A method for reconstructing the three-dimensional vector configuration of dendritic plant fiber roots based on fractal rules

Abstract

A method for reconstructing the 3D vector configuration of fibrous roots in dendritic plants based on fractal rules is proposed. This method involves collecting root growth data to obtain a raw image dataset of the plant species to be reconstructed. A machine annotation model is constructed to annotate the images in the raw image dataset, and then manually annotates the raw image dataset using the machine-annotated images as a reference. The skeleton of each image in the annotated dataset is extracted to obtain a skeleton feature dataset. Correlation analysis is performed on the skeleton feature dataset, and a fractal rule function model is obtained based on the analysis results. The front and side views of the root systems of the same species to be reconstructed are obtained, and 3D data points are annotated on them. The fractal rule function model is then used to classify the lateral roots and fibrous roots of the 3D root model, resulting in a 3D vector configuration. This design can effectively construct root fractal rules with high accuracy.

Description

Technical Field

[0001] This invention relates to a method for reconstructing the three-dimensional vector configuration of dendritic root plant fiber roots based on fractal rules, specifically applicable to the reconstruction and analysis of the three-dimensional configuration of plant root systems. Background Technology

[0002] The study of tree-like root systems is of great significance for agricultural engineers to gain a deeper understanding of their growth and development mechanisms, their interaction with the environment, optimize cultivation management, improve yield and quality, enhance stress resistance, and promote industrial development (Fang et al., 2009). In recent years, scanning equipment such as root analyzers has been widely used in plant root research, and the development of 3D modeling technology in plant root research has a long history (Baker, 1977). However, traditional analysis based on 2D images often fails to intuitively reflect the morphological structure and spatial distribution of the root system. Although some 3D root modeling software or algorithms exist on the market (Wasson et al., 2020, Yang et al., 2020), they still have many shortcomings when reconstructing complex tree-like root systems. On the one hand, existing software technologies (Wang et al., 2024, Wang et al., 2023) usually require complex theoretical foundations and professional equipment support, resulting in high barriers to entry and high costs. On the other hand, these software programs are often not very targeted and time-consuming when dealing with the complex structure of tree-like root systems, making it difficult to meet the needs of rapid analysis and decision-making. In addition, some software may have high data requirements, requiring a large amount of high-quality scan data to achieve good reconstruction results. However, in practical applications, obtaining such data is often costly and difficult.

[0003] The core of constructing a 3D model of a tree-like root system lies in extracting the root skeleton. Over the past 20 years, methods used for root skeleton extraction have primarily included thinning methods, path planning, distance exchange methods, and the snake model. In 2005, Tian Xuhong, Li Zhiyuan, Han Guoqiang, and others proposed a 3D skeleton extraction method based on the cross-sectional area algorithm. In 2006, Tian Xuhong, Han Guoqiang, Situ Zhiyuan, and others developed a skeletonization algorithm for extracting a superior 3D mesh model. In 2014, Li Pianzhen, Zhou Xuecheng, Zhang Changling, and others proposed a visualization method for the 3D configuration of plant roots based on this skeleton model. However, the aforementioned algorithms have extremely high requirements for raw image data and hardware / software equipment, and have high entry barriers and high usage costs.

[0004] Given the aforementioned limitations and the characteristics of tree-like root systems (with prominent main and lateral roots and fine, complex fibrous roots), this paper proposes a method that does not overly accurately simulate the surface undulations and texture of the root system. Instead, it utilizes Bézier curves to accurately simulate the three-dimensional configuration of the main and lateral roots, and then summarizes the fractal rules of tree-like roots to simulate fibrous roots, thereby reconstructing the three-dimensional configuration of the root system.

[0005] Fractals possess characteristics such as filling space in non-integer dimensions (Falconer, 2013) and self-similarity (Massopust, 2014), making them particularly suitable for tree-like root systems with strong self-similarity. In 2011, Xu Huijie proposed a modeling method for constructing root growth factors based on normal distribution combined with the mean of plant root characteristic parameters. In fact, although fractal technology (Rozenberg and Salomaa, 1980) has matured in two-dimensional modeling of plant roots (Brown and Liebovitch, 2010), and despite continuous progress in two-dimensional root reconstruction (Lee et al., 2023), its application in three-dimensional modeling of plant roots is still in the exploratory stage.

[0006] In laboratory environments, citrus rootstock seedlings are often used as research subjects. However, the growth period of seedling fibrous roots is insufficient, and their growth is regulated by multiple factors (Liu et al., 2023) and growth mechanisms (Silverman, 2007). Therefore, directly exploring the fractal rules between lateral roots and fibrous roots is not universally applicable. The taproot and lateral roots, on the other hand, have a longer growth period. Therefore, when exploring fractal rules, the focus should be on the relationship between the taproot and lateral roots. Image processing techniques, such as morphological dilatation and erosion, are used. While some advanced imaging techniques (Planchon et al., 2011) have been applied to the cellular field, image processing methods suitable for the complex structure of tree-like root systems still need to be explored. By differentiating the taproot and lateral roots by color as a reference, and then manually correcting and labeling the taproot and lateral roots, the root system skeleton is extracted, and root-related attribute data is recorded. This allows for the further derivation of three-dimensional fractal rules. Finally, by fusing optimized Bézier curves, a three-dimensional model is constructed. The simulation effect obtained by this model is unmatched by purely two-dimensional fractal models. Summary of the Invention

[0007] The purpose of this invention is to overcome the problems of complex methods, large computational load, and low accuracy in the existing technology, and to provide a simple and highly accurate method for reconstructing the three-dimensional vector configuration of dendritic root plant fiber roots based on fractal rules.

[0008] To achieve the above objectives, the technical solution of the present invention is:

[0009] In a first aspect, the present invention provides a method for reconstructing the three-dimensional vector configuration of dendritic root plant fiber roots based on fractal rules, comprising the following steps:

[0010] S1 collects plant root growth data for a specific type of tree-rooted plant to be reconstructed, and obtains the original image dataset of the plant root system.

[0011] S2 principal and lateral root annotation: Construct a machine annotation model to perform machine annotation on images in the original image dataset, and then manually and accurately annotate the original image dataset with reference to the machine-annotated images to obtain an annotated image set;

[0012] S3 extracts the skeleton from each image in the labeled image set, imports the skeleton data of each image into a table for data cleaning and organization, and obtains the skeleton feature dataset.

[0013] S4 performs correlation analysis on the skeleton feature dataset and obtains a fractal rule function model based on the analysis results by function fitting.

[0014] S5 acquires the front and side views of the root system of the same type of plant to be reconstructed, annotates it with three-dimensional data points, calls the fractal rule function model to perform fractal analysis on the lateral roots and fibrous roots of the three-dimensional root system model, obtains the three-dimensional data point model, and then uses the three-dimensional third-order continuous Bézier curve to simulate the three-dimensional root system model of the plant based on the three-dimensional data point model, thereby obtaining the three-dimensional vector configuration of the root to be reconstructed.

[0015] In S1, multiple rootstock seedlings of the plant to be reconstructed are selected, divided into n groups, and placed in an open experimental box for cultivation. Each month, one group of seedlings is selected for image and data collection. After n+1 months, the original image dataset of the plant root system is obtained.

[0016] In step S2, the original image dataset is input into the machine annotation model to perform principal and lateral root annotation on each root system image. The principal and lateral root annotation method of the machine annotation model is as follows:

[0017] First, median filtering is applied to the root system image. Then, dilation is performed on the principal and lateral root portions of the median-filtered image. Finally, full threshold segmentation is performed on the dilated image to obtain the machine-annotated image.

[0018] In step S3, the skeleton of each image in the labeled image set is extracted. The specific steps are as follows:

[0019] For each skeleton image, data measurement and extraction were performed:

[0020] First, record the relative length and relative depth of the main root, as well as the number of lateral roots on the main root; and record the relative length, relative depth, and relative angle between the main root and the lateral root for each lateral root from top to bottom.

[0021] The relative depth is the average depth of the root system along the skeleton length, which is the average value of the ordinate of the pixel.

[0022] The relative length is the sum of the number of pixels corresponding to the root system along the skeleton length;

[0023] Method for measuring the relative angle between the main root and lateral roots: Fit the current main root and lateral roots as rays, and calculate the angle between them using their slopes;

[0024] Import the measurement data of all skeleton images into spreadsheet software for data cleaning and organization to obtain the skeleton feature dataset;

[0025] In S4, the skeleton feature dataset is targeted;

[0026] Different types of data are paired into data pairs. Various correlation analysis methods are used to analyze the correlation between the data pairs. Data pairs with correlation analysis results greater than 0.5 are selected and excluded. Data pairs that are not useful for calculating fractal rules are excluded. For the remaining data pairs, various mathematical functions are used to fit the data. The mathematical function with the highest fit is selected as the fitting formula for the data pair.

[0027] Gaussian kernel functions were constructed by performing Gaussian kernel fitting on the fractal rule-related data that were not fitted.

[0028] Iterative formulas for generating fiber roots from different lateral roots:

[0029] ;

[0030] Where P represents a data point, and P0 is the initial growth point of the fibrous root on the lateral root. It is the growth deflection angle. It is the growth pitch angle, P n This represents the growth state of the fiber roots during the nth iteration, P. n+1 This represents the growth state of the fiber roots during the (n+1)th iteration. It is the growth step size in each iteration;

[0031] Based on the obtained fitting formula and the iterative formulas for the Gaussian kernel function and fiber roots, a fractal regular function model is constructed.

[0032] In step S5, a front view and a side view of the root system of the same type of plant to be reconstructed are obtained. The three-dimensional data points of the main root and lateral root are labeled on the front view and the side view. Then, the labeled data points are connected by a three-dimensional third-order continuous Bézier curve, and the thickness ratio of the main root and lateral root corresponding to the Bézier curve is set to obtain a three-dimensional model of the main and lateral roots of the plant to be reconstructed. The three-dimensional model data is imported into the fractal regular function model to construct its fiber root model.

[0033] The steps for connecting the labeled data points using a three-dimensional third-order continuous Bézier curve are as follows:

[0034] S51 breaks down the 3D data points of the labeled principal and lateral roots into a list of data points for each root, and calculates control points for each root separately:

[0035] The list of data points for each root is , P0, P N are the head and tail data points respectively;

[0036] Calculate the distance l between adjacent points before and after nq , l nh , and sequentially take out three adjacent points from the two-dimensional list, denoted as P n-1 , P n , P n+1 ; Use P n-1，i , P n，i , P n+1，i to represent the i-th dimensional coordinates of P n-1 , P n , P n+1 respectively, where i = 0, 1, 2 correspond to the three dimensions of the horizontal, vertical, and vertical directions of the three-dimensional coordinate system, then there are:

[0037] ; ;

[0038] Utilize l nq , l nh to calculate the proportionality coefficients k nq and k nh :

[0039] ; ;

[0040] Utilize the proportionality coefficients k nq and k nh to calculate the auxiliary points P n of P n1 , P n2 , P n3 :

[0041] , , ;

[0042] When 0 < n < N, calculate the previous control point of P n : ;

[0043] When 0 < n < N, calculate the next control point of P n : ;

[0044] When n = 0, calculate the next control point of P0: ;

[0045] When n = N, calculate the next control point of P N : ;

[0046] Insert all calculated control points into the data point list in order to obtain the control point list:

[0047] ;

[0048] S52 groups the control points of each root into groups of four, with the last point of the previous group serving as the starting point of the next group:

[0049] ;

[0050] For each group, perform Bézier curve interpolation. The Bézier curve basis functions are:

[0051] ;

[0052] Each group has four control points, which can be represented as follows: The control point within the group is represented by P. m m = 0, 1, 2, 3; C represents the number of combinations, t represents M t values ​​uniformly distributed between 0 and 1, and M is the number of interpolation points generated corresponding to the group control points.

[0053] Secondly, the present invention provides a method for constructing a fractal regular function model based on the reconstruction of citrus fiber roots, characterized in that: the fractal regular function model is based on the original image dataset of citrus roots, and the aforementioned method for reconstructing the three-dimensional vector configuration of tree-like root plant fiber roots based on fractal rules obtains the skeletal feature dataset of citrus root system;

[0054] For the skeletal feature dataset of citrus root systems, data from different species were paired into data pairs. Spearman's method was used for correlation analysis of these pairs, selecting pairs with a correlation greater than 0.5 and excluding those useless for calculating fractal rules. For the remaining data pairs relating root length to the number of its daughter roots, various mathematical functions were used for data fitting. The power function with the highest good of fit was selected as the fitting formula for the data pairs relating root length to the number of its daughter roots, resulting in fractal rule 1: Relationship between root length and the number of its daughter roots: Where the number of sub-roots is x, and the root length is y;

[0055] Meanwhile, Gaussian kernel functions were constructed by fitting Gaussian kernels to the relevant data of the fractal rules that were not fitted, resulting in Gaussian kernel function G1 for fractal rule 2: the distribution pattern of the angle between the current root and each sub-root; and Gaussian kernel function G2 for fractal rule 3: the distribution pattern of the ratio of the length of the current root to the length of the sub-root.

[0056] Thirdly, the present invention provides a system for reconstructing the three-dimensional vector configuration of dendritic root plant fiber roots based on fractal rules, characterized in that the system is used to execute the aforementioned method for reconstructing the three-dimensional vector configuration of dendritic root plant fiber roots based on fractal rules, specifically including: a planting sampling module, a main and lateral root annotation module, a skeleton extraction module, a fractal rule construction module, and a three-dimensional reconstruction fiber root module;

[0057] Planting sampling module: Used to collect plant root growth data for a specific type of tree-like root plant to be reconstructed, and obtain the original image dataset of the plant root system;

[0058] The primary and secondary root annotation module is used to build a machine annotation model to perform machine annotation on images in the original image dataset, and to perform manual and precise annotation on the original image dataset with reference to the machine-annotated images, so as to obtain an annotated image set.

[0059] Skeleton extraction module: This module extracts the skeleton from each image in the labeled image set, imports the skeleton data of each image into a table for data cleaning and processing, and obtains the skeleton feature dataset.

[0060] Fractal rule construction module: Performs correlation analysis on the skeleton feature dataset, and obtains the fractal rule function model based on the analysis results by function fitting;

[0061] The 3D reconstruction fiber root module is used to obtain the front and side views of the root system of the same type of plant to be reconstructed, label the 3D data points, and then use the 3D third-order continuous Bézier curve to simulate the 3D model of the plant root system. The fractal rule function model is called to perform fractal analysis on the lateral roots and fiber roots of the 3D root system model, thereby obtaining the 3D vector configuration of the root to be reconstructed.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] 1. In this invention, a method for reconstructing the three-dimensional vector configuration of tree-like root plant fiber roots based on fractal rules, machine annotation sequentially performs median filtering, dilation processing, and full threshold segmentation. Median filtering can effectively reduce noise while better preserving important information such as image edges. Compared with linear filtering methods such as mean filtering, median filtering has a better suppression effect on impulse noise such as salt-and-pepper noise. Dilation processing can effectively reduce segmentation errors and more accurately extract and label root regions. Finally, full threshold segmentation can clearly distinguish between root regions and background regions, laying the foundation for subsequent root region extraction and analysis.

[0064] 2. This invention provides a method for reconstructing the three-dimensional vector configuration of dendritic plant fiber roots based on fractal rules. It utilizes computer technology to assist in obtaining fractal rules, extracts key feature values ​​related to these rules based on skeletal feature data, and firstly uses correlation analysis to explore the mathematical function fitting relationship between data pairs. For those pairs that cannot be fitted, a Gaussian kernel function is constructed to maximize the reconstruction of the fractal rules. Then, the fractal rules are used to construct a fiber root model of the plant root system, solving the technical problem of existing technologies' difficulty in reconstructing plant fiber roots, achieving an accuracy of 87.5%.

[0065] 3. In the present invention, a method for reconstructing the three-dimensional vector configuration of tree-like root plant fiber roots based on fractal rules, a proprietary three-dimensional third-order continuous Bézier curve model is constructed according to the characteristics of the plant root system during the three-dimensional vector construction to connect data points. The original independent Bézier curves are constructed into multiple data linked lists. At the same time, color and thickness factors are introduced into the linked list attributes to effectively improve the simulation accuracy. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method of the present invention.

[0067] Figure 2 This is a schematic diagram of the system structure of the present invention.

[0068] Figure 3 This is a schematic diagram of the process used in Example 3.

[0069] Figure 4 This is a schematic diagram comparing the effects of different filtering methods in Example 3.

[0070] Figure 5 This is a schematic diagram comparing the effects of dilation and threshold segmentation in Example 3.

[0071] Figure 6 This is a schematic diagram comparing the fitting of different functions relating the root length to the number of its sub-roots in Example 3.

[0072] Figure 7 This is a schematic diagram of the probability distribution of Gaussian kernel functions G1 and G2 in Example 3.

[0073] Figure 8 This is a flowchart of the three-dimensional vector configuration of the fiber root in Example 3.

[0074] Figure 9 This is an interface diagram of the data point conversion program in Example 3.

[0075] Figure 10 This is a schematic diagram of the fiber root growth point in Example 3.

[0076] Figure 11This is a schematic diagram of the three-dimensional vector configuration of the fiber root in Example 3. Detailed Implementation

[0077] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] Example 1:

[0079] See Figure 1 A method for reconstructing the three-dimensional vector configuration of dendritic root plant fiber roots based on fractal rules includes the following steps:

[0080] S1 collects plant root growth data for a specific type of tree-rooted plant to be reconstructed, and obtains the original image dataset of the plant root system.

[0081] Multiple rootstock seedlings of the plant to be reconstructed were selected, divided into n groups, and placed in an open experimental box for cultivation. Each month, one group of seedlings was selected for image and data collection. After n+1 months, the original image dataset of the plant root system was obtained.

[0082] S2 principal and lateral root annotation: Construct a machine annotation model to perform machine annotation on images in the original image dataset, and then manually and accurately annotate the original image dataset with reference to the machine-annotated images to obtain an annotated image set;

[0083] The original image dataset is input into the machine annotation model to perform principal and lateral root annotation for each root system image. The principal and lateral root annotation method of the machine annotation model is as follows:

[0084] First, median filtering is applied to the root system image. Then, dilation is performed on the principal and lateral root portions of the median-filtered image. Finally, full threshold segmentation is performed on the dilated image to obtain the machine-annotated image.

[0085] S3 extracts the skeleton from each image in the labeled image set, imports the skeleton data of each image into a table for data cleaning and organization, and obtains the skeleton feature dataset.

[0086] The skeleton is extracted from each image in the labeled image set. The specific steps are as follows:

[0087] For each skeleton image, data measurement and extraction were performed:

[0088] First, record the relative length and relative depth of the main root, as well as the number of lateral roots on the main root; and record the relative length, relative depth, and relative angle between the main root and the lateral root for each lateral root from top to bottom.

[0089] The relative depth is the average depth of the root system along the skeleton length, which is the average value of the ordinate of the pixel.

[0090] The relative length is the sum of the number of pixels corresponding to the root system along the skeleton length;

[0091] Method for measuring the relative angle between the main root and lateral roots: Fit the current main root and lateral roots as rays, and calculate the angle between them using their slopes;

[0092] Import the measurement data of all skeleton images into spreadsheet software for data cleaning and organization to obtain the skeleton feature dataset;

[0093] S4 performs correlation analysis on the skeleton feature dataset and obtains a fractal rule function model based on the analysis results by function fitting.

[0094] For skeleton feature datasets;

[0095] Different types of data are paired into data pairs. Various correlation analysis methods are used to analyze the correlation between the data pairs. Data pairs with correlation analysis results greater than 0.5 are selected and excluded because they are not useful for calculating fractal rules. For the remaining data pairs, various mathematical functions (linear, logarithmic, inverse, second-order, third-order, composite, power function, sigmoid function, growth function, exponential function, and logistic function) are used to fit the data. The mathematical function with the highest fit is selected as the fitting formula for the data pair.

[0096] Gaussian kernel functions were constructed by performing Gaussian kernel fitting on the fractal rule-related data that were not fitted.

[0097] Fractal rule 1: The relationship between the root length and the number of its child roots is confirmed based on the length of the main root and the number of its lateral roots in each skeleton image;

[0098] Fractal rule 2: The distribution pattern of the angle between the current root and each child root is determined based on the relative angle data between the principal root and the lateral roots;

[0099] Fractal rule 3: The distribution pattern of the ratio of the current root length to the sub-root length is used to identify data groups based on the length of the main root and the length of its upper side root in each skeleton image.

[0100] Iterative formulas for generating fiber roots from different lateral roots:

[0101] ;

[0102] Where P represents a data point, and P0 is the initial growth point of the fibrous root on the lateral root. It is the growth deflection angle. It is the growth pitch angle, P n This represents the growth state of the fiber roots during the nth iteration, P. n+1 This represents the growth state of the fiber roots during the (n+1)th iteration. It is the growth step size in each iteration;

[0103] Based on the obtained fitting formula and the iterative formulas for the Gaussian kernel function and fiber roots, a fractal regular function model is constructed.

[0104] S5 acquires the front and side views of the root system of the same type of plant to be reconstructed, annotates the three-dimensional data points, and then uses a three-dimensional third-order continuous Bézier curve to simulate the three-dimensional model of the plant's root system. It calls the fractal rule function model to perform fractal analysis on the lateral roots and fibrous roots of the three-dimensional root system model, thereby obtaining the three-dimensional vector configuration of the root to be reconstructed.

[0105] Obtain the front and side views of the root systems of the same type of plant to be reconstructed. Label the three-dimensional data points of the main root and lateral roots in the front and side views. Then, connect the labeled data points using three-dimensional third-order continuous Bézier curves and set the thickness ratio of the main root and lateral roots corresponding to the Bézier curves to obtain the three-dimensional model of the main and lateral roots of the plant to be reconstructed. Import the three-dimensional model data into the fractal regular function model to construct its fiber root model.

[0106] The steps for connecting the labeled data points using a three-dimensional third-order continuous Bézier curve are as follows:

[0107] S51 breaks down the 3D data points of the labeled principal and lateral roots into a list of data points for each root, and calculates control points for each root separately:

[0108] The list of data points for each root is as follows: P0, P N These are the first and last data points, respectively.

[0109] Calculate the distance l between adjacent points before and after. nq , l nh Take three adjacent points sequentially from the two-dimensional list, and let them be P. n-1 ,P n ,P n+1 ; use P n-1，i P n，i P n+1，i P n-1 ,P n ,P n+1 Let the i-th coordinate, i=0,1,2, correspond to the horizontal, vertical, and other three dimensions of the three-dimensional coordinate system. Then we have:

[0110] ; ;

[0111] Using l nq , l nh Calculate the proportionality coefficient k nq and k nh :

[0112] ; ;

[0113] Using the proportionality coefficient k nq and k nh , calculate the auxiliary point P n of P n1 , P n2 , P n3 :

[0114] , , ;

[0115] When 0 < n < N, calculate the previous control point of P n : ;

[0116] When 0 < n < N, calculate the subsequent control point of P n : ;

[0117] When n = 0, calculate the subsequent control point of P0: ;

[0118] When n = N, calculate the subsequent control point of P N : ;

[0119] Insert all the calculated control points into the data point list in sequence to obtain the control point list:

[0120] ;

[0121] For the control point list of each root in S52, group them into groups of four control points, with the last point of the previous group as the starting point of the next group:

[0122] ;

[0123] Perform Bezier curve interpolation on each group respectively. The Bezier curve basis function is:

[0124] ;

[0125] Each group has four control points, which can be expressed as , and the control points within the group are expressed as P m , where m = 0, 1, 2, 3; C represents the combination number, and t represents M uniformly distributed t values between 0 and 1. M is the number of interpolation points corresponding to the control points of the group.

[0126] See Figure 2A system for reconstructing the three-dimensional vector configuration of dendritic plant fiber roots based on fractal rules is provided. The system is used to execute the aforementioned method for reconstructing the three-dimensional vector configuration of dendritic plant fiber roots based on fractal rules. Specifically, it includes: a planting sampling module, a main and lateral root annotation module, a skeleton extraction module, a fractal rule construction module, and a three-dimensional reconstruction fiber root module.

[0127] Planting sampling module: Used to collect plant root growth data for a specific type of tree-like root plant to be reconstructed, and obtain the original image dataset of the plant root system;

[0128] The primary and secondary root annotation module is used to build a machine annotation model to perform machine annotation on images in the original image dataset, and to perform manual and precise annotation on the original image dataset with reference to the machine-annotated images, so as to obtain an annotated image set.

[0129] Skeleton extraction module: This module extracts the skeleton from each image in the labeled image set, imports the skeleton data of each image into a table for data cleaning and processing, and obtains the skeleton feature dataset.

[0130] Fractal rule construction module: Performs correlation analysis on the skeleton feature dataset, and obtains the fractal rule function model based on the analysis results by function fitting;

[0131] The 3D reconstruction fiber root module is used to obtain the front and side views of the root system of the same type of plant to be reconstructed, label the 3D data points, and then use the 3D third-order continuous Bézier curve to simulate the 3D model of the plant root system. The fractal rule function model is called to perform fractal analysis on the lateral roots and fiber roots of the 3D root system model, thereby obtaining the 3D vector configuration of the root to be reconstructed.

[0132] Example 2:

[0133] A method for constructing a fractal regular function model based on the reconstruction of citrus fiber roots, wherein the fractal regular function model is based on the original image dataset of citrus roots, and the aforementioned method for reconstructing the three-dimensional vector configuration of tree-like root plant fiber roots based on fractal rules is used to obtain the skeletal feature dataset of citrus root system;

[0134] For the skeletal feature dataset of citrus root systems, data from different species were paired into data pairs. Spearman's method was used for correlation analysis of these pairs, selecting pairs with a correlation greater than 0.5 and excluding those useless for calculating fractal rules. For the remaining data pairs relating root length to the number of its daughter roots, various mathematical functions were used for data fitting. The power function with the highest good of fit was selected as the fitting formula for the data pairs relating root length to the number of its daughter roots, resulting in fractal rule 1: Relationship between root length and the number of its daughter roots: Where the number of sub-roots is x, and the root length is y;

[0135] Meanwhile, Gaussian kernel functions were constructed by fitting Gaussian kernels to the relevant data of the fractal rules that were not fitted, resulting in Gaussian kernel function G1 for fractal rule 2: the distribution pattern of the angle between the current root and each sub-root; and Gaussian kernel function G2 for fractal rule 3: the distribution pattern of the ratio of the length of the current root to the length of the sub-root.

[0136] Example 3:

[0137] See Figure 3 Fifty citrus rootstock seedlings were used as the experimental sample, divided into 5 groups of 10 seedlings each, and placed in an open experimental chamber with a sand-to-soil ratio of 3:1 for cultivation. The initial period was one month. Starting from the second month, one group of seedlings was taken out at the end of each month for image and data collection: specifically, the seedlings were washed, pruned, numbered, and placed horizontally into the water tank of the root system analyzer for image acquisition. After a six-month cultivation period, TIF images and related data of 50 citrus rootstock seedlings were obtained, forming the original image dataset of the citrus root system.

[0138] The software infrastructure used in implementing the model algorithm includes: Python 3.8, SPSS 27.0, PyCharm, and a series of external Python libraries.

[0139] Multi-view image analysis of each plant was conducted on the main-lateral roots and fibrous roots to facilitate the analysis of the fractal rules of fibrous roots relative to lateral roots. First, median filtering was applied to the root images. Then, the main-lateral root portion of the median-filtered images was dilated to reduce root breakage errors caused by threshold segmentation. Full threshold segmentation was then performed on the dilated images to obtain machine-annotated images. Using the segmented images as a reference, the main and lateral roots were manually corrected, the main-lateral root skeleton was extracted, and data such as the angle between the main and lateral roots, root growth length, and relative depth were calculated. The relationships between these data points were analyzed to construct the fractal rules of the citrus main-lateral root system.

[0140] See Figure 4 We selected relatively complex root systems as the targets for machine learning adjustment. This ensures that subsequent simpler root samples can adapt to the adjusted machine learning model as much as possible. Here, we chose complex root systems that are not sample sequences but belong to the same cultivation environment.

[0141] Figure 4 The images show the effects of three filters after multiple parameter adjustments. The results indicate that the mean and median filters are similarly effective, while the Gaussian filter performs poorly. Median filtering effectively reduces noise while preserving important image information such as edges. Compared to linear filtering methods like mean filtering, median filtering has a better suppression effect on impulse noise such as salt-and-pepper noise. Therefore, median filtering was selected as the preferred filter.

[0142] For two-dimensional digital images, the median filtering operation is defined as follows: for each pixel (x, y) in the image, the median value of the pixels in its neighborhood (usually a square window, such as 3x3, 5x5, etc., which is 3x3 in this embodiment) is taken as the filtered value of the pixel.

[0143] See Figure 5 Due to segmentation errors or the inherent characteristics of the root system (such as the possibility of losing finer parts of the root system during segmentation), the labeling of the blue root region is incomplete. To extract and label the root region more accurately, morphological operations need to be performed on the blue root region to compensate for possible segmentation defects. Therefore, an expansion filter is added.

[0144] After dilation and further thresholding, the root system and background regions can be clearly distinguished, laying the foundation for subsequent root region extraction and analysis. Global thresholding is performed using the Otsu method. The Otsu method is an adaptive threshold selection method whose advantage lies in automatically determining an optimal threshold based on the image's grayscale histogram, eliminating the need for manual specification. Its core principle is maximizing inter-class variance. Assuming the pixels in the image can be divided into two classes (foreground and background, which can be understood as the root system and non-root system in a root system image), let the threshold be t, the total number of pixels in the image be N, the number of pixels less than or equal to t be n1 with an average grayscale value of m1, and the number of pixels greater than t be n2 with an average grayscale value of m2. The average grayscale value of the image is m. G The formula for calculating the inter-class variance is:

[0145] ;

[0146] The Otsu method iterates through all possible thresholds (grayscale ranges) to find the one that maximizes the inter-class variance as the optimal threshold. The optimal threshold can classify the pixels in the image into two distinct classes as much as possible, effectively separating the root region and the background region in the binary image.

[0147] Local thresholding segmentation requires setting different thresholds for different images. The thresholds of the images processed by the root system analyzer are not the same. Machine learning models have difficulty automating the processing of a large number of images. At the same time, manually adjusting the threshold often fails to obtain a good segmentation threshold, so it is abandoned.

[0148] Figure 5 The full threshold segmentation in the dataset yielded ideal results, significantly reducing image noise and demonstrating reasonable threshold segmentation. However, the root system was the most complex in the sample images, resulting in a higher error rate. Therefore, such complex root systems were excluded from the dataset to reduce error. The machine learning model, after multiple training iterations and modifications, was then applied to the image dataset, resulting in a series of machine-annotated images.

[0149] Based on the machine-annotated images mentioned above, the original image dataset was manually annotated to obtain an annotated image set of citrus roots:

[0150] The images processed by the above model still rely on threshold segmentation, resulting in significant noise in color processing. Therefore, after applying the adjusted machine learning model to all data images, the results are only used as reference images for human correction. In the manually labeled images, red represents the principal root and yellow represents the lateral roots. The relative length, relative depth, and number of lateral roots on the principal root are recorded. Furthermore, the relative length, relative depth, and relative angle between the principal and lateral roots are recorded sequentially from top to bottom for each lateral root. Specifically: the relative depth is the average depth of the corresponding root system along the skeleton length, i.e., the average value of the pixel's ordinate; the relative length is the sum of the number of pixels in the corresponding root system along the skeleton length; the relative angle between the principal and lateral roots is calculated by fitting the current principal and lateral roots as rays and calculating the angle using their slopes.

[0151] The measurement data of all skeleton images were imported into spreadsheet software for data cleaning and organization to obtain a skeleton feature dataset of citrus roots.

[0152] For the skeleton feature dataset, different data types were paired into data pairs, and various correlation analysis methods (Kendall's method and Spearman's method) were used to analyze the correlation between these pairs. Nonparametric correlation analysis was performed using SPSS software, employing Kendall's tau_b method and Spearman's Rh0 method to explore the correlations between the number of lateral roots on the principal root (Yellow_root_count), the relative depth of the principal root (Red_root_depth), the relative depth of the lateral roots (Yellow_root_depth), the relative length of the lateral roots (Yellow_root_length), the relative length of the principal root (Total_red_root_length), and the relative angle between the principal and lateral roots (Angle_between_red_yellow).

[0153]

[0154]

[0155] Data pairs with correlation analysis results greater than 0.5 were selected, and those that were not useful for calculating fractal rules were excluded. For the remaining data pairs, various mathematical functions were used to fit the data, and the mathematical function with the highest fit was selected as the fitting formula for the data pair.

[0156] The data in the table above shows that the relationships among root attributes are better suited to the Spearman Rhh0 method. The number of lateral roots and the length of the taproot show a high positive correlation, making them suitable for function fitting. While there is some negative correlation between lateral root length and the depth of lateral roots, the number of lateral roots, and the relative average depth of the taproot, the correlations are generally low and not suitable for function fitting; they are only applicable for exploring growth trends.

[0157] In SPSS, the relationship between the number of lateral roots and the length of the principal root is obtained by fitting different function models based on the sample data. Figure 6 The horizontal axis represents the length of the principal root, and the vertical axis represents the number of lateral roots corresponding to the principal root. From top to bottom in the graph, the functions are: linear, logarithmic, inverse, second-order, third-order, composite, power function, sigmoid function, growing function, exponential function, and logistic function. The goodness-of-fit values ​​for each function model are as follows:

[0158]

[0159] As shown in the table, the power function exhibits the best R-squared and significance, with an R-squared value exceeding 70% and a significance level below 0.001, which falls within the acceptable error range for fitting functions in practical engineering. This leads to Fractal Rule 1: the relationship between root length and the number of its sub-roots. Where the number of sub-roots is x, and the root length is y;

[0160] In a laboratory environment, the probability density functions of the angle between the principal and lateral roots and the ratio of lateral to principal roots were investigated. Scatter plot observations revealed that these two distributions are quite complex and difficult to simulate with general function models. Therefore, a Gaussian kernel (radial basis function kernel, RBF) was used to fit the data. This is a rigorous, theoretically sound function model, highly suitable for fitting irregular data, similar to function interpolation, and has wide applications in data fitting. Based on Python libraries such as pandas, dill, scipy, and MATLAB, Gaussian kernel fitting was performed on the original data to obtain Gaussian kernel files (pkl) for the angle between the principal and lateral roots and the ratio of lateral to principal roots. The former stores the distribution pattern for each angle between 0° and 90° with an accuracy of 0.01; the latter stores the distribution pattern for the ratio of lateral to principal roots between 0 and 5 with an accuracy of 0.001. We obtain fractal rule 2: Gaussian kernel function G1 showing the distribution pattern of the angle between the current root and each child root; fractal rule 3: Gaussian kernel function G2 showing the distribution pattern of the ratio of the current root length to the child root length. See [link / reference] Figure 7 .

[0161] Depend on Figure 7It can be seen that the angle between the main and lateral roots is mainly concentrated at two peaks, around 40 degrees and 75 degrees. Overall, the angle between 40 degrees and 80 degrees is more common, decreasing towards both sides. The length of the lateral roots is generally shorter than that of the main root. Even if a few are longer than the main root, their length will not exceed 2.5 times the length of the main root.

[0162] like Figure 8 The initialization process involves inputting dual-view optical images (represented by the automated camera control on a laboratory workbench, maintaining a constant distance and horizontal height from the object) into the 3D coordinate point acquisition program. These images, denoted as model_0 and model_90, represent the front and side views of the object, respectively, with an image size of 960*960. The X and Y coordinates are obtained using the top-left corner of the front view as the origin, and the Z coordinate is obtained using the top-left corner of the side view, maintaining the same Y-axis. This process yields the data conversion from the dual-view images to 3D coordinate points. A relatively simple coordinate transformation method is used because in actual point marking, each pixel is extremely small, resulting in an error rate of up to 1%. For a model aimed at observing the 3D structure of a plant, this error rate is within acceptable limits. Figure 9 This is a flowchart illustrating the data point conversion process.

[0163] The left image is model_0, the right image is model_90, and the blue line is a horizontal auxiliary correction line. It includes three functions: import image, clear markers, and exit. Once all principal and lateral root data points have been plotted (operation time <= 1 minute), clicking exit will convert all data points into 3D coordinates. Data points belonging to the same root will be stored in the same list. Each data list is a 2D list, with the inner list having a uniform length of 3, storing the three axis coordinates of each data point. The outer list length depends on the number of data points for each root. Finally, the data is packaged into a txt file, named point.txt.

[0164] Next, the data in point.txt is imported into the 3D modeling program. First, the obtained 3D data coordinate list is connected using multiple consecutive third-order Bézier curves. To ensure compliance with the growth patterns of citrus roots and smooth connections at each data point, the smooth curve connection condition is defined as the first derivative at the current data point being 0. Furthermore, while traditional third-order Bézier curves are based on two dimensions, we extend them to three dimensions.

[0165] S51 breaks down the 3D data points of the labeled principal and lateral roots into a list of data points for each root, and calculates control points for each root separately:

[0166] The list of data points for each root is as follows: P0, P N These are the first and last data points, respectively.

[0167] Calculate the distance \(l\) between adjacent points before and after nq , \(l\) nh , successively take out three adjacent points from the two-dimensional list, and set them as \(P\) n-1 , \(P\) n , \(P\) n+1 ; use \(P\) n-1，i , \(P\) n，i , \(P\) n+1，i to represent the \(i\)-th dimensional coordinates of \(P\) n-1 , \(P\) n , \(P\) n+1 respectively, where \(i = 0, 1, 2\) correspond to the three dimensions of the horizontal, vertical, and vertical directions of the three-dimensional coordinate system, then there are:

[0168] ; ;

[0169] Use \(l\) nq , \(l\) nh to calculate the proportionality coefficients \(k\) nq and \(k\) nh :

[0170] ; ;

[0171] Use the proportionality coefficients \(k\) nq and \(k\) nh to calculate the auxiliary point \(P\) n of \(P\) n1 , \(P\) n2 , \(P\) n3 :

[0172] , , ;

[0173] When \(0 < n < N\), calculate the previous control point of \(P\) n : ;

[0174] When \(0 < n < N\), calculate the subsequent control point of \(P\) n : ;

[0175] When \(n = 0\), calculate the subsequent control point of \(P0\): ;

[0176] When \(n = N\), calculate the subsequent control point of \(P\) N : ;

[0177] Insert all the calculated control points into the data point list in order to obtain the control point list:

[0178] ;

[0179] S52 groups the control points of each root into groups of four, with the last point of the previous group serving as the starting point of the next group:

[0180] ;

[0181] For each group, perform Bézier curve interpolation. The Bézier curve basis functions are:

[0182] ;

[0183] Each group has four control points, which can be represented as follows: The control point within the group is represented by P. m m = 0, 1, 2, 3; C represents the number of combinations, t represents M t values ​​uniformly distributed between 0 and 1, and M is the number of interpolation points generated corresponding to the group control points.

[0184] We already have the current growth data model of the main and lateral roots, meaning the main and lateral roots have iterated to a certain generation. However, due to the complexity of the fiber roots, they are difficult to obtain, and the fiber roots have not grown. This paper aims to apply fractal rules to the main and lateral root model that has grown to a certain generation, to iterate out the fiber roots. We map these three laws to fractal rules as follows:

[0185] First, we determine y as the length of the mother root and x as the number of daughter roots using fractal rule 1. In this paper, y represents the current lateral root length. As we can see, this is a monotonically increasing function within its domain. For the number of daughter roots, x can only take integer values. This means that x can only take values ​​like 1, 2, 3, etc., when y reaches a certain size. For example, in the current model, if a lateral root has a length of 50, then the range of y is [0, 50]. Starting with x, we let x take positive integer values ​​to obtain a series of corresponding y0, y1, y2 values. When a value exceeds the range of y, x stops taking values. At this point, y0, y1, y2, etc., can be considered as the growth points corresponding to the fiber roots on the current lateral root. Of course, in practical applications, the length calculation must be implemented through the calculation of three-dimensional coordinate points. Figure 10 :

[0186] Once the growth point (red dot) is determined, it is necessary to consider how many iterations should be performed on each lateral root, the length of each iteration, and the direction of each iteration in three-dimensional space.

[0187] Regarding the number of iterations, the ratio of each lateral root to the corresponding fiber root can be obtained using the Gaussian kernel function G2. Since the lateral root data points are known, i.e., the lateral root lengths are known, the length L of the current fiber root can be calculated using this ratio. After obtaining the length, it is only necessary to define a growth step size, i.e., the length of each iteration, and then use the obtained length L / step size = (number of iterations - 1)...the last step size. The reason it is "number of iterations - 1" is because the last step size must be <= the growth step size. In this paper, based on the average interval between each pair of lateral root data points, the growth step size is defined as 50.

[0188] It is worth mentioning Figure 7 Essentially, it is based on the interpolation function. The original interpolation function is not continuous, but rather a series of data points with small intervals between each x. Then, different x are divided into intervals within the domain and their probabilities are statistically analyzed to obtain the probability distribution function. Therefore, this probability distribution function is also discontinuous, which is why it is plotted as an image for viewing.

[0189] Finally, the growth direction needs to be determined for each iteration to accurately pinpoint the location of the data points generated in each iteration. Note: Each fiber root will generate one and only one data point per iteration, based on... Figure 10 The growth direction (angle) required for each iteration will be generated by probability. Here it is represented by an angle. Let the pitch angle and yaw angle be the generated angles. In this way, we have completed the mapping from two-dimensional angle to three-dimensional angle.

[0190] Now, for any fiber root in the first generation, with a growth point, growth direction, growth step size for each iteration, and number of iterations, the final fiber root can be generated.

[0191] So how do we express the above theory as a recursive formula? On the original initial growth segment, we can give the growth direction and growth step size. Usually, we use + and - to represent the growth direction. Here we use them to represent the deflection angle (relative angle) and pitch angle.

[0192] Unlike traditional L-systems, the fractal rule proposed in this paper iteratively generates fiber roots based on a pre-constructed principal and lateral root model. Therefore, its initial string and recursive formula differ from those of conventional L-systems. The fractal rule is as follows:

[0193] Initial string: F;

[0194] Recursive formula:

[0195] F -> F [ + f ] [—f ] F;

[0196] f -> [ + f ] [—f ] ;

[0197] Definitions: F represents drawing the principal root forward by a certain length; [ represents saving the current drawing state (including position, direction, etc.);] ​​represents restoring the previously saved drawing state; + represents deflecting a certain angle along the relative angle, determined by the Gaussian kernel function G1; — represents deflecting a certain angle along the pitch angle, determined by the Gaussian kernel function G1; f represents drawing the lateral roots.

[0198] The number of lateral roots is determined by the power law relationship between the number of lateral roots and the length of the main root (fractal rule 1). Each independent lateral root "f" generates a corresponding growth angle and length by storing a probability function in the Gaussian kernel. Iterative replacement is performed whenever the critical condition is reached.

[0199] The corresponding formula is an iterative formula for generating fiber roots from different lateral roots:

[0200] ;

[0201] Where P represents a data point, and P0 is the initial growth point of the fibrous root on the lateral root. It is the growth deflection angle. It is the growth pitch angle, P n This represents the growth state of the fiber roots during the nth iteration, P. n+1 This represents the growth state of the fiber roots during the (n+1)th iteration. It is the growth step size in each iteration;

[0202] By using a length-quantity function, each lateral root is traversed to calculate the number of fiber roots that each lateral root should have when it grows to different lengths, thus determining the starting growth point of the fiber roots on each lateral root. After determining the growth point, an iterative formula for generating fiber roots from lateral roots is derived using an angle distribution function and a root length ratio distribution function. Based on each growth point, the position of the next growth point is continuously iterated. The growth length of each fiber root is limited by the lateral root according to the length ratio function; if the limit is exceeded, the iteration stops, and the fractal process ends. All data points obtained from the fractal process are stored in a data file. Finally, a three-dimensional third-order continuous Bézier curve model is used to plot all data points to obtain the model result.

[0203] Figure 11 The images are a physical photograph, a two-dimensional image scanned by a root system analyzer, and a three-dimensional model of the BFT-C3DM model. Since the same root system is analyzed according to the probability distribution function during each fractal iteration, four samples from different growth stages (No. 17, No. 19, No. 20, and No. 24) were randomly selected from 50 plants as verification samples. Note that since some main roots in the above figure also have many small lateral roots, in the experiment, the focus was on lateral roots with more fibrous roots or those whose coordinate points were easier to obtain from multiple angle views. Therefore, these small lateral roots were not completely simulated. Although they resemble fibrous roots, they are not fibrous roots.

[0204] By observing the morphological, structural, and fractal features of the three-dimensional model, we can analyze indicators such as root density distribution, angular distribution, bifurcation pattern, topological structure, porosity, and similarity.

[0205] Common methods for 3D modeling of plant roots include Micro-CT, X-ray, and MRI. A longitudinal comparison was conducted between this invention and the BET-C3DM method, focusing on four aspects: the amount of input data required for training the model, the memory usage of the results, the running time, and relative accuracy.

[0206] ;

[0207] This indicates that the proposed BFT-C3DM model has high modeling accuracy and can accurately reproduce the main root, lateral root, and fibrous root of citrus. At the same time, compared with common modeling algorithms on the market, this model has the advantages of small size, fast speed, small input data requirements, strong targeting, and good modeling accuracy, and can better balance the imbalance between modeling accuracy and model size.

[0208] Using advanced data analysis of 648 root data points from 50 citrus rootstock seedling samples, fractal rules for citrus were summarized. These rules were applied to the construction of three-dimensional fiber roots, using continuous Bézier curves to ensure a vector model. Four root systems from the sample were visualized for validation. The model was evaluated based on four characteristics: fiber root density fit, complexity fit, topological structure, and overall distribution trend. The average value was taken, resulting in a total model similarity of 87.5%. Furthermore, a longitudinal comparison was made with other commonly used modeling algorithms. This demonstrates the practicality and scientific validity of the fractal rule-based method for reconstructing three-dimensional fiber roots using a vector principal and lateral root model.

Claims

1. A method for reconstructing a three-dimensional vector configuration of fibrous roots of a tree-shaped root plant based on a fractal rule, characterized by, The method comprises the following steps: S1, collecting growth data of plant root system of a plant to be reconstructed of a certain kind of tree root, and obtaining an original image data set of the plant root system; S2, main-lateral root labeling, constructing a machine labeling model to machine label images in the original image data set, referring to the machine labeled images to manually and accurately label the original image data set to obtain a labeled image set; The machine labeling model labels the main-lateral roots of each root system image in the original image data set one by one, and the main-lateral root labeling method of the machine labeling model is as follows: First, the root system image is subjected to median filtering, then the main-lateral root part of the median filtered image is subjected to expansion processing, and the expanded image is subjected to full threshold segmentation to obtain a machine labeled image; S3, extracting a skeleton of each image in the labeled image set, importing the skeleton data of each image into a table for data cleaning and arrangement to obtain a skeleton feature data set; S4, performing correlation analysis on the skeleton feature data set, and obtaining a fractal rule function model based on the analysis result; The skeleton feature data set is subjected to correlation analysis, and a fractal rule function model is obtained based on the analysis result; The different kinds of data are combined into data pairs, a plurality of different correlation analysis methods are used to analyze the correlation of the data pairs, data pairs with a correlation greater than 0.5 are screened out, data fitting is performed on the remaining data pairs using a plurality of mathematical functions, and a mathematical function with the highest fitting degree is selected as the fitting formula of the data pair; The Gaussian kernel fitting is performed on the fractal rule related data pairs that have not been fitted to construct a Gaussian kernel function; An iteration formula for generating fiber roots of different lateral roots is as follows: ； where P represents the data points, P0is the initial growth point of the fiber root on the side root, is the growth deflection angle, is the growth pitch angle, P n is the growth state of the fiber root at the nth iteration, P n+1 is the growth state of the fiber root at the n+1th iteration, is the growth step length at each iteration; Based on the obtained fitting formula, Gaussian kernel function and iteration formula of fiber roots, a fractal rule function model is constructed; S5, obtaining a front view and a side view of the root system of the plant to be reconstructed of the same kind, marking three-dimensional data points of the main roots and lateral roots, then simulating a three-dimensional model of the root system of the plant using a three-dimensional three-order continuous Bezier curve, and calling the fractal rule function model to perform fractal on the lateral roots and fiber roots of the three-dimensional model of the root system, so as to obtain a three-dimensional vector configuration of the reconstructed root; Obtaining a front view and a side view of the root system of the plant to be reconstructed of the same kind, marking three-dimensional data points of the main roots and lateral roots of the front view and the side view, then connecting the marked data points using a three-dimensional three-order continuous Bezier curve, setting the thickness ratio of the Bezier curve corresponding to the main roots and lateral roots, and obtaining a three-dimensional model of the main roots and lateral roots of the plant to be reconstructed; and importing the three-dimensional model data into the fractal rule function model to construct a fiber root model; The connecting step of the three-dimensional three-order continuous Bezier curve on the marked data points is as follows: S51, splitting the three-dimensional data points of the marked main roots and lateral roots into a data point list of each root, and calculating control points respectively: The data point list of each root is , P0, P N respectively the first and last data points; Calculate the distance l between the front and rear adjacent points nq , l nh , take three adjacent points from the two-dimensional list in turn, set as P n-1 , P n , P n+1 ; use P n-1，i , P n，i , P n+1，i to represent the i-dimensional coordinates of P n-1 , P n , P n+1 , i=0,1,2 corresponding to the three dimensions of the three-dimensional coordinate system horizontal, vertical and vertical, then ； ； With l nq , l nh , the proportionality coefficient k nq and k nh are calculated: ； ； Using the proportionality factor k nq and k nh , the auxiliary points P n are calculated n1 , P n2 , P n3 : ， ， ； P is calculated when 0 < n < N n the preceding control point: ; P is calculated when 0 < n < N n the back control point of P: ; When n = 0, the back position control point of P0 is calculated: ; When n = N, calculate P N Back control point of : ; Inserting all the calculated control points into the data point list in order to obtain a control point list: ； S52, grouping the control point list of each root with four control points as a group, and taking the end point of the previous group as the starting point of the next group: ； Performing Bezier curve interpolation on each group respectively, and the Bezier curve basis function is as follows: ； Each group has four control points which can be expressed as The control points within the group are expressed as P m , m = 0, 1, 2, 3; C represents the number of combinations, t represents M values uniformly distributed between 0 and 1, and M is the number of interpolation points generated corresponding to the control points of the group.

2. The method of claim 1, wherein the method is characterized in that: In S1, multiple seedlings of the plant to be reconstructed are selected and divided into n groups, and the seedlings in each group are placed in an open experimental box for cultivation. An image and data set of the root system of the plant is obtained after n+1 months.

3. The method of claim 1, wherein the method is characterized in that: In S3, the skeleton of each image in the labeled image set is extracted, and the specific steps are as follows: For each skeleton image, the data is measured and extracted: First, the relative length and relative depth of the main root and the number of lateral roots on the main root are recorded. The relative length, relative depth, and relative angle between the main root and the lateral roots of each lateral root are recorded from top to bottom. The relative depth is the average depth of the corresponding root system on the skeleton length, that is, the average value of the pixel vertical coordinate. The relative length is the number of pixel points of the corresponding root system on the skeleton length. The relative angle between the main root and the lateral root is calculated by fitting the current main root and lateral root as a ray. The measurement data of all skeleton images are imported into a table software for data cleaning and arrangement to obtain a skeleton feature data set.

4. A method for constructing a fractal rule function model based on citrus fiber root weight reconstruction, characterized by: The fractal rule function model is based on the original image data set of the citrus root, and the skeleton feature data set of the citrus root system is obtained by using the method of claim 1-3. For the skeleton feature dataset of citrus root, different species data were combined into data pairs, the correlation analysis of data pairs was carried out by using Spearman method, the data pairs with correlation greater than 0.5 were selected, the data pairs useless for calculating fractal rule were excluded, the remaining root length and its owned sub-root number relationship data pairs were fitted by using a variety of mathematical functions respectively, the power function with the highest fitting degree was selected as the fitting formula of the root length and its owned sub-root number relationship data pair, and the fractal rule 1: the relationship between root length and its owned sub-root number was obtained: ; wherein, the sub-root number is x, and the root length is y; Meanwhile, the Gaussian kernel function is constructed by Gaussian kernel fitting for the fractal rule related data pairs that have not been fitted, to obtain the Gaussian kernel function G1 of the fractal rule 2: the distribution law of the angle between the current root and each child root; and the Gaussian kernel function G2 of the fractal rule 3: the distribution law of the length ratio of the current root and the child root.

5. A system for reconstructing a three-dimensional vector configuration of fibrous roots of a tree-shaped root plant based on fractal rules, characterized in that, The system is used to execute the method of claim 1-3, and specifically includes a planting and sampling module, a main and lateral root labeling module, a skeleton extraction module, a fractal rule construction module, and a three-dimensional reconstruction fiber root module. The planting and sampling module is used to collect growth data of the plant root system of the plant to be reconstructed, and obtain the original image data set of the plant root system. The main and lateral root labeling module is used to construct a machine labeling model to machine label the images in the original image data set, and to manually and accurately label the original image data set based on the machine labeled images to obtain a labeled image set. The skeleton extraction module is used to extract the skeleton of each image in the labeled image set, and to import the skeleton data of each image into a table for data cleaning and arrangement to obtain a skeleton feature data set. The fractal rule construction module is used to analyze the correlation of the skeleton feature data set, and to obtain a fractal rule function model based on the analysis result. Three-dimensional reconstruction fiber root module: for obtaining the front view and side view of the same kind of plant root to be reconstructed, marking three-dimensional data points, then simulating the three-dimensional model of the plant root by using three-dimensional three-order continuous Bezier curve, calling fractal rule function model to carry out fractal on the lateral root and fiber root of the three-dimensional model of the plant root, so as to obtain the three-dimensional vector configuration of the root to be reconstructed.

Images