Method for estimating leaf area of single plant of summer maize based on representative leaf

Abstract

The application discloses a kind of summer corn single plant leaf area estimation method based on representative leaf, to solve the technical problem that existing leaf area estimation method cannot consider convenience and precision simultaneously.Through in the stable window of leaf area of tasseling-matured period, only 3-5 representative leaves (preferably 4) are measured, and the estimation of single plant leaf area can be completed.Compared with the traditional method, the sampling labor intensity is significantly reduced without reducing the estimation accuracy, and the operation efficiency of single plant leaf area measurement is improved.The fitting function parameters of each corn are completely determined by the data of 3-5 leaves measured by the plant itself, and the linear equation set is solved without any pre-calibrated empirical coefficient or regression model, so that the estimation method can be directly applied to summer corn plants of different varieties, different planting densities and different geographical regions without any field calibration or model adjustment.

Description

Technical Field

[0001] This invention relates to the field of crop leaf area measurement technology, specifically to a method for estimating the leaf area of ​​a single summer maize plant based on representative leaves. Background Technology

[0002] The period from tasseling to milk stage in summer maize is a critical stage for grain formation and yield composition, and also the period when the plant's photosynthetic efficiency is at its highest. Among these stages, the leaf is the main organ for photosynthesis in summer maize, and the size of the leaf area (LA) directly affects the accumulation of photosynthetic products, biomass allocation, and final yield. Accurately estimating the leaf area per plant is of great significance for crop model parameterization, growth assessment, and yield prediction.

[0003] Currently, methods for obtaining single-plant leaf area are mainly divided into two categories: direct measurement methods and indirect estimation methods. Direct measurement methods include leaf area metering, grid method, punch-and-weigh method, and length-width coefficient method. Among these, the length-width coefficient method calculates single-leaf area by measuring the leaf length (L) and maximum width (W) and multiplying them by a shape factor (k). It has the advantages of simple calculation, low cost, and high accuracy, and is therefore widely used in research. However, direct measurement methods usually require measuring all leaves of the plant individually, which is cumbersome, time-consuming, and destructive, making it difficult to implement efficiently in large-scale field surveys.

[0004] Indirect estimation methods include regression coefficient methods, single-leaf representation methods, and image processing methods. The regression coefficient method predicts the leaf area of ​​a single plant by establishing a statistical regression model between the area of ​​a small number of leaves and the total area of ​​the plant. However, this model is often significantly affected by factors such as variety, density, and growth stage, resulting in insufficient universality. Single-leaf representation methods (such as the 7th leaf method and the leaf width sum method) estimate the leaf area of ​​a single plant by multiplying the area of ​​a leaf at a fixed leaf position by an empirical coefficient. This method is simple to operate but has low accuracy and poor adaptability to different varieties and leaf types, leading to larger errors. In recent years, with the development of image recognition and machine learning technologies, image processing methods based on photography or scanning can achieve higher accuracy in leaf area measurement. However, in cases where plants are tall after tasseling and leaves overlap, destructive sampling or complex image segmentation is still required, limiting its widespread application.

[0005] The information disclosed in this background section is intended only to enhance the understanding of the background technology of this disclosure and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] In view of at least one of the above technical problems, this disclosure provides a method for estimating the leaf area of ​​a single summer maize plant based on representative leaves, aiming to solve the technical problem that existing leaf area estimation methods cannot balance convenience and accuracy.

[0007] According to one aspect of this disclosure, a method for estimating the leaf area of ​​a single summer maize plant based on representative leaves is provided, comprising the following steps: (1) Obtain the total number of leaves N of the summer maize plants to be tested during the tasseling to milk stage; (2) Based on the number of undetermined parameters in the preset polynomial fitting function p Select the corresponding option p A representative leaf, and p Choose 3, 4, or 5; when p=3 At that time, select the first, eighth, and last leaves from top to bottom; when p=4 When selecting leaves, choose the 1st, 5th, 11th, and last leaf from top to bottom; when p=5 When selecting leaves, choose the first, second, eighth, and last two leaves from top to bottom; (3) Corresponding measurement p The single leaf area of ​​the representative leaf described in the paper S ; (4) Construction p-1 Polynomial fitting function y=a p-1 x p-1 +a p-2 x p-2 +…+a 1 x+a 0 ; in, x The leaf arrangement is from top to bottom. y This represents the area of ​​a single leaf corresponding to the phyllotaxis. (5) Based on the determination in step (2) p The coefficients of the polynomial fitting function are calculated based on the leaf area of ​​the corresponding representative leaf obtained from each leaf sequence and step (3). a 0 ，a 1 ，…，a p-1 ; (6) Based on the polynomial fitting function obtained in step (5), calculate the leaf order respectively. x =1, 2, ..., N The total leaf area of ​​a single plant is obtained by summing the estimated areas of the individual leaves. LA total .

[0008] In some embodiments of this disclosure, in step (4), a cubic polynomial fitting function is constructed. y= a 3 x 3 +a 2 x 2 +a 1 x+a 0 Furthermore, the first, fifth, eleventh, and last leaves from top to bottom were selected as representative leaves.

[0009] In some embodiments of this disclosure, in step (3), the leaf length of the leaf to be tested is measured. L and maximum leaf width D Calculate the area of ​​a single leaf S=k×L×D ;in, k This is the shape factor.

[0010] In some embodiments of this disclosure, in step (3), the shape coefficients corresponding to the blades at different positions are... k The values ​​are different.

[0011] In some embodiments of this disclosure, in step (3), several leaves are randomly collected from the field to be tested, and the leaf area is measured using a leaf area meter or a scanner. S s In addition to length L and width D, the average shape coefficient of the field or variety can be deduced. k s = S s / (L×D), let the shape factor k=k s .

[0012] In some embodiments of this disclosure, in step (5), based on the determination in step (2) p The leaf area of ​​the representative leaf measured in each leaf sequence and step (3) corresponds to the construction of a structure containing... p A system of linear equations: .

[0013] In some embodiments of this disclosure, in step (6), the total leaf area per plant is... .

[0014] One or more technical solutions provided in the embodiments of this application have at least one of the following technical effects or advantages: 1. By measuring only 3-5 representative leaves (preferably 4) within the stable leaf area window of the tasseling to milk stage, the leaf area of ​​a single plant can be estimated. Compared with traditional methods, this method significantly reduces the labor intensity of sampling and improves the operational efficiency of single-plant leaf area measurement without reducing the estimation accuracy.

[0015] 2. The fitting function parameters for each corn plant are uniquely determined by solving a system of linear equations based on data from 3 to 5 leaves measured on that plant. No pre-calibrated empirical coefficients or regression models are required, thus allowing the estimation method to be directly applied to summer corn plants of different varieties, planting densities, and geographical regions without any on-site calibration or model adjustment.

[0016] 3. The coefficients of the polynomial fitting function directly determine the curve shape of the leaf area distribution along the phyllotaxis, including the slope of the rising segment, the peak position, and the steepness of the falling segment. These parameters are related to biological traits such as the position of the ear leaf and the concentration of leaf area. Therefore, by analyzing the values ​​of the fitting coefficients, it is possible to diagnose whether there are measurement errors, plant abnormalities, or diseases. It can also be used for morphological comparison between different varieties and for monitoring growth dynamics.

[0017] 4. Based on empirical value charts, the shape coefficients of corresponding leaf positions are determined, thus taking into account the changes in leaf shape with leaf position. This can effectively reduce the systematic error in single leaf area measurement and improve the estimation accuracy of total leaf area of ​​a single plant. Attached Figure Description

[0018] Figure 1 This is a spatial distribution map of leaf area of ​​a single summer maize plant at an experimental station in Zhengzhou, as shown in one embodiment of this application.

[0019] Figure 2 This is a diagram showing the leaf area coefficient k values ​​in one embodiment of this application.

[0020] Figure 3 This is a spatial distribution map of the leaf LA of a single summer maize plant fitted with different functions in one embodiment of this application.

[0021] Figure 4 The following is a quadratic function simulation of the spatial distribution curve of leaf area for different leaf groups in one embodiment of this application (Figures a, b, c, d, e, and f correspond to leaf groups 12, 13, 14, 15, 16, and 17, respectively).

[0022] Figure 5 The following is a cubic function simulation of the spatial distribution curve of leaf area for different leaf groups in one embodiment of this application (Figures a, b, c, d, e, and f correspond to leaf groups 12, 13, 14, 15, 16, and 17, respectively).

[0023] Figure 6The following is a quadratic function simulation of the spatial distribution curve of leaf area for different leaf groups in one embodiment of this application (Figures a, b, c, d, e, and f correspond to leaf groups 12, 13, 14, 15, 16, and 17, respectively). Detailed Implementation

[0024] To better understand the technical solution of this application, the above technical solution will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] To address the technical problem that existing leaf area estimation methods cannot balance convenience and accuracy, this paper discloses a method for estimating the leaf area of ​​a single summer maize plant based on representative leaves. Taking a single maize plant as the object, the method measures the leaf area of ​​a small number of specific leaf positions, and then reconstructs the leaf area of ​​all leaves of the whole plant based on the spatial distribution function. The aim is to use the fewest leaf measurement data to most accurately infer the leaf area of ​​all leaves of the whole maize plant, thereby achieving an accurate estimation of the total leaf area of ​​a single plant.

[0026] Considering that the leaf area of ​​summer maize changes dynamically throughout its growth period, measurements taken during rapid leaf growth or the onset of senescence are insufficient to represent the typical state of the plant at that stage, leading to unstable or unrepeatable estimation results. Through long-term practical research, the inventors have discovered that the tasseling-to-milk stage of summer maize is a critical period for the plant's transition from vegetative to reproductive growth, which determines maize yield. During this period, all leaves of the summer maize plant are fully expanded, the total leaf area reaches its maximum and remains relatively stable, and the vertical distribution of leaves exhibits a single-peak curve pattern of "smaller at the top and bottom, larger in the middle," with the leaf area near the ear being the largest, gradually decreasing upwards and downwards, and the lower leaves decreasing at a faster rate than the upper leaves. Therefore, in this embodiment, summer maize during the tasseling-to-milk stage is used as the target, and leaf samples are taken and measured during this specific period. This utilizes the stability of the leaf area during this period, avoiding estimation errors caused by improper measurement timing, thereby improving the repeatability and reliability of this estimation method.

[0027] Specifically, in this embodiment, based on statistical analysis of nearly 30 years of observation data from 35 agricultural meteorological observation stations in Henan Province, the tasseling period of summer maize in Henan Province is between July 25th and August 10th, and the milk stage is between August 15th and August 31st. Therefore, in this example, a random survey was conducted at 36 survey points in 23 counties (cities) of Henan Province from 2023 to 2025, including 15 survey points in 2023, 11 survey points in 2024, and 10 survey points in 2025. The selected survey plots showed uniform growth of summer maize to ensure they could represent the local average planting level. The field survey time window was then set to August 10th each year, a date that falls during the transition between the tasseling and milk stages, a plateau period after the leaf area has reached its peak and has not yet significantly decreased. In other embodiments, the field survey time window can be set within a range of August 10th ± 5 days each year, depending on meteorological and climatic conditions. During the sampling process, four fixed measuring points were set up in the field. Ten plants were selected at each measuring point, and their height was measured. The plants were divided into three groups according to the dispersion of their height data. The average height of each group was used as the reference height for sampling. One plant was taken at each reference height, for a total of three plants. The plants were cut off at ground level, the leaves were separated from the main stem, the leaf sequence was recorded, and the plants were placed in a plastic bag and taken back.

[0028] In addition, in this embodiment, to ensure the accuracy of the estimation, before the sampling survey, the summer maize plants in the target field are sampled and observed to confirm that they are in the tasseling to milk stage and that the leaves have no obvious diseases, pests or mechanical damage. Plants with severe missing or deformed leaves are removed.

[0029] Before reconstructing the whole-plant leaf area distribution curve, it is necessary to first determine the length of the curve's domain, i.e., the total number of leaves. The total number of leaves per summer maize plant varies among different varieties and under different growth conditions (usually 12–17 leaves). Through practical research, the inventors discovered that existing estimation methods, such as the representative leaf method (e.g., the 7th leaf method), completely disregard the differences in the total number of leaves, assuming all plants have the same leaf arrangement structure. This leads to significant estimation errors for extreme leaf groups such as 12 or 17 leaves. Therefore, in this embodiment, before measurement, the summer maize plant to be measured is observed and counted leaf by leaf from top to bottom, and the total number of leaves N is recorded.

[0030] Specifically, in this example, actual field surveys revealed six common types of total leaf counts for summer maize plants: 12, 13, 14, 15, 16, and 17. Based on the total leaf count, individual plants were grouped: 5 survey points for the 12-leaf group, 11 for the 13-leaf group, 12 for the 14-leaf group, 5 for the 15-leaf group, 2 for the 16-leaf group, and 1 for the 17-leaf group. Furthermore, all subsequent steps were calculated based on the total leaf count N of the plant. By using the total leaf count as an independent parameter, subsequent steps such as leaf order selection, curve fitting, and summation could be adaptively adjusted for each plant, ensuring the universality and high accuracy of this estimation method across different leaf groups.

[0031] In measuring the leaf area of ​​individual leaves, the inventors discovered that existing representative leaf methods, such as the single-leaf representation method and the odd-even leaf method, suffer from efficiency and accuracy issues. Specifically, for the single-leaf representation method, such as the 7th-leaf method, the area of ​​the 7th leaf from top to bottom is multiplied by an empirical coefficient of 9.04 to represent the total leaf area of ​​the plant. Although this method is relatively simple to operate and requires measuring a small number of leaves, the final leaf area estimation accuracy is low, with a relative error typically of 5% to 6%. Furthermore, the empirical coefficient is heavily dependent on variety, density, and region, exhibiting poor transferability. As for the odd-even leaf method, it represents a single plant by summing the areas of all odd-numbered and even-numbered leaves. Compared to the single-leaf representation method, this method improves accuracy, but it requires measuring about half of the leaves (e.g., 7 leaves for a 14-leaf plant), resulting in relatively low measurement efficiency and cumbersome work.

[0032] Therefore, in this embodiment, a specific phyllotaxis combination is selected for the leaves of the plant to be measured. Specifically, in this example, the number of undetermined parameters of the polynomial function used for subsequent leaf area fitting is determined. p ( p ≥3), select p A representative set of leaves is selected so that the leaf sequence of these leaves is spatially rationally distributed and can uniquely and stably determine all the parameters of the polynomial. Specifically, for the quadratic fitting function, in this example, three leaves with leaf sequences of 1, 8, and the last leaf are selected from top to bottom; for the cubic fitting function, four leaves with leaf sequences of 1, 5, 11, and the last leaf are selected from top to bottom; and for the quartic fitting function, five leaves with leaf sequences of 1, 2, 8, and the last two leaves are selected from top to bottom.

[0033] For example, when establishing a cubic fitting function for a plant with a total of 12 leaves, leaves 1, 5, 11, and 12 are selected. From a purely mathematical fitting perspective, leaves 11 and 12 selected in this example are adjacent in leaf order, and the two sampling points are relatively close. It is generally believed that this sampling may affect the stability of parameter solution. The inventor also had this understanding in the early stages of practice. The inventor tried to use a percentage rule for leaf order selection, see the percentage rule represented by equation (1), the 11th leaf... i Phylogeny of a representative leaf N i for: (1).

[0034] The calculation result of Equation (1) is rounded to the nearest whole number or rounded down to obtain the actual leaf order. However, after comparing the actual measured leaf area with the estimated result, the inventors found a certain deviation. Therefore, the inventors conducted further research and found that although the percentage rule can achieve a relatively uniform leaf order selection on the surface, the position of the two middle points selected depends on the total number of leaves N. For example, for a cubic fitting function, when p=4 and N=14, the third leaf order based on the percentage rule is approximately the 9th or 10th leaf. However, based on the inventors' experience, the peak value of corn leaves usually appears near the 7th to 9th leaves, and the 9th to 10th leaves have already begun to decline. Therefore, a fixed leaf order is used in this example, and experiments have shown that this fixed leaf order selection can obtain a higher estimation accuracy (RE=1.37% for the 12-leaf group, r=0.989). For the reasons, see [link to relevant documentation]. Figure 1 Based on four consecutive years of observation data from three varieties at an agricultural meteorological experimental station in Zhengzhou, the leaf area distribution (LA) of individual leaves during the tasseling-milk stage of summer maize exhibits a unimodal curve distribution, with smaller areas at the top and bottom and larger areas in the middle. This distribution shows a clear spatial and hierarchical pattern, with the LA being largest near the ear leaf and gradually decreasing upwards and downwards. The rate of LA decrease is greater for lower leaves than for upper leaves. The spatial distribution patterns in 2022, 2023, and 2025 show good consistency. However, due to varietal differences, the LA of the upper and middle leaves in 2024 was significantly smaller than in other years, although the spatial variation pattern of leaf area was the same as in other years. Therefore, the inventors believe that the leaf area distribution curve during the tasseling-milk stage of summer maize possesses high smoothness and biological regularity, namely, the lower leaf area monotonically decreases with leaf order. Thus, measurements from two adjacent points can provide effective local slope information, and combined with sampling points at the top and upper middle parts, the morphology of the entire curve can be uniquely and stably determined.

[0035] After determining the phyllotaxis combination of representative leaves, the area of ​​the selected representative leaves needs to be measured. Commonly used leaf area measurement methods include leaf area metering, grid method, and perforation and weighing method. The inventors found that although the above methods are highly accurate, they require the leaves to be separated from the plant for processing, which is cumbersome and destructive to the plant, making them unsuitable for subsequent observations where the plant needs to be preserved. The traditional length-width coefficient method estimates the area by measuring the leaf length and maximum width and then multiplying it by the shape coefficient. Although this method is simple and fast, current applications use a uniform shape coefficient k value (usually a fixed value between 0.75 and 0.78) for all leaves. However, the inventors found in long-term observation that the shape of maize leaves varies with leaf position, showing a pattern of narrow and long upper leaves (smaller k value), wide and short middle leaves (larger k value), and thin and long lower leaves (smaller k value). If the same shape coefficient k value is used for all leaves, the area of ​​the upper leaves will be overestimated, the middle leaves underestimated, and the lower leaves overestimated, thus introducing systematic errors.

[0036] Therefore, in this embodiment, to accurately and efficiently obtain the area of ​​the selected representative leaves, the shape coefficient is adaptively selected based on leaf position stratification and the inventor's long-term practical experience. Specifically, for each selected leaf, the leaf length L (cm) and maximum leaf width D (cm) are measured with a ruler, and then different shape coefficients are selected according to the leaf position of the leaf. k Value, specific experience k See value Figure 2 (The shape coefficients corresponding to leaf positions 1-17 are 0.67, 0.75, 0.75, 0.78, 0.79, 0.80, 0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.78, 0.77, 0.74, and 0.73, respectively.) Based on the shape coefficients corresponding to different leaf positions, the single leaf area S = k × L × D can be calculated. Therefore, by using differentiated shape coefficient values ​​for different leaf positions, the biological fact that the shape of maize leaves changes with node position can be more accurately reflected, thus helping to improve the accuracy of single leaf area measurement.

[0037] In other embodiments, a small number of leaves are randomly collected from the field to be tested, and the measured area is obtained by scanning or leaf area metering. S s And the corresponding leaf length and maximum leaf width, thus deduce the average shape coefficient of the field or the variety. k s = S s / (L×D), and then use it as a shape factor for calculating the area of ​​representative leaves. However, experiments have shown that this method is less reliable than the empirical method in this example. But compared to the conventional method of using a fixed shape factor between 0.75 and 0.78 for different fields and varieties, the accuracy can be effectively improved.

[0038] Furthermore, based on the measured leaf surface data of representative leaves, the leaf area of ​​all leaves (12-17 leaves) of the whole plant is reconstructed, thereby calculating the total leaf area.

[0039] Commonly used population statistical regression models often first establish the leaf area of ​​a single leaf using a large sample size (usually dozens or even hundreds of plants). LA sig Total leaf area per plant LA total Linear or nonlinear regression equations between them, for example LA total = a × LA sig + b However, this method requires the prior collection of a large amount of data to calibrate the regression coefficients, and the regression relationship is only applicable to populations with the same variety, density, and growth conditions as the modeling sample. Once the conditions change, recalibration is required. In addition, such regression models are essentially statistical average relationships and cannot reflect the true variation between individual plants, resulting in significant errors in the prediction of extreme plants.

[0040] Therefore, in this embodiment, a function equation is independently constructed and solved for each maize plant to be tested, so as not to rely on any pre-established empirical regression coefficients. The specific steps include the following: (11) The form of the fitting function is predetermined as follows: p-1 Polynomial of degree: y=a p-1 x p-1 +a p-2 x p-2 +…+a 1 x+a 0 (2).

[0041] in, p The same number of representative leaves were selected; x Phyllostachys from top to bottom ( x =1, 2, ..., N ), y The area of ​​a single leaf (cm²) corresponding to this phyllotaxis. 2 ), a0 ，a 1 ，…，a p-1 These are the parameters to be determined.

[0042] Furthermore, the fitting function in this example differs from conventional statistical regression analysis that uses polynomials as a black-box fitting tool and employs least squares methods based on a large number of samples. In this case, the coefficients of the fitting function collectively determine the complete shape of the leaf area distribution curve along the phyllotaxis. Specifically, the constant term... a 0 The primary influence is on the initial value of the top leaf (phyllography 1); the coefficient of the linear term. a 1 Used to control the initial slope of the curve in the rising segment; coefficients of quadratic and higher terms. a 2 , a 3 The coefficients, in turn, progressively influence the curve's curvature, peak position, asymmetry, and the steepness of the descent, directly reflecting the specific biological characteristics of the plant's leaf spatial distribution, such as the peak phyllotaxis position, the width of the ear-leaf region, and the rate of decline in lower leaf area. Therefore, by analyzing the values ​​of the fitting coefficients, we can diagnose measurement errors, plant abnormalities, or diseases, and it can also be used for morphological comparisons between different varieties and for monitoring growth dynamics. Furthermore, by solving the system of equations to obtain a set of definite coefficients, the leaf area spatial distribution curve of the plant can be completely reconstructed.

[0043] (12) Select the p Phylogeny of a representative leaf x 1 ，x 2 ，…，x p and its measured leaf area y 1 ，y 2 ，…，y p Substituting each into the polynomial, we obtain the following: p A system of linear equations: (3).

[0044] This system of equations is a linear system that can be solved directly (e.g., using Cramer's rule or matrix inversion) to obtain the parameters. a 0 ，a 1 ，…，a p-1 Then, the spatial distribution curve function of leaf area specific to this plant is obtained.

[0045] (13) Calculate the total leaf area of ​​a single plant LA total , leaf order x =1, 2, ..., N After substituting the values ​​into the obtained polynomial function, the estimated area of ​​each leaf is obtained. Then, the total leaf area of ​​a single plant is calculated by summing the results. LA total : (4).

[0046] Therefore, by using polynomial function fitting, no prior calibration is required, and no assumptions about variety, density, or region need to be made beforehand. This allows the measurement data for each plant to independently determine its fitting function. Even if new varieties or abnormal climates alter the leaf area distribution pattern, the fitting remains applicable as long as the functional form of the unimodal curve is still approximately valid, whereas regression models would completely fail in this situation. Furthermore, since the number of equations equals the number of unknowns, the original curve can be accurately recovered when there are no measurement errors. When random errors exist in actual measurements, the low condition number of the coefficient matrix due to the selected leaf order makes the parameter solution robust to measurement noise.

[0047] Specifically, this example uses a cubic function with 14 leaves (N=14). During the tasseling to milk stage of summer maize, four leaves (p=4) with leaf numbers 1, 5, 11, and 14 are selected. The corresponding leaf areas are measured and substituted into the established cubic function. The resulting system of four linear function equations is as follows: (5).

[0048] Corresponding solution parameters a 3 、a 2 、a 1 、a 0 Then for x =1, 2, ..., N For other phyllotaxis, after calculating the area of ​​the single leaf corresponding to the phyllotaxis, the total leaf area of ​​a single plant is obtained by summing the results based on equation (4). LA total .

[0049] See Figure 1 Based on the average LA observation data from a Zhengzhou agricultural meteorological experimental station for four consecutive years from 2022 to 2025, see [reference]. Figure 3The spatial distribution of LA (latitude and longitude) of individual summer maize plants was fitted using quadratic, cubic, and quartic functions, respectively. It was observed that the quartic function curve was closer to the measured value. Furthermore, the model's fitting effect was evaluated using absolute error (AE) and relative error (RE). Smaller errors indicate higher simulation accuracy. The correlation coefficient (r) was also used to characterize the correlation between simulated and measured values; the closer r is to 1, the stronger the positive correlation between the simulated and measured values. Specific results are shown in Table 1 (where * indicates significant (significance less than 0.05), and ** indicates highly significant (significance less than 0.01)).

[0050] Table 1 Error analysis of different fitting function types

[0051] Based on Table 1, the absolute coefficients R of cubic and quartic functions compared to quadratic functions are... 2 It is large, and the AE and RE of the quadratic function are minimized.

[0052] Furthermore, this example performs error analysis on the simulation of single-plant leaf area using different polynomial fitting functions. See [link / reference] Figure 4 As can be seen from the spatial distribution diagram of the quadratic function simulation, the quadratic function can simulate the variation pattern of LA (leaf length) of a single summer maize plant. Among them, the 16-leaf group showed the best simulation effect and the smallest simulation error, while the 17-leaf group had the largest simulation error. The corresponding error analysis is shown in Table 2.

[0053] Table 2 Simulation errors of quadratic functions with different leaf groups

[0054] See Figure 5 As can be seen from the spatial distribution diagram of the cubic function simulation, the cubic function can simulate the variation pattern of LA (leaf length) of a single summer maize plant. Among them, the 12-leaf group showed the best simulation effect and the smallest simulation error, while the 17-leaf group had the largest simulation error. The corresponding error analysis is shown in Table 3.

[0055] Table 3 Simulation errors of cubic functions with different leaf groups

[0056] See Figure 6 As can be seen from the spatial distribution diagram of the quartic function simulation, the quartic function can simulate the variation pattern of LA (leaf length) of a single summer maize plant. Among them, the 17-leaf group showed the best simulation effect and the smallest simulation error, while the 13-leaf group had the largest simulation error. The corresponding error analysis is shown in Table 4.

[0057] Table 4 Simulation errors of different leaf groups for quartic functions

[0058] As can be seen from the above data, when applying the quadratic, cubic, and quartic function methods to estimate the leaf area of ​​a single plant, the correlation coefficients for all leaf groups were greater than 0.95. In contrast, the quadratic function method had a high RE (irreactivity ratio) of 10.16% for the 17-leaf group, and the quartic function method had a RE of 2.60% for the 13-leaf group, both less stable than the cubic function. The maximum RE of the cubic function method across all leaf groups was only 2.78%, far lower than the maximum RE of the quadratic function (10.16%), and it achieved the best balance between accuracy and operational efficiency (4 leaves). Therefore, in this embodiment, the cubic function is chosen as the preferred fitting model.

[0059] To illustrate the advantages of the polynomial function fitting calculation method based on a specific leaf order disclosed in this embodiment, the quadratic function method, cubic function method, quartic function method, and common seventh leaf correlation method, eighth leaf correlation method, ninth leaf correlation method, and odd-even leaf method were analyzed and compared on the same 36 survey point data. The results are shown in Table 5.

[0060] Table 5 Comparative Analysis of Different Methods for Calculating LA in Individual Plants

[0061] It is evident that the odd-even leaf method has the highest accuracy (RE=1.29%, r=0.99), but it requires measuring approximately half of the leaves (e.g., 7 leaves need to be measured for a 14-leaf plant), resulting in lower work efficiency. The cubic function method is second only to the odd-even leaf method in accuracy (RE=1.70%, r=0.99), while only requiring the measurement of 4 leaves, making its operational efficiency approximately 1.75 times that of the odd-even leaf method. The single-leaf correlation method has the largest error (RE>4.9%), with a correlation coefficient of only 0.78–0.86. Therefore, quadratic, cubic, and quartic function curves can all simulate the spatial distribution of leaves, with the cubic function curve exhibiting the smallest error and the highest correlation coefficient, thus providing a better simulation of the spatial distribution pattern of leaf LA in summer maize.

[0062] Although some preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0063] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this application and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for estimating the leaf area of ​​a single summer maize plant based on representative leaves, characterized in that, Includes the following steps: (1) Obtain the total number of leaves N of the summer maize plants to be tested during the tasseling to milk stage; (2) Based on the number of undetermined parameters in the preset polynomial fitting function p Select the corresponding option p A representative leaf, and p Choose 3, 4, or 5; when p=3 At that time, select the first, eighth, and last leaves from top to bottom; when p=4 When selecting leaves, choose the 1st, 5th, 11th, and last leaf from top to bottom; when p=5 When selecting leaves, choose the first, second, eighth, and last two leaves from top to bottom; (3) Corresponding measurement p The single leaf area of ​​the representative leaf described in the paper S ; (4) Construction p-1 Polynomial fitting function y=a p-1 x p-1 +a p-2 x p-2 +…+a 1 x+a 0 ; in, x The leaf arrangement is from top to bottom. y This represents the area of ​​a single leaf corresponding to the phyllotaxis. (5) Based on the determination in step (2) p The coefficients of the polynomial fitting function are calculated based on the leaf area of ​​the corresponding representative leaf obtained from each leaf sequence and step (3). a 0 ，a 1 ，…，a p-1 ; (6) Based on the polynomial fitting function obtained in step (5), calculate the leaf order respectively. x =1, 2, ..., N The total leaf area of ​​a single plant is obtained by summing the estimated areas of the individual leaves. LA total .

2. The method for estimating the leaf area of ​​a single summer maize plant according to claim 1, characterized in that, In step (4), a cubic polynomial fitting function is constructed. y=a 3 x 3 +a 2 x 2 +a 1 x+a 0 Furthermore, the first, fifth, eleventh, and last leaves from top to bottom were selected as representative leaves.

3. The method for estimating the leaf area of ​​a single summer maize plant according to claim 1, characterized in that, In step (3), the leaf length of the leaf to be tested is measured. L and maximum leaf width D Calculate the area of ​​a single leaf S=k×L×D ;in, k This is the shape factor.

4. The method for estimating the leaf area of ​​a single summer maize plant according to claim 3, characterized in that, In step (3), the shape coefficients corresponding to the blades at different positions k The values ​​are different.

5. The method for estimating the leaf area of ​​a single summer maize plant according to claim 3, characterized in that, In step (3), several leaves are randomly collected from the field to be tested, and the leaf area is measured using a leaf area meter or a scanner. S s In addition to length L and width D, the average shape coefficient of the field or variety can be deduced. k s = S s / (L×D), let the shape factor k=k s .

6. The method for estimating the leaf area of ​​a single summer maize plant according to claim 1, characterized in that, In step (5), based on the determination in step (2) p The leaf area of ​​the representative leaf measured in each leaf sequence and step (3) corresponds to the construction of a structure containing... p A system of linear equations: 。 7. The method for estimating the leaf area of ​​a single summer maize plant according to claim 1, characterized in that, In step (6), the total leaf area of ​​a single plant is... 。

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