Method for measuring leaf area index based on fisheye image

Abstract

The application discloses a kind of leaf area index measurement method based on fish-eye image, through the way that smart phone is equipped with super wide-angle lens and plants canopy fish-eye image is shot, based on the farmland leaf area index monitoring method of machine vision technology.The design points of the application include that the shooting mode of mobile phone+fish-eye camera is applied to crop canopy, efficient image processing is carried out to fish-eye image, and simple and fast LAI difference calculation method is designed using the definition and integral formula of LAI.Meanwhile, the application is tested and applied in multiple fields and experimental scenes, and the measurement results of traditional instruments and professional software are verified in accuracy.The results show that the equipment and algorithm of the application can effectively adapt to LAI measurement tasks including sunny day, rainy day and other different scenes, have good accuracy and stability for paddy field and dry land, and can be well popularized to different agricultural monitoring tasks.

Description

Technical Field

[0001] This invention belongs to the field of crop phenotypic monitoring technology. Specifically, it refers to a method for measuring crop leaf area index by taking fisheye images of plant canopies using a smartphone equipped with an ultra-wide-angle camera, and performing image processing based on machine vision technology. Background Technology

[0002] The leaf area index (LAI) of vegetation canopy is an important reference indicator for studying plant growth status and physiological characteristics. It not only reflects the morphological structure of the vegetation community but also the canopy's response to changes in the external environment. Therefore, accurate measurement of LAI is of great significance for evaluating crop growth, identifying environmental stresses in farmland, and exploring plant growth patterns.

[0003] LAI is numerically defined as the integral of leaf area density over canopy depth (Equation 1), which is the distribution of leaves on different horizontal planes at different heights. Conceptually, it is equivalent to the sum of the upper surface area (light-receiving surface) of all leaves per unit land area.

[0004]

[0005] In the formula, H is the specified canopy height, and l(h) is the leaf area density function at height h.

[0006] Traditional methods for measuring LAI include destructive sampling, litter sampling, and point-slant sampling. These methods require manual collection of crop leaves, which is labor-intensive and damages the plants, resulting in the inability to obtain continuous observation data for the same vegetation cover area. In terms of indirect measurement techniques, optical instruments are widely used. Commonly used instruments include Li-cor canopy analyzers, TRAC instruments, and AccuPAR devices. They are characterized by non-destructive testing, convenience, and high efficiency, and are widely used in ground measurement of LAI. However, there are still some application problems with the current mature measuring instruments: (1) Due to the low resolution of the instrument lens and the inability to adjust the aperture, the instrument can only be used when the solar altitude angle is below 15-20°, and the time available for measurement is limited each day; (2) Instruments designed based on optical principles need to be inserted under the crop canopy and horizontally towards the sky for measurement, which makes it impossible for the instrument to detect low-growing vegetation or seedlings (the canopy depth is insufficient for the instrument to enter); (3) Mainstream LAI measuring instruments are expensive, rely on imports, and require professional operation, making it difficult to promote their application in the field. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method for calculating leaf area index based on fisheye images. The method involves capturing fisheye images of plant canopies using a smartphone equipped with an ultra-wide-angle lens, and then calculating the leaf area index of farmland based on machine vision technology.

[0008] The key design features of this invention include applying a mobile phone + fisheye camera shooting mode to crop canopy, performing efficient image processing on fisheye images, and designing a simple and fast LAI difference calculation method using the definition and integral formula of LAI. Based on the definition of LAI and optical measurement principles, this invention designs an extended shooting method using a smartphone equipped with a fisheye lens. It utilizes the smartphone's rear camera and a lightweight external lens to construct a convenient fisheye image acquisition device, and optimizes the image processing through machine vision algorithms to achieve real-time monitoring of crop leaf area index (LAI) on a mobile phone. This method is applicable to various scenarios, exhibits high accuracy, strong stability, and low cost, and is of great significance for realizing large-scale, high-throughput crop phenotypic monitoring and growth evaluation.

[0009] The technical solution adopted in this invention is: a leaf area index calculation method based on fisheye images, comprising the following steps:

[0010] Step 1: Acquire fisheye images of different types of canopies;

[0011] Step 2: Process the acquired fisheye image using image processing technology to reduce background noise and obtain a distortion-free, computable pixel matrix.

[0012] Step 3: Divide the processed fisheye image into an infinite number of rings. The pixels on each ring are approximately on the same plane. Calculate the vegetation contact frequency in the rings and integrate it to obtain the leaf area index value.

[0013] Furthermore, in step 1, fisheye images of different types of canopies are collected using a smartphone and a fisheye lens. First, the smartphone is connected to the shooting pole via Bluetooth. The fisheye lens is then aligned with the main rear camera lens of the smartphone and fixed in place, thus forming a simple measuring pole. After the lens is mounted, the camera angle is determined according to the type and development level of the plant being photographed. When shooting, the camera should be kept away from canopies with uneven growth at the edges and kept horizontal.

[0014] Furthermore, the imaging photosensitive plane of the fisheye lens is a circle inscribed in the camera's target surface. A coordinate system is established with the center of this circle as the origin. Therefore, the viewing angle θ at each point in the image can be calculated using Equation 2:

[0015]

[0016] In the formula, x and y are the pixel coordinates, and R is the radius of the image.

[0017] Furthermore, the specific implementation method of step 2 is as follows;

[0018] (21) Use downsampling to proportionally reduce the image resolution to speed up the process, and use image cropping program to cut out the invalid areas around the image.

[0019] (22) Based on the HSV color space threshold, vegetation pixel classification is performed, and the vegetation ratio and gap score in each ring are extracted. Different segmentation methods are adopted according to different shooting angles: the RGB image is converted into an HSV image by the algorithm, and the upper and lower limits of the threshold are set. Pixels that exceed the limit are classified as non-vegetation pixels and are not included in the contact score calculation. When the image is taken from inside the canopy upward, the sky pixel is used as the segmentation subject, and the vegetation pixel is obtained after removing the sky pixel. When the shooting angle is overhead, the vegetation is used as the segmentation subject, and the vegetation coverage is obtained directly.

[0020] Furthermore, in step 3, the image annular region is segmented based on the PIL program package to obtain the central circle within the 0-15° observation zenith angle range, as well as concentric annular regions within the ranges of 15-30°, 30-45°, 45-60°, and 60-75°. Considering that the region outside 75° is close to the sampling edge, has severe distortion and a lot of noise, only the part within 75° is calculated.

[0021] Furthermore, the specific implementation method of step 3 is as follows;

[0022] Based on the concept of LAI and the definition of Equation (1), a Poisson calculation model based on contact frequency and gap fraction is proposed. Contact frequency, proposed by Warren Wilson, refers to the probability of sunlight contacting vegetation elements in the canopy when it enters the canopy. Gap fraction refers to the probability of natural light directly entering the reference plane. Under the assumption that the leaves are opaque, the leaf coverage measured in the image analysis is the one-way contact fraction.

[0023]

[0024] In the formula, H is the canopy height, and l(h) is the leaf area density function at height h;

[0025] At a canopy height of h, the average contact fraction is taken as the plant height integral value of the unidirectional contact fraction of each leaf layer, and its calculation formula is:

[0026]

[0027] In the formula, H represents the canopy height, and L(h) represents the leaf area density corresponding to each height h of the plant canopy, that is, the leaf area per unit volume of the canopy. This refers to the direction vector of the observation position, θ v The zenith angle in the direction of observation. Let G be the azimuth angle of the observation direction, and G be the leaf area projection function at height h. Substituting equation (1) into the equation, we get:

[0028]

[0029] (4) shows the correlation between LAI and contact frequency, where By combining equations (5) and (6), we can obtain:

[0030]

[0031]

[0032] Introduction Let θ be the probability density function of the blade tilt angle distribution model, where θ l The zenith angle is the direction in which the blade is tilted. Let be the azimuth angle of the blade tilt, and normalize the condition constraints using equations (7) and (8):

[0033]

[0034]

[0035] By combining the above formulas, the fraction of the canopy space can be obtained. Average contact fraction The relationship between LAI and Nilson is optimized by Nilson into an exponential relationship in equation (9):

[0036]

[0037] in, and Similarly, based on the circular field of view of the fisheye image, without considering the orientation of the incident light rays, it is assumed that the gap fraction measurement depends only on the observed zenith angle θ. v The leaf area index (LAI) is calculated by taking the angle between the incident light direction and the normal vector of the light sensor at the bottom of the canopy. cal The calculation formula can be summarized as follows:

[0038]

[0039] Welles proposed a discrete numerical analytical method for the integral (10) based on multi-view observations, which uses multiple zenith observation angles to divide the rings and segment the average vegetation gap fraction in each ring. Perform a difference operation on the integral (10):

[0040]

[0041] In the formula Si (θ v ) for cos i θ v -1 And W i sinθ v dθ, i represents the angle of division, and the coefficient varies depending on the angle of the division ring.

[0042] Furthermore, five zenith observation angles are used to divide the rings, namely 0-15°, 15-30°, 30-45°, 45-60°, and 60-75°, corresponding to i=1 to i=5 respectively.

[0043] This invention is an applied development based on years of research on non-destructive monitoring of leaf area index in the fields of plant phenotyping and optical remote sensing. Compared with other similar instruments and software, this invention has achieved some new progress and advantages:

[0044] (1) The use of a smartphone with a camera and an extension rod for shooting simplifies the measurement operation. The operation of the smartphone optimizes the data storage and transmission process and significantly reduces costs, making it suitable for promotion to the field management level.

[0045] (2) Image processing and integral calculation are based on Python. The backend code is simple to write and easy to modify. It is suitable for debugging a single image and batch processing of a large number of images. Preprocessing reduces the impact of weather and lighting on gap fraction measurement and provides full visualization conditions for operation and debugging.

[0046] (3) Two perspectives, overhead and low-angle, were designed according to different crops and different field scenes, which made up for the shortcomings of LAI instruments in monitoring low canopies and eliminated the limitation that the instruments could not be used for measurement when the light was strong.

[0047] (4) The algorithm reads the EXIF ​​information (location, time) of the mobile phone image and adds a real-time solar zenith angle calculation function, which can correct the LAI calculation results.

[0048] (5) During the process of completing the present invention, a large-scale sampling experiment was conducted. Comparative experiments were carried out in the fields of common crops such as rice, corn and wheat with traditional methods and commonly used instruments to verify the practicality and accuracy of the present invention. Attached Figure Description

[0049] Figure 1 Schematic diagram of the imaging principle of a fisheye lens;

[0050] Figure 2 Example of a combination of mobile phone + fisheye lens + extension stick;

[0051] Figure 3 Methods and procedures for acquiring canopy fisheye images;

[0052] Figure 4 Definition of Observational Zenith Angle and Schematic Diagram of Fisheye Image Ring Separation Calculation;

[0053] Figure 5 Fisheye image processing and calculation workflow;

[0054] Figure 6 : Accuracy verification of rice shooting test results (the horizontal axis in the right figure is the LAI calculated by the fisheye camera algorithm, and the vertical axis is the LAI value measured by the instrument).

[0055] Figure 7 Verification of rice paddy shooting test results under different scenarios (weather) (the horizontal axis in the right figure is the LAI calculated by the fisheye camera algorithm, and the vertical axis is the LAI value measured by the instrument).

[0056] Figure 8 Verification of rice field overhead photograph test results (the horizontal axis in the right figure is the LAI calculated by the fisheye camera algorithm, and the vertical axis is the LAI value measured by professional software);

[0057] Figure 9 Verification of wheat aerial photography test results at different growth stages (the horizontal axis in the right figure is the LAI calculated by the fisheye camera algorithm, and the vertical axis is the LAI value measured by the oblique photography method);

[0058] Figure 10 : Validation of wheat aerial photography test results (the horizontal axis in the right figure is the LAI calculated by the fisheye camera algorithm, and the vertical axis is the LAI value measured by the oblique photography method). Detailed Implementation

[0059] The technical solution of the present invention will be further described below with reference to the figures and embodiments. The present invention provides a method for calculating leaf area index (LAI) based on fisheye images, comprising the following steps:

[0060] Step 1: Acquire fisheye images of different types of canopies using fisheye imaging technology;

[0061] Currently, most mainstream optical instruments measure the leaf area index (LAI) by measuring the light transmittance within the canopy. Therefore, the wider the field of view, the greater the range of canopy depth that can be obtained, and the more accurate the calculated LAI. The fisheye lens in photography can be applied to this scenario, leading to the development of Digital Hemispherical Photography (DHP) for leaf area index. Unlike ordinary camera lenses, fisheye lenses have a smaller focal length and a wider field of view. External light is significantly refracted at the convex lens, allowing incident light rays with a small angle to the camera plane to fall on the imaging target surface, achieving a 180° hemispherical image. The imaging sensor plane is a circle tangent to the camera target surface. By establishing a coordinate system with the center of this circle as the origin, the viewing angle θ at each point (pixel) in the image can be calculated using Equation 2. Figure 1 ):

[0062]

[0063] In the formula, x and y are pixel coordinates, and R is the radius of the image (1 / 2 of the height of the camera target surface, such as an image with a resolution of 1920×1080 with a height of 1080 and a radius of 540).

[0064] This invention utilizes a smartphone and a fisheye lens to acquire fisheye images of different types of canopies. The smartphone's shooting capabilities and resolution can meet the requirements for canopy image acquisition. Figure 2 The fisheye lens and extension rod are assembled in a simple manner. First, the phone and the shooting rod are connected via Bluetooth. Then, the fisheye lens is aligned with the phone's rear main camera and fixed in place, forming a basic measuring rod. This assembly method effectively avoids noise from road surfaces and people in the wide-angle field of view, reducing the impact of edge effects on the calculation results. After the lens is mounted, according to... Figure 3 The illustrated process involves acquiring fisheye images of different types of canopies. First, the camera angle is determined based on the plant type and development stage. Figure 3 Taking corn in the tasseling stage (shot from inside the canopy looking upwards) and rice in the seedling stage (shot from above the canopy looking downwards) as examples, when shooting, stay away from the unevenly growing edges of the canopy and keep the camera level.

[0065] Step 2: Process the acquired fisheye image using image processing technology to reduce background noise and obtain a distortion-free, computable pixel matrix.

[0066] After acquiring fisheye images, they need to be processed into a computationally achievable image format. Machine vision-based image processing technology will perform a series of operations and calculations from the image to LAI values. Image preprocessing technology is a process of adjusting and balancing the color space, brightness perception, and topological structure attributes of the original image using visual algorithms. The purpose is to highlight the reference subject (vegetation) in the image, reduce noise, eliminate problems such as inconsistent image brightness caused by changes in external light and camera aperture adjustments, standardize the image color space, and parameterize the brightness gamut, thereby improving the accuracy and speed of subsequent visual feature extraction and calculation. Subject segmentation technology is an important part of image processing. Canopy fisheye images are divided into foreground and background, and segmentation technology extracts plant pixels from the background. Threshold-based image segmentation methods are a region-parallel technique that uses one or more set thresholds to divide the image's gray-level histogram into several categories, assuming that objects with gray levels within the same range belong to the same category. Directly utilizing the gray-level characteristics of the image makes this type of method computationally efficient and widely applicable. Image post-processing techniques involve performing pixel statistics and geometric transformations on the vegetation portion after removing the background to extract the canopy gap fraction, and finally calculate the LAI.

[0067] (21) After image acquisition is completed, image preprocessing is performed. The image resolution is reduced proportionally by downsampling to speed up the operation. The invalid areas around the image are cut off by using the image cropping program. The fisheye image is a part that is tangent to the rectangular acquisition plane of the camera. Therefore, there are invalid parts that are occluded at the four corners that need to be cropped.

[0068] (22) Based on the HSV color space threshold, vegetation pixel classification is performed to extract the vegetation proportion and gap rate in the image. Different segmentation methods are adopted according to different shooting angles. The HSV color space (Hue, Saturation, Value) decomposes brightness from color to better perceive the color and brightness differences of different objects in the image. After converting the RGB image to an HSV image through the algorithm, upper and lower thresholds are set. Pixels exceeding the limits are classified as non-vegetation pixels and are not included in the contact score calculation. When the image is taken from inside the canopy upwards (looking up), the sky pixels are used as the segmentation subject, and vegetation pixels are obtained after removing the sky pixels; when the shooting angle is looking down, the vegetation is used as the segmentation subject, and the vegetation coverage is obtained directly.

[0069] (23) Based on the PIL program package, the image annular region is segmented to obtain the central circle within the 0-15° observation zenith angle range, as well as the concentric annular regions within the ranges of 15-30°, 30-45°, 45-60° and 60-75°. Considering that the region outside 75° is close to the sampling edge, has severe distortion and a lot of noise, only the part within 75° is calculated.

[0070] Perform the segmentation operation of step (3) on each ring segmented in (23) to obtain the segmentation results of vegetation and non-vegetation pixels on each ring. Finally, calculate the value of LAI by combining equation (11) based on the segmentation calculation results of each ring, including the proportion of vegetation pixels, the fraction of one-way gaps, etc.

[0071] Step 3: Divide the fisheye image after HSV segmentation into an infinite number of rings. The vegetation units corresponding to the pixels on each ring are approximately on the same plane at the same height. Calculate the vegetation contact frequency (coverage) in the rings based on the segmentation results of each vegetation and non-vegetation pixel and integrate it to obtain the LAI value.

[0072] LAI is a variable describing the leaf area density of the canopy at a certain height. Based on the concept of LAI and the definition of equation (1), researchers proposed a Poisson model based on contact frequency and gap fraction. Contact frequency, proposed by Warren Wilson, refers to the probability of sunlight contacting vegetation elements within the canopy when it enters the canopy. Gap fraction refers to the probability of natural light directly entering the reference plane. Under the assumption of leaf opacity, the leaf coverage (ratio) measured in image analysis is the one-way contact fraction. At a canopy height of h, the average contact fraction is used as the plant height integral value of the one-way contact fraction of each leaf layer, and its calculation formula is:

[0073]

[0074] In the formula, H represents the canopy height, and L(h) represents the leaf area density corresponding to each height h of the plant canopy, that is, the leaf area per unit volume of the canopy. This refers to the direction vector (v—view) of the observation position, θ v The zenith angle in the direction of observation. Let G be the azimuth angle of the observation direction, and G be the leaf area projection function at height h. Substituting equation (1) into the equation, we get:

[0075]

[0076] (4) shows the correlation between LAI and contact frequency, where By combining equations (5) and (6), we can obtain:

[0077]

[0078]

[0079] Introduction Let θ be the probability density function (l—leaf) of the blade tilt angle (elevation angle, azimuth angle) distribution model, where θ l The zenith angle is the direction in which the blade is tilted. Let be the azimuth angle of the blade tilt, and normalize the condition constraints using equations (7) and (8):

[0080]

[0081]

[0082] By combining the above formulas, the fraction of the canopy space can be obtained. Average contact fraction The relationship between LAI and Nilson is optimized by Nilson into an exponential relationship in equation (9):

[0083]

[0084] in, and Similarly, based on the circular field of view of a fisheye image, the orientation of the incident light rays can be disregarded, assuming that the gap fraction measurement depends only on the observed zenith angle θ. v That is, the angle between the incident light direction and the normal vector of the light sensor at the bottom of the canopy. In this example, the leaf area index (LAI) is calculated. cal The calculation formula can be summarized as follows:

[0085]

[0086] P0(θ v )and Similarly, Welles proposed a discrete numerical analytical method for the integral (10) based on multi-view observations, using five zenith observation angles to divide the rings and segment the average vegetation gap fraction in each ring. Difference the integral (10):

[0087]

[0088] In the formula S i (θ v ) for cos i θ v -1 And W i sinθ v The coefficient dθ varies depending on the chosen ring angle. This invention will calculate LAI based on the above derivation process and the difference formula (11). cal value, Figure 4 This illustrates the definition of the observed zenith angle and the principle of ring division calculation. Taking a point q at a canopy height h as an example, the distance from point q to the center (zenith) in the fisheye image is r. q If the radius of the circle is R, then the observed zenith angle at point q is sinθ. v =rq / R, thus allowing the calculation of W at each point. i and S i (θ v The values ​​of ) are used to divide the annulus in this invention. The zenith observation angles are 0-15°, 15-30°, 30-45°, 45-60°, and 60-75°, corresponding to the cases of i = 1-5.

[0089] During the design process of this invention, fisheye images of crop canopies in the field were continuously acquired and measured using LAI instruments to verify the accuracy of the image processing method and test its applicability in different scenarios. The test crops included rice and wheat, and the test scenarios included experimental fields and actual farmland. The weather conditions used included sunrise, sunset, sunny days, and cloudy days. Image acquisition tests were also conducted at different stages of crop growth.

[0090] The results of the method of this invention were tested through a field experiment. Table 1 shows the details of the verification experiment, the application of the invention in different scenarios, and the verification method. After selecting sites in the experimental fields of relevant crops or actual farmland, a fisheye camera and a professional LAI measuring instrument were used for measurement. When shooting from above, the camera and instrument were at the same angle, and the same location inside the canopy was selected for measurement. The instrument collected four points from left to right and averaged the LAI, while the camera took 6-10 fisheye images for subsequent processing. When shooting from above, the camera's field of view was larger, so the measurement results from other professional software were used for verification. In the verification experiment, the instrument selected was the LI-cor-LAI-2200 canopy analyzer, and the professional software used was Can-eye, developed by the French National Institute for Agricultural Research (INRA) based on MCR.

[0091] Table 1 Application scenarios of the verification experiments of this invention

[0092]

[0093] This invention has been applied in multiple field and experimental scenarios, and its accuracy has been verified against the measurement results of traditional instruments and professional software. Figure 6 The results displayed are an illustration of an image taken from below in a rice field during the jointing and booting stage, and the LAI calculated using the algorithm of this invention. cal Values ​​and instrument measurement results LAI mea The accuracy comparison showed a correlation coefficient R of 0.6332 and a root mean square error (RMSE) of 0.1216, indicating good results. In the verification experiment, we selected different time periods and weather conditions throughout the day for shooting and measurement at 135 sampling points (Table 1). Figure 7Examples of fisheye images in various scenarios and verification accuracy with instrument measurement results are shown. Overcast scenes are a common time period for instrument measurements, during which instrument results are relatively stable. The algorithm of this invention has a correlation coefficient R of 0.6283 and a root mean square error (RMSE) of 0.1785, indicating relatively small errors. However, the algorithm's errors are higher on sunny days and at sunset, reaching 0.3081 and 0.3419, respectively. On rainy days, water droplets on the lens affect image segmentation, resulting in an RMSE of 0.2378. In tests shooting from below in rice paddies, the algorithm adapts to different weather and environments. The error is relatively stable on overcast days, while the measured values ​​on sunny and rainy days show good correlation with the actual values.

[0094] In the early growth stages of rice plants (mainly the seedling and tillering stages) when the plants are short, instruments cannot penetrate the canopy for measurement. Generally, oblique photography or sampling scanning methods are used. In the testing process of this invention, an overhead view is used when the rice is in the seedling stage. Figure 8 The calculated values ​​showed a high correlation with the measured values ​​from other methods, with an R value of 0.9049, while the root mean square error (RMSE) was only 0.0223. The results indicate that under overhead shooting conditions, the present invention can avoid the limitation of instruments being unable to enter the field and also has good accuracy and stability.

[0095] In our application with dryland crop wheat, we primarily verified the correlation and accuracy between overhead camera views and measurements taken using instruments and other methods, and conducted photography and sampling at various growth stages of wheat. According to... Figure 9 During the relatively short seedling and tillering stages of wheat, the test results showed errors of 0.0333 and 0.0316, respectively, indicating high precision. However, during the jointing and booting stage when wheat gradually closes the canopy, the correlation coefficient R reached 0.9909, and the RMSE was 0.1840, showing a good correlation with the measured values ​​of traditional methods.

[0096] Based on the test results of different scenarios and different crops, the following conclusions can be drawn from the specific implementation process of this invention:

[0097] (1) The device and algorithm of the present invention can effectively adapt to LAI measurement tasks in different scenarios, and have good accuracy and stability for paddy fields and dry land.

[0098] (2) This invention effectively avoids the problem of time-consuming and labor-intensive traditional methods, and provides an accurate solution for LAI measurement in the early growth stage of various crops when the plant height is relatively short, filling the gap in LAI monitoring in the early stage of crop development.

Claims

1. A method for calculating leaf area index based on fisheye images, characterized in that, Includes the following steps: Step 1: Acquire fisheye images of different types of canopies; Step 2: Process the acquired fisheye image using image processing technology to reduce background noise and obtain a distortion-free, computable pixel matrix. Step 3: Divide the processed fisheye image into an infinite number of rings. The pixels on each ring are approximately on the same plane. Calculate the vegetation contact frequency in the rings and integrate it to obtain the leaf area index value. The specific implementation method of step 3 is as follows; Based on the concept of LAI and the definition of Equation (1), a Poisson calculation model based on contact frequency and gap fraction is proposed. Contact frequency, proposed by Warren Wilson, refers to the probability of sunlight contacting vegetation elements in the canopy when it enters the canopy. Gap fraction refers to the probability of natural light directly entering the reference plane. Under the assumption that the leaves are opaque, the leaf coverage measured in the image analysis is the one-way contact fraction. (1) In the formula, H Canopy height, l ( h )for h Leaf area density function at height; exist h At canopy height, the average contact fraction is taken as the plant height integral value of the unidirectional contact fraction of each leaf layer, and its calculation formula is: (3) In the formula H Canopy height, L(h) This indicates that each height *h* of the plant canopy corresponds to the leaf area density of that layer, which is the leaf area per unit volume of the canopy. This refers to the direction vector of the observation position. The zenith angle in the direction of observation. The azimuth angle of the observation direction. G For high h The leaf area projection function at that location, by substituting equation (1), yields: (4) Equation (4) represents the correlation between LAI and contact frequency, where By combining equations (5) and (6), we can obtain: (5) (6) Introduction Let be the probability density function of the blade tilt angle distribution model, where The zenith angle is the direction in which the blade is tilted. Let be the azimuth angle of the blade tilt, and normalize the condition constraints using equations (7) and (8): (7) (8) By combining the above formulas, the fraction of the canopy space can be obtained. Average contact fraction The relationship between LAI and Nilson is optimized by Nilson into an exponential relationship in equation (9): (9) in, and Similarly, based on the circular field of view of the fisheye image, without considering the orientation of the incident light rays, it is assumed that the gap fraction measurement depends only on the observed zenith angle. The leaf area index (LAI) is calculated by taking the angle between the incident light direction and the normal vector of the light sensor at the bottom of the canopy. cal The calculation formula can be summarized as follows: (10) Welles proposed a discrete numerical analytical method for the integral (10) based on multi-view observations, which uses multiple zenith observation angles to divide the rings and segment the average vegetation gap fraction in each ring. Perform a difference operation on the integral (10): (11) In the formula for And W i for , i represents the angle of division, and the coefficient varies depending on the angle of the division ring.

2. The leaf area index calculation method based on fisheye images as described in claim 1, characterized in that: In step 1, fisheye images of different types of canopies are collected using a smartphone and a fisheye lens. First, connect the smartphone to the shooting stick via Bluetooth, align the fisheye lens with the main rear camera lens of the smartphone and fix it in place to form a simple measuring stick. After mounting the lens, determine the camera angle according to the type and development level of the plant being photographed. When shooting, stay away from canopies with uneven growth at the edges and keep the camera level.

3. The leaf area index calculation method based on fisheye images as described in claim 2, characterized in that: The imaging sensor plane of a fisheye lens is a circle inscribed in the camera's target surface. A coordinate system is established with the center of this circle as the origin. The viewing angle at each point in the image can then be calculated using Equation 2. θ : (2) In the formula, x, y For pixel coordinates, R is the radius of the image.

4. The leaf area index calculation method based on fisheye images as described in claim 1, characterized in that: The specific implementation method of step 2 is as follows; (21) Use downsampling to proportionally reduce the image resolution to speed up the process, and use image cropping program to cut out the invalid areas around the image; (22) Based on the HSV color space threshold, vegetation pixel classification is performed, and the vegetation ratio and gap score in each ring are extracted. Different segmentation methods are adopted according to different shooting angles: the RGB image is converted into an HSV image by the algorithm, and the upper and lower limits of the threshold are set. Pixels that exceed the limit are classified as non-vegetation pixels and are not included in the contact score calculation. When the image is taken from inside the canopy upward, the sky pixel is used as the segmentation subject, and the vegetation pixel is obtained after removing the sky pixel. When the shooting angle is overhead, the vegetation is used as the segmentation subject, and the vegetation coverage is obtained directly.

5. The leaf area index calculation method based on fisheye images as described in claim 1, characterized in that: In step 3, the image annular region is segmented based on the PIL program package to obtain the central circle within the 0-15° observation zenith angle range, as well as concentric annular regions within the ranges of 15-30°, 30-45°, 45-60°, and 60-75°. Considering that the region outside 75° is close to the sampling edge, has severe distortion and a lot of noise, only the part within 75° is calculated.

6. The leaf area index calculation method based on fisheye images as described in claim 1, characterized in that: Five zenith observation angles were used to divide the rings, namely 0-15°, 15-30°, 30-45°, 45-60°, and 60-75°, corresponding to i=1 to i=5 respectively.

Images