Summer Maize Leaf Area Index Estimation Using Approximate Days After Sowing and Dual-Domain Paired-Difference Features

Abstract

Residue-soil mixing and reduced spectral sensitivity complicate summer maize leaf area index (LAI) estimation from unmanned aerial vehicle multispectral imagery. We compared full-plot and canopy domains, paired differences, neighborhood statistics, and approximate days after sowing (DAS), calculated from a common reference date. Five input schemes (B₀–B₄) and four algorithms were evaluated using 345 samples collected on five dates in one growing season. Spatial validation comprised ten repetitions of five-fold grouped cross-validation, with preprocessing and feature selection restricted to training data. For gradient boosting decision trees, R² increased from 0.515 for B₀ to 0.686 for B₃ and 0.846 for B₄, whereas RMSE decreased from 0.834 to 0.671 and 0.470. Low-LAI Bias decreased from 0.580 to 0.343 and 0.160. Fixed-capacity controls supported conditional improvements after adding paired differences and neighborhood statistics. Approximate DAS produced the largest sequential RMSE reduction, mainly through between-date adjustment. Time-baseline and training-fold residual analyses distinguish calendar-time adjustment from within-date predictive information. High-LAI underestimation and unseen-date errors delimit application beyond the sampled dates and production-field conditions. Within this defined scope, the framework provides a reproducible comparison of image-domain representations under heterogeneous production conditions.

1. Introduction

Leaf area index (LAI), defined as the one-sided leaf area per unit ground area, is an important biophysical parameter linking canopy radiation interception, evapotranspiration, photosynthesis, and crop growth status. It is also a key remote-sensing variable for crop growth monitoring and field management [1]. Ground instruments and destructive measurements can provide plot-scale reference values, but their measurement efficiency, observation geometry, and spatial representativeness limit continuous application at the field scale [2]. Satellite remote sensing provides regional coverage, yet it is often constrained by revisit intervals, cloud contamination, and mixed pixels. Precision agriculture therefore requires data sources that balance temporal scheduling, spatial resolution, and observation cost [3], and the value of field remote sensing depends on whether the information can be linked to actual management units [4]. UAVs can acquire centimeter-level, multi-temporal reflectance imagery during key growth stages, supporting LAI estimation at a scale closer to ground sampling. However, radiometric correction, geometric consistency, and observation conditions must still be strictly controlled [5,6]. This study examines how the statistical domain of UAV imagery affects LAI error at different canopy stages.

Existing remote-sensing approaches for crop LAI estimation can be broadly grouped into physical models, empirical vegetation indices, and sample-driven models. Physical models connect leaf optical properties, canopy structure, and reflectance through canopy radiative transfer processes. They have clear mechanistic interpretability, but the inversion results can be affected by prior parameters, equifinality, and observation geometry [7,8]. Empirical vegetation indices are easy to calculate and map, and combinations of multispectral red-edge and near-infrared bands have been used for maize LAI estimation [9]. The PROSAIL model, which couples the leaf optical properties model PROSPECT with the canopy radiative transfer model SAIL, can also be combined with UAV multispectral imagery to expand the spectral response range when training samples are limited [10]. Sample-driven methods use nonlinear regression to integrate spectral bands, vegetation indices, and spatial statistical information. Previous maize studies have shown that combining spectral and image spatial statistics can improve LAI estimation [11], but model performance still changes markedly across growth stages and complex smallholder-field backgrounds [12]. Multi-source data fusion and hyperspectral–multispectral comparisons further indicate that new information is useful only when the added features provide new canopy information, rather than simply increasing input dimensionality [13,14]. These studies provide several viable routes, but they have not directly clarified the respective roles of full-plot statistics, canopy statistics, and their inter-domain differences. GBDT sequentially fits regression trees to reduce prediction error [15], whereas RF averages randomized trees [16]. SVR uses a kernel-based regression function [17], and Ridge regularizes linear coefficients [18]. Recent maize studies examine multisource UAV features [19], hyperspectral and accumulated-temperature information across sowing dates [20], and computer-vision representations [21]. These examples motivate comparing model classes and input representations without assuming equivalent transferability.

The unresolved issue is most evident when sparse early canopies coexist with a residue background. Existing studies usually either calculate statistics from all pixels within a fixed plot or remove background first and retain only canopy pixels. The first strategy allows residue and bare-soil reflectance to enter the model. Simulation and ground observations have shown that residue cover can substantially alter canopy reflectance and vegetation indices in the low-LAI range [22]. The second strategy reduces the influence of pure soil pixels, but it may also remove information related to vegetation cover and inter-row structure. In UAV maize imagery, the proportion of soil background has been identified as an important source of early-stage LAI uncertainty [23]. Under rice-wheat rotation residue backgrounds, a specially designed residue-soil-adjusted red-edge index mainly improved low-LAI estimation [24]. The difficulty is that soil type, canopy structure, and background spectra jointly alter the LAI-reflectance relationship [25], while residue and soil cannot always be stably separated in the visible to near-infrared range [26]. Recent multi-platform experiments also show that soil moisture, residue, shadow, and canopy cover jointly affect vegetation indices [27]. Without placing the full-plot domain, canopy domain, and inter-domain differences into the same progressive control framework, it is difficult to determine whether low-LAI overestimation originates from model form, input dimensionality, or a mismatch between the image statistical domain and the green canopy. As a result, the overall accuracy may appear acceptable, while LAI can be systematically overestimated during early management stages.

This study compares full-plot and canopy-domain representations to examine how background screening, paired differences, and neighborhood information affect LAI estimation. Calendar-time information is evaluated separately to distinguish between-date adjustment from within-date prediction. Spatially grouped validation addresses prediction at new locations on dates represented in training [28]. Unseen-date prediction is assessed as a separate sensitivity analysis.

We address three questions: how inter-domain spectral contrasts vary across observation dates; how prediction changes across spectral representations under matched comparisons; and how approximate DAS affects overall and within-date performance. We also examine low- and high-LAI errors and distinguish spatial prediction on represented dates from prediction on unseen dates. Overall, R² describes predictive performance across the pooled observations, while RMSE, Bias, and Slope characterize errors within restricted LAI ranges.

2. Materials and Methods

2.1. Study Area and Observation Design

The study was conducted in Guangrao County, Dongying City, Shandong Province, China (sample center approximately 37°12′58″ N, 118°32′10″ E). The area lies on the Yellow River Delta alluvial plain and has a warm-temperate monsoon climate. Samples were collected from farmer-managed summer maize fields under winter wheat-summer maize rotation, with wheat residue retained at the soil surface. The fields were independently managed by multiple farmers rather than subjected to one prescribed experimental treatment. Cultivar or hybrid, planting density, row spacing, fertilization, irrigation, crop protection, and actual sowing date consequently varied among fields; complete field-level records were not available for consistent reporting. This production-field setting enabled the method to be evaluated across management conditions encountered in local farming practice. For consistency with the original analysis, DAS denotes an approximate calendar-time reference calculated from 1 June 2025, rather than verified field-specific days after sowing. Figure 1c displays all five sampling dates over an LAI surface interpolated only from the 29 July observations; this background is retained solely as spatial context and does not represent the other dates.

Figure 1. Location of the study area and sampling points. (a) Shandong Province within China; (b) Dongying City, Guangrao County, and the sampled production fields; (c) sampling locations from all five dates over an LAI surface interpolated from the 69 observations on 29 July 2025. Point colors identify sampling date. The background surface is single-date spatial context and is not interpreted as LAI on the other four dates.

Five UAV campaigns and corresponding ground LAI observations were conducted on 2 July, 16 July, 29 July, 14 August, and 10 September 2025. Of 347 records, two from the second campaign were excluded under an objective coordinate-validity check because their recorded longitudes fell outside the valid geographic range of −180° to 180°; one was a malformed coordinate with a missing decimal separator. The analysis retained 345 samples. Sampling locations were generally selected anew in each campaign, spanning a range of visually distinct canopy conditions across farmer-managed fields; they were not monitored as permanent plots. Table 1 summarizes the observations by date.

Table 1. Sample size and LAI descriptive statistics for each observation date.

No.	Date	Approx. DAS (d)	n	LAI Range	Mean ± SD	Main Canopy and Background Characteristics
1	2 July 2025	31	68	0.31–0.79	0.464 ± 0.129	Residue and bare soil mixed
2	16 July 2025	45	67	0.47–1.93	1.225 ± 0.366	Canopy expansion, background still visible
3	29 July 2025	58	69	1.37–3.55	2.607 ± 0.513	Canopy nearly closed
4	14 August 2025	74	68	2.33–4.66	3.521 ± 0.607	High LAI and local heterogeneity
5	10 September 2025	101	73	1.85–4.53	2.821 ± 0.477	Senescence-stage spectral changes
Total	—	—	345	0.31–4.66	—	—

Note: approximate DAS is the number of days from the common reference date, 1 June 2025, rather than verified field-specific days after sowing. Low LAI denotes LAI < 1 (n = 80), and high LAI denotes LAI ≥ 3 (n = 89). An em dash (—) indicates not applicable.

2.2. UAV Multispectral Imagery and Ground LAI

Five multispectral campaigns were conducted with a DJI Matrice 350 RTK platform (SZ DJI Technology Co., Ltd., Shenzhen, China) carrying a MicaSense RedEdge-P dual-camera multispectral system (AgEagle Aerial Systems Inc., Wichita, KS, USA). The system acquired ten bands. Of these, the five bands retained as analysis-ready orthomosaics in the original processing workflow were used consistently across all campaigns: blue (475 nm; 32 nm bandwidth), green (560 nm; 27 nm), red (668 nm; 14 nm), red-edge (717 nm; 12 nm), and near-infrared (842 nm; 57 nm). Flights were performed at 120 m above ground level and 8 m s⁻¹, with 75% forward and side overlap and a nadir-looking camera. Image acquisition was scheduled between 10:00 and 14:00 under sunny, adequately illuminated, cloud-free and haze-free conditions, with wind speed below 10 m s⁻¹. Raw images were processed in Pix4Dmapper (version 4.5.6; Pix4D SA, Prilly, Switzerland) for radiometric correction, aerial triangulation, and orthomosaic generation. Radiometric correction combined factory calibration parameters with ground reflectance calibration-panel data. The verified ground sampling distance ranged from 0.0765 to 0.0782 m, and all 25 band rasters used WGS84/UTM zone 50N (EPSG:32650). A 1 m × 1 m window was extracted around each sample coordinate.

Ground LAI was measured on each flight date using an LAI-2200C Plant Canopy Analyzer (LI-COR Biosciences, Lincoln, NE, USA), with field measurements synchronized as closely as practicable with the UAV campaign. At each sample point, one unobstructed above-canopy reference reading (A) was followed by six below-canopy readings (B) taken diagonally between maize rows, with the sensor held at the standard field position approximately 1 m above the ground and below the canopy. A 270° view cap was oriented away from the operator and direct sunlight. The six B readings were averaged and paired with the corresponding A reference in FV2200 software (version 2.1.1; LI-COR Biosciences, Lincoln, NE, USA) to calculate one LAI estimate for that point; they were not six independently calculated LAI estimates. Scattering correction was applied using the white scattering-correction accessory and the FV2200 procedure. No additional clumping or row-structure correction was applied. The LAI value reported by FV2200 was used as the reference variable for model development and evaluation.

2.3. Dual-Domain Representation, Paired Differences, and Multi-Scale Neighborhood Statistics

The full-plot domain comprised valid pixels in a 1 m × 1 m window centered on each sample. It included canopy, residue, soil, shadow, and mixed pixels. Canopy pixels were selected by NDVI-based Otsu thresholding [29]. Thresholds were estimated separately for observation dates represented in the current outer training fold. A pooled-training threshold served as the fallback when the target date was absent from training, as in LODO. Thresholds were fixed before predicting the corresponding validation samples. If no pixel passed the threshold, canopy statistics reverted to full-plot statistics and the event was recorded. Supplementary Table S1 reports these events separately for repeated spatial validation and LODO.

For each domain, band reflectance was averaged over the retained pixels. Vegetation indices were then computed from these domain-mean band values; they were not averages of pixel-wise index values. Corresponding full-plot and canopy statistics were denoted by F_full and F_canopy. Their paired difference was defined as

ΔF = F_canopy − F_full

(1)

ΔF represents the difference between two statistical descriptions of the same sampling window; the physical plot is unchanged. Neighborhood labels of 1 m and 2 m denote square-window side lengths centered on the sample coordinate. Band and NDVI means, standard deviations, ranges, and coefficients of variation summarize local variation. The 1 m neighborhood shares the support of the full-plot window. Consequently, highly correlated mean features were removed during within-family pruning at |ρ| ≥ 0.90, whereas the retained dispersion statistics provided distinct summaries of local reflectance heterogeneity.

2.4. Vegetation Indices and B₀–B₄ Feature Schemes

Candidate spectral features included five original reflectance bands and 20 vegetation indices, covering greenness, red-edge response, soil-background adjustment, chlorophyll sensitivity, and wide dynamic range. The applicable ranges and saturation issues of classical vegetation indices for LAI have been systematically discussed [30]. Based on the progressive relationship between the image statistical domain and additional information, five main schemes, B₀–B₄, were designed (Table 2). B₄ introduced DAS only on the basis of B₃, and the relationship among the schemes is shown in Figure 2c. The formulas and references for the 20 candidate vegetation indices are listed in Table 3.

Table 2. Inputs and within-fold maximum number of selected features for the progressive B₀–B₄ schemes.

Scheme	Scheme Name	Inputs	Feature Limit
B0	Full-plot domain	Full-plot domain bands and indices	12
B1	Canopy domain	Canopy-domain bands and indices	12
B2	Dual-domain	Full-plot domain + canopy domain	20
B3	Dual-domain paired difference	B2 + corresponding paired differences + multi-scale neighborhood statistics	20
B4	DAS-assisted model	B3 + DAS	21

Note: feature limits are upper bounds after training-only imputation, family-specific redundancy pruning, and stability selection. Standardization was fitted after feature selection within the model pipeline. Actual selected counts may differ by fold. Approximate DAS was available only for B₄ among the main schemes.

Figure 2. Analysis workflow: (a) data acquisition and preprocessing; (b) dual-domain representation; (c) feature and model pipeline; and (d) validation and error diagnosis. Training-derived canopy thresholds, preprocessing, feature selection, and model fitting are confined to training data. The main spatial validation, fixed-capacity controls, sequential RMSE summaries, stratified errors, and unseen-date sensitivity analysis answer separate questions. Approximate DAS supplies calendar-time conditioning; the workflow does not impose a physiological growth curve or a physical constraint.

Table 3. Vegetation indices used for LAI estimation, their formulas, and references.

Index	Remote-Sensing Meaning	Formula	References
NDVI	Normalized difference vegetation index	(NIR − R)/(NIR + R)	[30]
RVI	Ratio vegetation index	NIR/R	[30]
NDRE	Red-edge normalized difference index	(NIR − RE)/(NIR + RE)	[31]
LCI	Leaf chlorophyll index	(NIR − RE)/(NIR + R)	[9]
OSAVI	Optimized soil-adjusted vegetation index	1.16(NIR − R)/(NIR + R + 0.16)	[32]
GNDVI	Green normalized difference vegetation index	(NIR − G)/(NIR + G)	[33]
EVI2	Two-band enhanced vegetation index	2.5(NIR − R)/(NIR + 2.4R + 1)	[34]
CIRE	Red-edge chlorophyll index	NIR/RE − 1	[35]
MTCI	MERIS terrestrial chlorophyll index	(NIR − RE)/(RE − R)	[36]
WDRVI (α = 0.15)	Wide dynamic range vegetation index	(0.15NIR − R)/(0.15NIR + R)	[37]
MCARI	Modified chlorophyll absorption ratio index	[(RE − R) − 0.2(RE − G)](RE/R)	[38]
TCARI	Transformed chlorophyll absorption ratio index	3[(RE − R) − 0.2(RE − G)(RE/R)]	[38]
NDVI_RE	Red-edge–red normalized index	(RE − R)/(RE + R)	[39]
NIR/RE	Near-infrared/red-edge ratio	NIR/RE	[31]
RE/R	Red-edge/red ratio	RE/R	[31]
CIG	Green chlorophyll index	NIR/G − 1	[33]
MSAVI2	Modified soil-adjusted vegetation index	[2NIR + 1 − √((2NIR + 1)2 − 8(NIR − R))]/2	[40]
SAVI	Soil-adjusted vegetation index	1.5(NIR − R)/(NIR + R + 0.5)	[41]
WDRVI (α = 0.05)	Wide dynamic range vegetation index	(0.05NIR − R)/(0.05NIR + R)	[37]
WDRVI (α = 0.20)	Wide dynamic range vegetation index	(0.20NIR − R)/(0.20NIR + R)	[37]

Note: B, G, R, RE, and NIR represent blue, green, red, red-edge, and near-infrared reflectance, respectively. α is the weighting coefficient of WDRVI. The reference column gives the source of the index definition or the formula used in this study.

2.5. Within-Fold Feature Screening and Model Pool

Feature screening was performed within each outer training fold. Missing values were replaced by training medians, with zero used for entirely missing columns. Constant features were removed. Relevance combined the absolute Spearman correlation with the univariate linear-regression F statistic from f_regression. Non-finite F values were set to zero, and positive F values were normalized by the maximum candidate F value. The composite score was S = 0.60|ρ| + 0.40F_norm. The larger weight on |ρ| made the monotonic association with LAI the primary ranking criterion, while F_norm supplemented it with univariate linear separation. The 0.60/0.40 ratio was used as a balanced engineering setting for these complementary criteria. Features were ranked by this score, and greedy pruning removed candidates with an absolute Spearman correlation of ≥0.90 with a retained feature within the same family. Inner spatial groups were formed from outer-training coordinates using K-means, with min(12, max(4, floor(n_train/12))) groups and up to five GroupKFold splits. Selection frequency across inner training subsets defined stability. A frequency of 0.60 was the primary eligibility threshold. If a predefined feature family had no eligible member, its highest-ranked candidate could enter at a frequency of at least 0.40, preserving representation of that family against variation among inner spatial splits. The full algorithm, family quotas, seeds, and fallback rules are provided in Supplementary Methods S1. Standardization was fitted after selection. Outer-validation LAI values were not used for these operations.

The model pool included gradient boosting decision tree (GBDT) [15], random forest (RF) [16], support vector regression (SVR) [17], and ridge regression (Ridge) [18]. GBDT used 120 weak learners, a learning rate of 0.03, a tree depth of 2, a minimum of 8 samples per leaf node, and a subsampling ratio of 0.80. RF used 300 trees, a maximum depth of 6, a minimum of 6 samples per leaf node, and square-root feature sampling. SVR used a radial basis function (RBF) kernel with C = 10, ε = 0.10, and γ = scale. The α value of Ridge was set to 10. The same parameters were used for all feature schemes in the four model types, so that cross-scheme comparisons focused on differences in input information rather than on re-tuning.

2.6. Ablation Controls, Spatial Validation, and Leave-One-Date-Out Test

A difference-only control (D₀) tested whether paired differences could replace absolute domain information. Separate fixed-capacity controls limited B₂, B₂+ΔF, B₃, and B₄ to at most 12 selected features, denoted B₂(12), B₂+ΔF(12), B₃(12), and B₄(12). D₀ is a separate diagnostic, not the first step of a nested chain. The fixed-capacity comparisons shared spatial folds and GBDT settings. Their differences describe conditional changes under the stated selection procedure, rather than order-independent feature contributions.

To make the stepwise comparison in the main B₀–B₄ sequence explicit, we calculated the sequential relative RMSE reduction between adjacent schemes as

$$I_k={\displaystyle \frac{{\mathit{RMSE}}_{k-1}-{\mathit{RMSE}}_k}{{\mathit{RMSE}}_{k-1}}}\times 100\%$$

(2)

where k indexes the next scheme in the B₀–B₄ sequence. We also report the share of the total B₀–B₄ RMSE reduction as

$$C_k={\displaystyle \frac{{\mathit{RMSE}}_{k-1}-{\mathit{RMSE}}_k}{{\mathit{RMSE}}_{B_0}-{\mathit{RMSE}}_{B_4}}}\times 100\%$$

(3)

Both quantities are descriptive and order-dependent. They are not independent feature contributions because the main schemes differ in input composition and maximum feature limits. The fixed-capacity controls were retained to assess module additions under a common upper limit.

Spatial groups were generated by K-means using projected sample coordinates in WGS84/UTM zone 50N (EPSG:32650), in meters. Each repetition used 25 groups, n_init = 10, and random_state = 1000 + r, where r ranged from 0 to 9. Twenty-five groups balanced spatial granularity with sufficient membership for five-fold validation: group sizes ranged from 3 to 28 samples, with a median of approximately 14 samples and a median group diameter of approximately 210 m. All groups therefore retained at least three samples, and ten repeated groupings reduced sensitivity to any single small-group allocation. GroupKFold assigned entire groups to five validation folds, and all models shared these assignments. The minimum and median validation-to-nearest-training distances were 11.2 and 89.2 m. Because K-means grouping does not impose an explicit separation buffer, we also evaluated 25 m and 50 m buffers. The corresponding B₄ RMSEs were 0.469724 and 0.470910, compared with 0.469648 without an added buffer, showing that performance was nearly unchanged under these stricter distance settings. Main validation estimates prediction at new locations on dates represented in training [42].

LODO held out each observation date in turn and fitted preprocessing, canopy thresholds, feature selection, and models using the other four dates. It was not used for model selection. We describe it as unseen-date sensitivity analysis: holding out an intermediate date is temporal interpolation with respect to DAS, whereas holding out the earliest or latest date is extrapolation. Neither case is equivalent to the main spatial validation. Target samples may also differ in spectral conditions and LAI distribution [43]. A secondary threshold-transfer comparison replaced the pooled-training threshold with the nearest training-date threshold to assess the canopy fallback mechanism.

2.7. Evaluation Metrics and Error Stratification

For each repeat, all out-of-fold predictions were summarized to calculate the coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), Bias, and the predicted-versus-measured regression Slope:

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-{ŷ}_i\right)}^2}{{\sum }_{i=1}^n{\left(y_i-ȳ\right)}^2}}$$

(4)

$$\mathit{RMSE}=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}{\left(y_i−{\hat{y}}_i\right)}^2}{n}}}$$

(5)

$$\mathit{MAE}=\left({\displaystyle \frac{1}{n}}\right){\sum }_{i=1}^n\left|y_i-{ŷ}_i\right|$$

(6)

$$\mathit{Bias}=\left({\displaystyle \frac{1}{n}}\right){\sum }_{i=1}^n\left({ŷ}_i-y_i\right)$$

(7)

$$\mathit{Slope}={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}\left(y_i-\overline{y}\left)\right({\hat{y}}_i-\overline{\hat{y}}\right)}{{\displaystyle {\sum }_{i=1}^n}{\left(y_i−\overline{y}\right)}^2}}$$

(8)

Here, the observed and predicted LAI values are indexed by i; overbars denote their sample means, and n is the sample size. Positive Bias indicates overestimation. LAI and its absolute-error metrics are reported without area-ratio unit labels. Overall R² measures predictive performance. Low-LAI (<1, n = 80) and high-LAI (≥3, n = 89) evaluation emphasizes RMSE, Bias, and Slope because restricted reference ranges can produce strongly negative stratified R². Relative RMSE and Bias equal 100 times the corresponding absolute metric divided by the mean observed LAI in that subset (Supplementary Table S2). Metrics are summarized across ten complete repetitions, and error bars show descriptive between-repetition SD. Conditional spatial-block intervals for paired scheme differences and high-LAI slopes are reported in Supplementary Tables S3 and S4.

3. Results

3.1. Dual-Domain Differences Across Observation Periods

Mean LAI increased from 0.464 ± 0.129 in the first observation period to 3.521 ± 0.607 in the fourth observation period, and then decreased to 2.821 ± 0.477 in the fifth observation period during senescence. Low-LAI samples were mainly concentrated in the first and second observation periods. Early background mixing was therefore the main stage for testing low-LAI overestimation.

Dual-domain differences showed a clear stage pattern (Figure 3). In the first observation period, the mean proportion of retained canopy pixels was only 0.300, and mean |ΔNDVI| was 0.128. In the second observation period, these values changed to 0.747 and 0.051, respectively. In the third observation period, the retained canopy-pixel proportion increased to 0.984, and mean |ΔNDVI| decreased to 0.006, indicating that the full-plot domain and the canopy domain were close to each other. In the fourth observation period, the retained proportion decreased to 0.724 and mean |ΔNDVI| increased again to 0.071. In the fifth observation period, the two metrics converged again. These changes indicate that inter-domain differences were mainly concentrated in the early low-LAI stage and weakened markedly as canopy cover increased.

Figure 3. Descriptive changes across five observation dates in mean LAI, retained canopy-pixel proportion, and mean absolute inter-domain NDVI difference. Values are printed in each cell. Colors are normalized within each row and therefore compare dates within a metric, not magnitudes among different metrics. These descriptive sample summaries are separate from the training-fold thresholds used for validation.

3.2. Overall Accuracy and Cross-Model Consistency

For GBDT, overall R² increased from 0.515 for B₀ to 0.598 for B₁ and 0.605 for B₂, further increased to 0.686 for B₃, and reached 0.846 for B₄ (Figure 4a; Table 4). The corresponding RMSE decreased from 0.834 to 0.759, 0.752, 0.671, and 0.470 (Figure 4b). Compared with B₀, RMSE decreased by 19.6% for B₃ and by 43.7% for B₄.

Figure 4. Main spatial validation. (a,b) GBDT R² and RMSE, shown as means ± descriptive SD across ten repetitions. (c–f) Mean OOF predictions across repetitions for each of 345 samples under B₄ with GBDT, RF, SVR, and Ridge. Colors identify the observation dates as in Figure 1; dashed lines show 1:1 agreement. Scatterplots show per-sample averages, whereas panels (a,b) summarize complete repetitions. Conditional paired intervals are reported in Supplementary Table S3.

Table 4. Overall and stratified accuracy of GBDT under ten repetitions of five-fold spatial group cross-validation.

Scheme	Scheme Name	Overall R2	Overall RMSE	Low-LAI RMSE	Low-LAI Bias	High-LAI RMSE	High-LAI Bias	High-LAI Slope
B0	Full-plot domain	0.515 ± 0.021	0.834 ± 0.018	0.843 ± 0.030	+0.580 ± 0.028	1.199 ± 0.033	−0.965 ± 0.022	−0.067 ± 0.043
B1	Canopy domain	0.598 ± 0.015	0.759 ± 0.014	0.721 ± 0.041	+0.383 ± 0.022	1.074 ± 0.023	−0.878 ± 0.016	0.001 ± 0.025
B2	Dual-domain	0.605 ± 0.014	0.752 ± 0.013	0.729 ± 0.046	+0.395 ± 0.024	1.060 ± 0.018	−0.881 ± 0.014	0.034 ± 0.023
B3	Dual-domain paired difference	0.686 ± 0.015	0.671 ± 0.016	0.694 ± 0.028	+0.343 ± 0.012	0.899 ± 0.019	−0.726 ± 0.018	0.163 ± 0.023
B4	DAS-assisted model	0.846 ± 0.002	0.470 ± 0.004	0.298 ± 0.005	+0.160 ± 0.005	0.666 ± 0.008	−0.465 ± 0.008	0.241 ± 0.018

Note: values are means ± descriptive SD across ten repetitions. Low LAI denotes LAI < 1 and high LAI denotes LAI ≥ 3. Relative RMSE (%) and Bias (%) are provided in Supplementary Table S2 using each subset’s observed mean. Conditional paired RMSE intervals are provided in Supplementary Table S3. Restricted-range R² is not used as the principal stratified performance measure.

The cross-model results did not change the main conclusion. The R² increments from B₂ to B₃ were 0.081, 0.080, 0.034, and 0.164 for GBDT, RF, SVR, and Ridge, respectively, and RMSE decreased by 0.081, 0.082, 0.035, and 0.145. The R² increments from B₃ to B₄ were 0.160, 0.101, 0.070, and 0.063, respectively, and RMSE decreased by 0.201, 0.120, 0.080, and 0.064.

3.3. Early Low-LAI Overestimation and the Auxiliary Role of DAS

The low-LAI subset showed systematic overestimation. The RMSE and Bias of B₀ were 0.843 and 0.580, respectively. B₁ reduced them to 0.721 and 0.383, consistent with an initial benefit from canopy-domain screening. The RMSE/Bias values of B₂ were 0.729/0.395, those of B₃ decreased to 0.694/0.343, and those of B₄ further decreased to 0.298/0.160 (Figure 5a,b). Compared with B₀, B₄ reduced low-LAI Bias by 72.4%.

Figure 5. Low-LAI errors. (a,b) GBDT RMSE and Bias as means ± descriptive SD across ten repetitions. (c,d) Mean OOF predictions for all 80 samples with measured LAI < 1 under B₃ and B₄. Colors indicate observation dates; dashed lines show 1:1 agreement. Conditional paired intervals are reported in Supplementary Table S3.

Adding approximate DAS reduced the large low-LAI predictions observed under B₃ (Figure 5c,d). Under identical spatial assignments, B₄ improved substantially over B₃, while time-only GBDT and training-date means achieved RMSEs of 0.456245 and 0.453940, compared with 0.469648 for B₄. A further model predicted spectral residuals after subtracting date means calculated within each training fold and restored the corresponding training mean at prediction; its RMSE was 0.461445 and its pooled date-centered R² was −0.033469. These diagnostics show that date-associated variation accounted for much of the overall B₃-to-B₄ improvement. After the date means were removed, the residual analysis did not show a positive pooled date-centered increment over the training-date-mean reference. The controlled B₀–B₄ comparisons nevertheless remain informative about the relative performance of the spectral input schemes under identical spatial folds.

3.4. Paired Differences, Neighborhood Statistics, and Feature-Count Controls

The difference-only diagnostic D₀ achieved R² = 0.590 and RMSE = 0.767. B₂(12), which retained absolute information from both domains, achieved R² = 0.606 and RMSE = 0.751. In this comparison, differences alone did not replace the predictive value of the absolute domain information. D0 and B₂(12) are alternative representations rather than successive steps of a nested feature chain.

Under the common 12-feature upper limit, RMSE decreased from 0.751 for B₂(12) to 0.726 for B₂+ΔF(12), 0.669 for B₃(12), and 0.465 for B₄(12). The corresponding mean changes were −0.024953, −0.057431, and −0.203943 (Figure 6a). In the main B₀–B₄ sequence, RMSE reductions relative to the immediately preceding scheme were 0.075316 (B₀ to B₁), 0.006552 (B₁ to B₂), 0.081206 (B₂ to B₃), and 0.201308 (B₃ to B₄). These reductions corresponded to 9.03%, 0.86%, 10.80%, and 30.00% of the preceding RMSE, respectively (Figure 6b). Because the main schemes differ in input composition and maximum feature limits, these values are descriptive sequential changes rather than independent causal feature contributions.

Figure 6. Feature-count controls and sequential RMSE summaries. (a) Performance of the separate D0 diagnostic and four controls with at most 12 selected features. Values are printed in each cell; colors are normalized within each metric and are not contribution percentages. Upward (↑) and downward (↓) arrows in (a) indicate that higher R₂ values and lower RMSE or |Bias| values represent better performance, respectively. (b) RMSE reductions between adjacent main B₀–B₄ schemes. Each bar reports the reduction relative to the preceding scheme, its percentage of the preceding RMSE, and its share of the total B₀–B₄ RMSE decline. These quantities are descriptive and order-dependent because the main schemes differ in input composition and feature limits.

3.5. High-LAI Underestimation and Unseen-Date Prediction

Although B₄ markedly improved overall and low-LAI accuracy, high-LAI samples were consistently underestimated across the four regression models. The high-LAI RMSE values of GBDT, RF, SVR, and Ridge were 0.666, 0.792, 0.834, and 0.950, respectively. Their Bias values were −0.465, −0.625, −0.542, and −0.736, and their Slope values were 0.241, 0.165, 0.169, and 0.189, respectively (Figure 7a–d).

Figure 7. High-LAI and unseen-date diagnostics. (a–d) Mean OOF predictions for 89 samples with measured LAI ≥ 3. Dashed lines show 1:1 agreement and solid lines show linear trends; panels report sample size, RMSE, Bias, and Slope. Conditional spatial-block slope bounds are provided in Supplementary Table S4. (e) B₄ LODO RMSE by model and held-out date; labels give date-specific sample size and measured LAI range.

Unseen-date prediction produced substantial date-specific errors (Figure 7e). For GBDT B₄, pooled LODO RMSE was 1.106, and R² was negative within each held-out date. The second date had RMSE = 1.578. Replacing the pooled-training canopy threshold with the nearest training-date threshold reduced the mean of the five date-specific RMSEs only from 1.0499 to 1.0455. For the first date, fallback frequency decreased from 51/68 to 29/68 samples. Fewer fallback events therefore did not resolve the unseen-date prediction limitation. Pooled RMSE and the unweighted mean of date-specific RMSEs are distinct summaries.

4. Discussion

4.1. Effects of the Image Statistical Domain

The early observation date showed marked inter-domain contrast: about 30% of pixels were retained by the descriptive canopy mask, and mean |ΔNDVI| was 0.128. Low-LAI Bias decreased from 0.580 for B₀ to 0.383 for B₁. This comparison is consistent with a contribution from background screening, although it does not isolate every cause of error. Residue and soil can alter vegetation indices and early-stage LAI estimation [22,23]. Comparing two statistical domains within the same image window provides a direct way to assess this sensitivity.

The canopy domain does not mean complete background removal. Residue and soil may have similar reflectance patterns in the visible to near-infrared range, and these patterns are affected by moisture content [26]. The Otsu threshold can also be influenced by shadows, senescent leaves, and illumination changes. Therefore, the role of B₁ is to shift the statistical center toward the green canopy, not to guarantee that all retained pixels are pure canopy pixels. The residue-soil-adjusted red-edge index can improve low-LAI estimation [24], and soil-adjusted vegetation indices reduce background effects from the perspectives of the soil line or brightness correction [40,41]. However, these indices are still calculated within a fixed image domain. The dual-domain design in this study further separates the question of which pixels are used for statistics from the question of which indices are calculated, allowing background correction to occur first at the level of the remote-sensing statistical domain.

Full-plot and canopy statistics were most similar at the third observation date, whereas their contrast increased again at the fourth. Such differences may reflect canopy cover, inter-row gaps, shadows, senescence, and background conditions. These alternatives were not separated experimentally. Soil and canopy properties can jointly influence spectral responses [25,27], so inter-domain contrasts should not be treated as a monotonic function of approximate DAS.

4.2. Paired Differences, Neighborhood Statistics, and DAS Play Different Roles

The fixed-capacity comparison supports a modest conditional improvement after adding paired-difference features to absolute dual-domain inputs. The differences explicitly represent contrasts between two statistical descriptions of the same window. They may simplify the representation available to a fitted model, but this comparison does not establish a distinct physical mechanism. Earlier maize studies similarly motivate examining combinations of spectral and spatial information through controlled comparisons [11,13].

Neighborhood statistics provided an additional improvement under the fixed-capacity comparison. Their variability measures summarize local reflectance heterogeneity rather than directly observing vertical canopy structure. The effect is conditional on the selected features, sample distribution, and validation design [19,44]. It should therefore be distinguished from evidence that the same features will improve prediction in new years or locations.

Approximate DAS provided a calendar-time reference that adjusted the prediction baseline across observation dates. In this statistical sense, it acted as a temporal constraint or date-conditioning variable; no explicit physiological trajectory or physical bound was imposed. Because the same five dates were represented in training and validation, DAS could partly identify observation date, and date-associated variation accounted for much of the overall B₃-to-B₄ improvement. The controlled B₀–B₄ comparisons still show how prediction changed among spectral input schemes under identical spatial folds. This distinction separates the comparative value of those schemes from the additional between-date adjustment supplied by approximate DAS.

4.3. Persistent High-LAI Underestimation

All four B₄ models underestimated high LAI, with regression slopes ranging from 0.165 to 0.241. This shared behavior is consistent with limited spectral sensitivity, but it does not identify a unique cause. The high-LAI sample distribution, fixed hyperparameters, measurement uncertainty, and one-season design may also contribute. Vegetation-index saturation is a relevant explanation [30,31,35,39], rather than a mechanism proved by these comparisons.

Two-dimensional multispectral reflectance mainly describes the spectral response of the upper canopy surface and has limited sensitivity to vertical leaf distribution, canopy height, inter-layer occlusion, and ear-layer structure. A systematic review of spectral saturation in high-density vegetation reported that sensor band position, canopy structure, and observation mode jointly determine the saturation level, and recommended integrating airborne light detection and ranging (LiDAR), radar, or three-dimensional structural information [45]. Three-dimensional point clouds derived from UAV oblique imagery have been used to estimate maize LAI and canopy height simultaneously [46]. Compared with nadir orthomosaics, oblique photography can obtain more complete canopy-layer point clouds [47]. Canopy complexity metrics from airborne laser scanning (ALS) and unmanned aerial vehicle (UAV) stereo imagery can also serve as predictors of maize LAI [48]. Therefore, future work should introduce digital surface models (DSMs), digital terrain models (DTMs), canopy height models (CHMs), point-cloud height percentiles, canopy volume, or row-structure indicators into the existing dual-domain spectral representation to test whether three-dimensional canopy information can reduce high-LAI underestimation.

The present results motivate testing structural observations alongside the existing spectral representation. They do not demonstrate that two-dimensional imagery imposes an irreducible accuracy limit. Additional data and independently evaluated alternatives would be needed to distinguish sensitivity limitations from sampling, reference measurement, and model effects.

4.4. Validation Scope and Future Applications

Comparing four regression algorithms reduced reliance on a single model specification. Consistent directions of change across these algorithms support the reported scheme comparisons within this dataset, but do not isolate a causal feature effect. Fixed hyperparameters provide a common reference rather than an exhaustive search for each algorithm’s best performance [14,48].

Repeated spatial validation estimates performance at new sample locations on dates represented in training. It does not establish performance in independent fields, seasons, or unseen dates. Spatial grouping and buffer sensitivity reduce some concerns about close neighbors [28,42], but cannot establish the absence of residual spatial dependence. LODO additionally changes date coverage and the target spectral and LAI distributions. Its substantial date-specific biases should guide application scope rather than be obscured by pooled accuracy [43].

The farmer-managed setting spans management conditions encountered in local production, but incomplete field-level records of cultivar, planting density, row spacing, fertilization, irrigation, and crop protection limit management-specific interpretation. Sampling locations were generally selected anew across campaigns rather than maintained as permanent plots. Other uncertainties include canopy segmentation and the mismatch between instrument and image support areas. Approximate DAS provides a common calendar reference rather than verified crop age for each field. As a sensitivity check within this single season, replacing approximate DAS with cumulative growing degree days for the same five campaign dates produced nearly identical model behavior because both variables encoded the same date sequence. Growing degree days or observed phenological stages may become more informative across environments when reliable field-specific sowing dates, temperature records, and independent multi-year or multi-site observations are available [20,49].

5. Conclusions

This study provides a reproducible comparison of full-plot, canopy, paired-difference, neighborhood, and approximate-DAS inputs for summer maize LAI estimation under residue-mixed conditions. Spectral scheme comparisons and fixed-capacity controls support conditional benefits from changing the image representation. These findings apply to the sampled production-field conditions and the stated validation design.

Approximate DAS supplied a statistical time reference and accounted for much of the improvement across dates. The controlled comparisons still support relative differences among the spectral schemes under the stated spatial validation, while the time-baseline and residual diagnostics show that the B₃-to-B₄ gain was dominated by between-date adjustment.

High-LAI underestimation and unseen-date biases remained important limitations. The results support application to new locations under dates and production conditions represented in training. Further evaluation should combine field-level agronomic information, reliable developmental or thermal-time descriptors, and canopy structural observations across independent seasons and locations. Within its stated scope, the dual-domain framework offers a reproducible basis for comparing background screening, paired differences, and neighborhood information in farmer-managed maize fields.