracted from UAV hyperspectral images in this study primarily includes canopy original spectral reflectance (OSR), first-order differential spectral reflectance (FDSR), and vegetation indices (VIs). Additionally, simple, advanced, and higher-order texture features were derived using Haralick texture extraction methods.

The optimal combination of variables for estimating LAI was determined using the SPA. SPA is a forward variable selection algorithm based on the projection analysis of vectors (Sun et al., 2019). Initially, a set of vectors is randomly selected as the starting variables. These vectors are then projected onto the unselected vectors, and the magnitudes of the projected vectors are compared. The variable with the largest projected vector is selected, and this process is repeated through several iterations. Ultimately, the optimal combination of variables is chosen based on the minimum root mean square error (RMSE) of cross-validation.

Partial Least Squares Regression (PLSR) is a statistical method used to develop a linear regression model by projecting independent and dependent variables into a new space. This method involves both the extraction of principal components from the independent and dependent variables and the maximization of the correlation between these components during the regression modeling process (Tao et al., 2020). Random Forest Regression (RFR) is a machine learning technique that integrates a large number of decision trees (Yue et al., 2018). The accuracy of the RFR model is primarily influenced by the number of decision trees (ntree) and the number of nodes (mtry), with mtry typically set to one-third of the input variables and ntree set to 500. Gaussian Process Regression (GPR) is a method based on Bayes’ theorem that models the relationship between dependent and independent variables using a kernel function (Liu et al., 2022b). Compared to other popular machine learning methods, GPR models are simpler to optimize and particularly suitable for training on small sample datasets. In this study, MATLAB software was used for training and validating LAI models with the aforementioned machine learning methods. A total of 96 samples (replicates 2 and 3 for each growth stage) were used for model training, while 48 samples (replicate 1 for each growth stage) were reserved for model validation.

Our flowchart from different types of spectral and texture extraction to model construction and evaluation in this study is shown in Figure 2 .

The coefficient of determination (R²), root mean square error (RMSE), and normalized root mean square error (NRMSE) were used to evaluate the accuracy of the models. The corresponding equations are shown in Equations 3–5:

Where x i is the measured potato LAI; y i is the estimated potato LAI; y ¯ is the mean value of the measured potato LAI; n is the number of samples.

In the field experiment, LAI values of potato at each growth stage in 48 experimental plots were determined. A total of 144 LAI samples were obtained at three growth stages of potato in 2019. The box line plot of potato LAI is shown in Figure 3 . With the dynamic change of potato growth stage, the mean LAI value first decreased and then levelled off. During the tuber formation stage, the LAI ranged from 0.43 to 3.29, with an average of 1.50. During the tuber growth stage, the LAI ranged from 0.34 to 3.00, with an average of 1.32. During the starch accumulation stage, the LAI varied from 0.29 to 3.75, with an average of 1.28.

The correlation coefficients between different types of characterization variables and the LAI of potatoes across multiple growth stages are presented in Figures 4 , 5 . LAI exhibited a highly significant correlation with OSR in the wavelength ranges of 454–702 nm and 718–950 nm (p< 0.01), with a particularly strong correlation observed at 750–922 nm ( Figure 4A ). The correlation between LAI and FDSR showed greater variability after the first-order derivation of OSR, with highly significant correlations occurring at 454–506 nm, 550–642 nm, 690–774 nm, and 790–950 nm (p< 0.01). The highest correlation between LAI and FDSR was noted at 734–758 nm ( Figure 4B ). The VIs selected in this study also demonstrated highly significant correlations with LAI across multiple growth stages of potatoes ( Figure 5A ). Additionally, the extracted Haralick textures, including Inverse Difference Moment, Cluster Shade, Haralick Correlation, Mean, Sum Average, Low Grey-Level Run Emphasis, Short Run High Grey-Level Emphasis, and Long Run Low Grey-Level Emphasis, showed highly significant correlations with LAI ( Figure 5B ).

The variables with the highest correlation to LAI across multiple growth stages of potatoes were 886 nm for OSR (r = 0.55, p< 0.01), 742 nm for FDSR (r = 0.67, p< 0.01), NDRE for VIs (r = 0.65, p< 0.01), and the Mean for Haralick texture (r = -0.50, p< 0.01). The mean absolute correlation coefficients of OSR (450–950 nm), FDSR (450–950 nm), VIs, and Haralick texture features with LAI were 0.48, 0.35, 0.53, and 0.17, respectively. These results suggest that VIs may better capture the spatial variability of potato LAI, whereas Haralick texture features may be less effective.

The results of filtering five feature datasets using the SPA method are presented in Table 3 , including OSR, FDSR, VIs, Haralick textures, and their combined features. From a total of 125 OSR features, 125 FDSR features, 30 VIs, 28 textures, and 308 combined features, 10, 7, 8, 10, and 17 features were selected, respectively. This selection indicates that the unselected features were either uninformative or contained redundant information for estimating LAI across multiple growth stages of potatoes.

Although the selected wavelengths for LAI estimation using OSR and FDSR differ, they share a common characteristic: these wavelengths span the visible to near-infrared regions and exhibit a high correlation with LAI. Typically, VIs containing near-infrared or red-edge wavelengths are chosen for LAI estimation. Three features were selected from simple textures, five from advanced textures, and two from higher-order textures; however, not all of these features achieved a high correlation with LAI. For instance, features such as Inertia, Sum of squares: variance, Difference entropy, and Information measures of correlation IC1 did not fully reach the highly significant correlation level with LAI. This suggests that the SPA method helps to prevent the omission of features that significantly contribute to LAI estimation. In total, four OSR, seven FDSR, three VIs, and three textures were selected from the combined features, all of which remained highly sensitive to LAI, except for Inertia, which did not achieve a highly significant correlation. These findings indicate that the integration of different types of features is crucial for accurately estimating LAI across multiple growth stages in potatoes.

The calibration and validation results obtained using PLSR, RFR, and GPR based on the variables screened in Table 3 are presented in Figure 6 . X1, X2, X3, X4 and X5 in Figure 6 represent OSR, FDSR, VIs, Haralick textures and All. Among the models, the LAI estimation model constructed using the GPR method demonstrated higher fitting accuracy and lower error compared to the others. When using the same regression method, LAI estimation based on different types of spectral information was more accurate than that based on Haralick texture features, with the best results achieved using the GPR method with VIs (Calibration: R² = 0.63, RMSE = 0.41, NRMSE = 31.32%; Validation: R² = 0.63, RMSE = 0.34, NRMSE = 22.84%). Although using Haralick texture features alone to estimate LAI across multiple growth stages of potatoes is not ideal, combining texture features with different forms of spectral information can enhance the accuracy of LAI estimation, suggesting that Haralick texture can compensate for the limitations of spectral information. Compared to the PLSR and RFR methods, the GPR method was the most accurate for estimating multi-stage LAI in potatoes using 17 features that included both spectral and texture information (Calibration: R² = 0.68, RMSE = 0.38, NRMSE = 29.04%; Validation: R² = 0.70, RMSE = 0.30, NRMSE = 20.28%).

The fitted relationship between the estimated and measured LAI values of potatoes across multiple growth stages, obtained using the best regression method based on four types of spectral information, one type of texture, and a combination of spectral and texture features, is illustrated in Figure 7 . The results indicate the following: (1) Estimating LAI using only spectral information or Haralick textures yields significant errors, particularly with Haralick textures, leading to low model accuracy (R² = 0.45, RMSE = 0.41, NRMSE = 27.60%). (2) Among the spectral information, VIs demonstrated the best estimation performance (R² = 0.63, RMSE = 0.34, NRMSE = 22.84%). (3) The combination of spectral information and texture features reduced the error in LAI estimation across multiple growth stages and enhanced the accuracy of the model. Notably, when LAI was greater than 2, the estimates based on the fused sensitive features were closer to the 1:1 line with the measured values (R² = 0.70, RMSE = 0.30, NRMSE = 20.28%), suggesting that integrating multiple types of features can mitigate the inaccuracies associated with using a single type of feature for LAI estimation.

The study combines three types of spectra and Haralick textures with the GPR machine learning method to estimate LAI in two potato varieties. Figure 8 illustrates the effect of this estimation to assess the model’s applicability across different growth stages. The results showed that the performance of the method proposed in this study differed significantly in the estimation of LAI for the three growth stages, as evidenced by the poorer performance of the model in terms of accuracy in tuber growth ( Figure 8B ). This is due to the high canopy cover of potato in tuber growth compared to the other two growth stages. Spectral information saturation is more severe and textural information contribution is reduced. In contrast, the accuracy of the model was satisfactory in all three growth stages, although it still varied, so the method of combining different types of spectral information with Haralick textures still has potential for predicting potato LAI in different growth stages.

The optimal estimation model of potato LAI for multiple growth stages was constructed based on the three spectral information and Haralick textures, and the model was used to generate the spatial distribution map of potato LAI in the study area, as shown in Figure 9 . This method helps to provide a more comprehensive understanding of the growth conditions and spatial distribution pattern in the study area. Analyzing LAI spatial distribution maps aids in assessing plant water use efficiency, optimizing irrigation and fertilizer strategies, and enhancing overall water and fertilizer efficiency. Additionally, it supports early detection of pests and diseases, minimizing yield loss, and serves as a preliminary tool for predicting crop yields, ultimately improving agricultural production and management.

The spectral reflectance of the potato canopy reflects the crop’s physiological and geometrical characteristics, while VIs enhance the contrast between crop and soil, allowing for the quantitative description of crop growth. This spectral information is frequently used to estimate crop growth parameters such as LAI (Kayad et al., 2022). The three types of spectra used in this study varied significantly in their sensitivity to LAI across multiple growth stages of potatoes ( Figures 4A , B , 5A ). After differential transformation, FDSR reduced the effects of soil background and overlapping signal interference compared to OSR, thereby enhancing the sensitivity of spectral signals to LAI across different growth stages ( Figures 4A, B ). This finding is consistent with the results obtained by Zhang et al. (2022a) using differentially transformed spectra to estimate the LAI of rice. The VIs selected in this study exhibited higher sensitivity to LAI across multiple growth stages than OSR and FDSR. This increased sensitivity is due to the combination of multiple bands, which can mitigate the interference of external environmental signals on LAI response ( Figure 5A ). However, previous studies by Liu et al. (2022a) and Shi et al. (2022) have shown that the sensitivity of VIs to LAI across different growth stages can be affected by climatic variations and varietal differences, potentially limiting the accuracy of LAI estimation models. Spatial information such as texture of high-resolution UAV remote sensing data correlates with the spatial structure of the crop, reflecting more effectively the shading and internal structural information of the crop canopy. Given the importance of texture information in describing changes in canopy structure, this study attempted to use Haralick texture features to estimate LAI. The application of Haralick texture in the estimation of crop physicochemical parameters has not been extensively investigated. It remains unclear whether the sensitive bands of texture features align with the spectral bands. To address this, we employed the PCA downscaling method, which preserves the majority (>90%) of the image information and offers a robust foundation for subsequent studies. However, compared to canopy spectral information, the simple, advanced, and higher order textures did not effectively capture changes in LAI across multiple growth stages due to the low sensitivity of Haralick texture to potato LAI ( Figure 5B ), which is similar to the previous work of Qiao et al. (2024). The extraction of texture features from an image is often affected by a variety of factors, such as noise in the image and changes in lighting conditions, which may interfere with the stability of the texture features. This limitation may be related to the size of the window used for texture extraction and the calculation method employed. Consequently, we conclude that Haralick texture alone does not adequately reflect changes in LAI across multiple growth stages of potatoes.

To reduce the number of input parameters for the LAI estimation model and minimize errors due to subjective variable selection, the feature variables obtained using the SPA algorithm are presented in Table 3 . For both OSR and FDSR, the characteristic wavelengths identified after SPA screening, although not identical, fall within the visible to near-infrared regions. Since LAI is determined by plant leaves, and the absorption and reflection of pigments within these leaves, along with scattering between leaf tissues, influence the crop canopy spectra across the visible to near-infrared ranges, the differences in the sensitive spectral positions of various transformed spectral data and LAI are expected to be minimal (Zhou et al., 2022). The eight VIs selected through screening all include red-edge or near-infrared wavelengths, as these spectral regions are more responsive to changes in LAI ( Figures 2A, B ), a finding consistent with studies by Tao et al. (2020) and Liu et al. (2022a) in monitoring winter wheat LAI. The fact that not all of the 10 variables selected from the 28 Haralick textures achieved a highly significant correlation with potato LAI suggests that the variables identified by the SPA algorithm are objectively determined, allowing for the retention of those that significantly contribute to LAI estimation and thereby avoiding the large estimation errors that can result from subjective variable selection. To evaluate the performance of combining spectral and texture information for LAI estimation, four OSR, seven FDSR, three VIs, and three textures were selected from 308 combined features, underscoring the importance of feature fusion in accurately estimating LAI in potatoes across multiple growth stages ( Table 3 ).

Compared to traditional algorithms, machine learning regression models can make effective use of data when dealing with complex data and obtain higher model prediction accuracy. The modeling and validation results obtained using the GPR method for the variables identified in Table 3 were superior to those achieved with the PLSR and RFR methods. This finding aligns with the results reported by Caballero et al. (2022) for estimating LAI in winter wheat. The superior performance of GPR may be attributed to its ability to effectively handle nonlinear relationships between independent and dependent variables, as well as its suitability for small sample datasets (Upreti et al., 2019; Zhang et al., 2022b). In this study, the modeling and validation datasets were small, and the spectral and texture information extracted from UAV hyperspectral imagery likely exhibited a stronger nonlinear relationship with LAI, making GPR a fitting choice for constructing the LAI estimation model. Analyzing the results in Table 3 , the accuracy of LAI estimation across multiple growth stages of potatoes was higher when using the three forms of spectral information compared to Haralick texture alone. This is consistent with the findings of Zhang et al. (2022b) in estimating LAI for maize, where the grey-scale covariance matrix texture was less effective than crop canopy spectral information. Among the spectral information types, the order of performance in estimating LAI was VIs, FDSR, and OSR, which corresponds to the sensitivity of these spectral types to LAI ( Figures 4A , B , 5A ). Although Haralick texture alone was not effective for estimating potato LAI ( Table 3 , Figure 3 ), combining it with crop canopy spectral features improved the accuracy of LAI estimation, consistent with Zhou et al (Zhou et al., 2022), who combined wavelet texture with spectral features for estimating rice LAI. Further illustrating that different types of feature coupling provide unique and complementary information with great potential in crop monitoring (Ochiai et al., 2024). Yu et al. (2023) also demonstrated that combining different types of features can improve the prediction performance of LAI in potato. This study highlights the limitations of Haralick texture, but also demonstrates its value as auxiliary information when combined with spectral features for LAI estimation. The combination of spectral and Haralick texture information in this study explained 69% of the variability in LAI across multiple growth stages in potatoes, which is lower than the 85% of spatial variability in maize LAI explained by Zhang et al. (2022b) using fusion information. This discrepancy may be due to differences in crop variety and canopy structure.

Haralick texture differs from spectral information in response to potato canopy structure, and their complementary information helps to improve LAI estimation accuracy. This complementary information can enhance the accuracy of LAI estimation. In this study, models for LAI estimation that integrated both spectral and texture data outperformed those relying on a single type of data. Thus, combining spectral information with Haralick textures offers valuable insights for LAI estimation across various growth stages of potatoes. The study derived the spatial and temporal distribution of potato LAI at the field scale using the optimal estimation model ( Figure 9 ), facilitating the assessment of the model’s potential for practical field applications. Despite achieving satisfactory results, some limitations remain. Future research should consider incorporating additional crop structural characteristics, such as vegetation cover, plant height, and volume, to improve model construction. This study compared the potential of three machine learning methods for UAV estimation of LAI in wheat, but found that deep learning performed better for potato biomass prediction (Liu et al., 2024c), suggesting that deep learning has greater potential for application in the field of UAV spectral monitoring of crop growth. Therefore, future research will deeply explore the application of methods such as deep learning in this field. In addition, since the UAV and ground data used in this study were limited to a single location, within one year, and two varieties, we will further explore the impact of multi-year and multi-variety potato data on improving the performance of Haralick texture features. Future work will focus on different varieties and multiple years of data to analyze the robustness of canopy spectra and Haralick texture features in estimating potato LAI.