Standing tree cutting degree parameter automatic inversion method based on ground-based laser radar and deep learning

Abstract

The invention provides a standing tree cutting degree parameter automatic inversion method based on a ground-based laser radar and deep learning, and relates to the technical field of forest tree measurement. The method comprises the following steps: acquiring an original three-dimensional laser point cloud based on multi-station scanning, and acquiring a clean trunk point cloud; and generating a high-density diameter-height observation data set through axial skeletonization extraction and slicing processing in combination with circle fitting calculation. A variable parameter cutting degree equation model introducing a relative tree height ratio and a height-diameter ratio factor is constructed, and a residual sum of squares objective function is established; and iteratively solving the optimal shape parameter vector by using a nonlinear least square algorithm, and outputting a model parameter of the target stumpage when a precision evaluation index is met. According to the method, the problem of measurement errors caused by branch and leaf shielding in a complex under-forest environment is effectively solved, a traditional destructive survey mode of cutting down and analyzing trees is replaced, non-destructive, high-precision and automatic inversion of standing tree cutting degree parameters is achieved, and the efficiency and the digital level of forest resource monitoring are improved.

Description

Technical Field

[0001] This invention relates to the field of forest measurement technology, and in particular to an automatic inversion method for standing tree taper parameters based on ground-based lidar and deep learning. Background Technology

[0002] The standing timber taper equation is a mathematical model describing the variation of trunk diameter with height, and it forms the basis for accurately calculating standing timber volume, biomass, and yield. Currently, the construction or calibration of taper equations is typically based on relevant forestry standards, primarily employing the traditional analytical timber survey method. This method requires felling sample trees, manually measuring the diameter with and without bark in sections, and then fitting parameters using statistical software. While existing binary volume models or simple taper equations can meet basic estimation needs, they often require variable parameter taper equations that incorporate relative tree height ratios when dealing with trunk morphology exhibiting significant nonlinear characteristics. With the development of precision forestry, the requirements for the timeliness and non-destructive nature of individual tree parameter measurements are increasing. Ground-based lidar technology, due to its ability to rapidly acquire high-density three-dimensional point cloud data of forest trees, has become an important tool in forestry surveys. Simultaneously, deep learning algorithms in computer vision have achieved breakthroughs in three-dimensional point cloud semantic segmentation, making it possible to automatically separate trunks and branches from complex forest scenes. Directly extracting trunk diameter sequences from ground-based lidar data and then inverting taper equation parameters is an inevitable trend to replace traditional destructive sampling.

[0003] However, existing ground-based lidar-based forest measurement technologies still have significant shortcomings. First, the automation level of data processing is low and the accuracy is limited. In complex forest environments, canopy shading and branch adhesion lead to high point cloud noise, making it difficult for traditional geometric fitting algorithms to accurately separate the trunk and branches, resulting in large errors in the extraction of the upper diameter, which directly affects the fitting accuracy of higher-order parameters in the taper equation.

[0004] Secondly, the model inversion lacks specificity. Existing methods mostly focus on directly calculating volume and lack a mechanism to combine high-density point cloud data with specific mathematical models that conform to regional standards. This makes it impossible to output standardized model parameters that meet the needs of forestry management, making it difficult to directly apply the measurement results to the existing forest resource management system.

[0005] Third, sampling is costly and environmentally damaging. Traditional methods rely on felling trees, which not only damages forest resources but also has a long and costly sample collection cycle, making it difficult to quickly update the taper parameters of specific tree species over a large area. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide an automatic inversion method for timber taper parameters based on ground-based lidar and deep learning. This invention solves the problems of resource destruction and low efficiency of traditional analytical timber methods, as well as the poor segmentation accuracy and difficulty in inverting standardized model parameters of existing lidar technology in complex environments.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] An automatic inversion method for standing timber taper parameters based on ground-based lidar and deep learning includes:

[0009] The original three-dimensional laser point cloud of the target tree is obtained based on a preset multi-station scanning scheme, and the original three-dimensional laser point cloud is semantically segmented to obtain a clean tree trunk point cloud containing only the tree trunk surface.

[0010] Calculate the tree height value of the clean tree trunk point cloud;

[0011] The clean tree trunk point cloud is extracted by axial skeletonization to obtain the central axis of the tree trunk, and the clean tree trunk point cloud is sliced ​​along the central axis of the tree trunk at a preset slice interval to obtain multiple tree trunk point cloud slices at different heights.

[0012] Geometric center localization and circle fitting calculation are performed on each of the tree trunk point cloud slices to obtain the corresponding cross-sectional diameter and slice height. All the cross-sectional diameters, slice heights and tree height values ​​are combined to obtain a high-density diameter-height observation dataset.

[0013] A variable parameter taper equation model was constructed that incorporates the relative tree height ratio;

[0014] Substitute the high-density diameter-height observation dataset into the variable parameter taper equation model, and construct the residual sum of squares objective function to characterize the deviation between the observed and predicted values, using the undetermined shape parameter vector as the independent variable.

[0015] The objective function of residual sum of squares is solved iteratively using a nonlinear least squares algorithm to obtain the optimal shape parameter vector. A predicted taper curve is then generated based on the optimal shape parameter vector. When the accuracy evaluation index of the predicted taper curve meets a preset threshold, the parameters of the variable parameter taper equation model of the target standing tree are output.

[0016] The present invention discloses the following technical effects:

[0017] This invention provides an automatic inversion method for standing tree taper parameters based on ground-based lidar and deep learning. By introducing deep learning semantic segmentation technology, this invention achieves accurate extraction of tree trunk point clouds in complex forest environments, effectively solving the problem of low accuracy in upper diameter measurement caused by branch and leaf obstruction and noise in existing lidar technology. Combining the non-destructive sampling advantages of ground-based lidar, it replaces the destructive survey method of traditional felled analytical trees, significantly reducing sample collection costs and protecting forest resources. At the same time, by integrating standardized variable parameter taper equations into a nonlinear least squares inversion framework, it can directly output model parameters that conform to specific forestry metrology and monitoring standards, overcoming the shortcomings of existing inversion methods that lack specificity and are difficult to directly apply to forest management systems, and realizing automated, high-precision, and standardized inversion of standing tree taper parameters. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart of an automatic inversion method for timber taper parameters based on ground-based lidar and deep learning, provided for an embodiment of the present invention;

[0020] Figure 2 A flowchart illustrating the construction process of tree trunk point cloud slices provided in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, this invention provides an automatic inversion method for standing timber taper parameters based on ground-based lidar and deep learning, including:

[0024] Step 100: Obtain the original three-dimensional laser point cloud of the target tree based on the preset multi-station scanning scheme, and perform semantic segmentation on the original three-dimensional laser point cloud to obtain a clean tree trunk point cloud containing only the tree trunk surface.

[0025] Step 200: Calculate the tree height value of the clean tree trunk point cloud;

[0026] Step 300: Axial skeletonization extraction is performed on the clean tree trunk point cloud to obtain the central axis of the tree trunk, and the clean tree trunk point cloud is sliced ​​along the central axis of the tree trunk at a preset slice spacing to obtain multiple tree trunk point cloud slices at different heights.

[0027] Step 400: Perform geometric center localization and circle fitting calculation on each of the tree trunk point cloud slices to obtain the corresponding cross-sectional diameter and slice height, and combine all the cross-sectional diameters, slice heights and tree height values ​​to obtain a high-density diameter-height observation dataset;

[0028] Step 500: Construct a variable parameter taper equation model that incorporates the relative tree height ratio;

[0029] Step 600: Substitute the high-density diameter-height observation dataset into the variable parameter taper equation model, and construct a residual sum of squares objective function to characterize the deviation between the observed and predicted values, using the undetermined shape parameter vector as the independent variable;

[0030] Step 700: Iteratively solve the objective function of the residual sum of squares using a nonlinear least squares algorithm to obtain the optimal shape parameter vector, and generate a predicted taper curve based on the optimal shape parameter vector. When the accuracy evaluation index of the predicted taper curve meets a preset threshold, output the parameters of the variable parameter taper equation model of the target standing tree.

[0031] Furthermore, the specific implementation process of step 100 is as follows:

[0032] This embodiment first deploys multiple ground-based lidar scanning stations with overlapping fields of view around the target tree to ensure sufficient overlap between adjacent stations, fully covering the circumference of the tree trunk and reducing blind spots. After acquiring multi-view mono-station lidar point clouds, this embodiment uses an iterative nearest-point algorithm to uniformly transform all mono-station lidar point clouds to the same reference coordinate system, generating a registration point cloud set. Subsequently, this embodiment performs distance-based filtering on the registration point cloud set to remove environmental noise and airborne particles far from the target tree in the background, and voxelizes or fuses redundant data in the overlapping areas, thereby obtaining a high-density original 3D lidar point cloud with good signal-to-noise ratio.

[0033] This embodiment constructs and utilizes a semantic segmentation network based on a point cloud deep learning architecture to process data. This network employs an encoder-decoder structure, enabling it to directly process unstructured 3D point cloud data. During the inference phase, the original 3D laser point cloud is input into a pre-trained trunk semantic recognition model. The model extracts high-dimensional geometric features, including spatial coordinates, reflection intensity, and local neighborhood relationships, point-by-point using a multilayer perceptron. Based on these high-dimensional geometric features, this embodiment calculates the probability value of each point cloud data point belonging to the trunk category using a fully connected layer and a Softmax normalization function. When this probability value is greater than a preset confidence threshold, the point cloud data point is assigned a trunk semantic label; otherwise, it is assigned a non-trunk label, thereby achieving point-by-point classification of the trunk point cloud.

[0034] This embodiment extracts the set of points labeled as tree trunks from the original 3D laser point cloud based on semantic tags, forming a preliminary tree trunk point cloud. Given that semantic segmentation may generate a small amount of drift noise or misclassified points at the tree trunk edges, this embodiment further performs statistical outlier removal processing on the preliminary tree trunk point cloud. Specifically, this embodiment traverses each point in the preliminary tree trunk point cloud, calculates its average distance to its k nearest neighbors, and calculates the mean and standard deviation of the average distance of all points globally. Points whose average distance is greater than the sum of the global mean and standard deviation are defined as outliers and removed, ultimately resulting in a clean tree trunk point cloud with a smooth surface, clear texture, and containing only the tree trunk surface, providing a reliable data foundation for subsequent high-precision taper parameter inversion.

[0035] The expression for the tree trunk semantic recognition model is:

[0036] ;

[0037] in, Given a point cloud Output the probability distribution of each point belonging to the trunk category; The input is the high-dimensional geometric feature matrix of the original 3D laser point cloud data; For parameters The nonlinear mapping function of deep neural networks; is the set of weights and bias parameters learned through training in the network; Softmax is the normalized exponential function; Predictive semantic labels for point cloud data points.

[0038] Specifically, this embodiment utilizes deep learning technology to construct a tree-based semantic recognition model, which is essentially a probabilistic mapping system from geometric space to semantic space.

[0039] Specifically, the model's input receives a high-dimensional geometric feature matrix of the original 3D laser point cloud data. This high-dimensional geometric feature matrix refers to the numerical set formed after feature encoding of the discrete point cloud acquired by the lidar. Its source is the original observation data from the laser scanning equipment, and its function is to serve as the underlying data foundation of the model. The specific values ​​typically include the 3D spatial coordinates of each point, the laser echo intensity value, and the normal vector or curvature features describing the local neighborhood geometry. The core processing unit of the model employs a deep neural network nonlinear mapping function. This function refers to the complex mathematical operation rules defined by a multi-layer neural network structure, used to abstract the low-level geometric features of the input layer by layer into high-level semantic representations.

[0040] The operational logic of this mapping function strictly depends on the set of weights and bias parameters learned through training in the network. These parameter sets refer to the real number matrix that is continuously iteratively optimized and finally solidified during the model supervised training phase using labeled sample data and the backpropagation algorithm. Their source is the mathematical convergence result of the training process, and their values ​​are usually a series of specific floating-point numbers. Their function is to store recognition knowledge about the tree trunk morphology (such as cylindricality and vertical continuity).

[0041] In the output layer of the model, this embodiment uses a normalized exponential function to process the raw feature response values ​​of the neural network output. The normalized exponential function is a mathematical transformation tool that compresses any real-number vector to a value between zero and one, with a sum of one. Its function is to transform the network's feature scores into a statistically significant probability distribution. Finally, based on the probability distribution of each output point belonging to the trunk category, the model selects the category corresponding to the maximum probability as the predicted semantic label for the point cloud data point, thereby achieving automatic identification and extraction of the trunk point cloud.

[0042] Furthermore, the specific implementation process of step 200 is as follows:

[0043] This embodiment, after acquiring a clean tree trunk point cloud containing only the trunk surface, first establishes or confirms a global coordinate system for the point cloud data, ensuring that the Z-axis of this coordinate system is perpendicular to the horizontal ground and parallel to the gravitational growth direction of the standing tree. This embodiment traverses all discrete laser data points contained in the clean tree trunk point cloud, extracting the vertical coordinate value of each data point along the Z-axis, thereby constructing a set of Z-axis coordinate values ​​containing the vertical height information of all surface points of the standing tree. This step, through the traversal and coordinate analysis of massive amounts of unstructured point cloud data, achieves the mapping of complex three-dimensional spatial morphology to single-dimensional vertical height information, providing a quantitative data foundation for subsequently determining the growth boundary of the standing tree.

[0044] This embodiment performs statistical sorting or extreme value retrieval on the set of Z-axis coordinate values ​​to determine the physical boundaries of the target standing tree in vertical space.

[0045] Specifically, this embodiment selects the largest coordinate value from the set and defines it as the treetop tip position. This parameter physically represents the vertical limit of the highest point of the trunk or the tip of the main shoot that can be detected by the lidar. Simultaneously, this embodiment selects the smallest coordinate value from the set and defines it as the root collar starting position. This parameter physically represents the geometric starting point in the vertical direction at the junction of the trunk base and the soil surface, typically corresponding to the felling position of the standing tree or the zero point of its height above the ground.

[0046] This embodiment calculates the tree height physical quantity based on the geometric boundaries determined above. The value at the top of the treetop is subtracted from the value at the beginning of the root collar; the difference is the calculated tree height value of the clean trunk point cloud. This tree height value quantitatively describes the vertical span of the target standing tree from the root to the top, and is a key tree measurement factor reflecting the tree's growth status. The calculated tree height value is then stored and used in subsequent steps for normalizing relative tree height ratios and constructing the height-to-diameter ratio factor in the variable parameter taper equation, thereby providing necessary macroscopic constraints for the inversion of the taper parameter.

[0047] Furthermore, such as Figure 2 As shown, this embodiment first performs a coarse layering operation with equal intervals on the Z-axis direction of the global coordinate system on the acquired clean tree trunk point cloud, thereby obtaining multiple initial layered subsets. The geometric centroid of each initial layered subset is then calculated to form a layered centroid point set. Subsequently, this embodiment uses a cubic B-spline interpolation algorithm to perform spatial curve fitting on the layered centroid point set, constructing a central axis of the tree trunk that runs through the interior of the trunk. Equal-distance divergent sampling is then performed along this central axis to obtain a series of ordered axis sampling nodes. Based on this, this embodiment calculates the tangent vector at each axis sampling node, constructs a local normal plane passing through the node and perpendicular to the tangent vector, and uses this local normal plane as a spatial retrieval reference to extract all point cloud data points located within a preset distance range on both sides of the plane, thereby completing the accurate acquisition of tree trunk point cloud slices.

[0048] Specifically, the implementation process of step 300 is as follows:

[0049] This embodiment first performs a coarse layering process on the acquired clean tree trunk point cloud based on the Z-axis of the global coordinate system, dividing the entire point cloud into multiple initial layered subsets continuously distributed in the vertical direction according to a preset vertical interval. This embodiment calculates the geometric centroid of each initial layered subset, thereby generating a layered centroid point set that reflects the center position of the tree trunk at different heights. Subsequently, this embodiment uses a cubic B-spline interpolation algorithm to perform three-dimensional spatial curve fitting on the layered centroid point set. By solving the control vertex and node vectors, a three-dimensional curve that smoothly penetrates the interior of the clean tree trunk point cloud while maintaining geometric continuity is constructed, and this curve is marked as the central axis of the tree trunk. This central axis accurately represents the bending shape and growth direction of the standing tree as its height changes.

[0050] This embodiment performs equidistant diffuse sampling along the central axis of the generated trunk based on a preset slice spacing, generating a series of axis sampling nodes arranged in an orderly manner along the axis, ensuring a uniform distribution of slice positions along the trunk's growth path. This embodiment utilizes differential geometry principles to calculate the tangent vector of each axis sampling node on the central axis of the trunk; this tangent vector indicates the instantaneous growth direction of the trunk at that node. Furthermore, this embodiment constructs a local normal plane passing through each axis sampling node and strictly perpendicular to the corresponding tangent vector. This local normal plane establishes the reference spatial orientation for subsequent extraction of the trunk cross-section, effectively correcting cross-sectional deformation errors caused by trunk tilting or bending.

[0051] This embodiment sets a preset slice thickness threshold using the local normal plane as a spatial reference. This threshold defines the effective physical thickness range of the slice along the axial direction to accommodate discrete point cloud data. This embodiment traverses each data point in the clean tree trunk point cloud and calculates the vertical Euclidean distance from each data point to the local normal plane corresponding to the current axis sampling node. This embodiment retrieves and extracts all point cloud data points located on both sides of the local normal plane whose absolute value of the vertical Euclidean distance is less than the slice thickness threshold. The set of these extracted point cloud data points is defined as a tree trunk point cloud slice at the current height, thus completing the accurate discretization extraction from three-dimensional volume data to two-dimensional cross-sectional data with specific height attributes.

[0052] Furthermore, the specific implementation process of step 400 is as follows:

[0053] This embodiment constructs a local projection plane for each extracted tree trunk point cloud slice. This local projection plane is directly defined by the local normal plane established in the preceding steps to ensure that the projection direction is strictly parallel to the instantaneous growth axis of the tree trunk at that height. This embodiment uses an orthogonal projection transformation matrix to map all discrete 3D point cloud data points contained within the tree trunk point cloud slice onto this local projection plane, thereby transforming the discrete point set in 3D space into a 2D projected point set in a 2D plane coordinate system. Subsequently, this embodiment uses a least-squares circle fitting algorithm to process the 2D projected point set, establishing a distance error objective function regarding the center coordinates and radius parameters. It then uses iterative regression calculations to find the optimal solution until the fitting circle parameters that minimize the sum of squared Euclidean distance errors from all projected points to the circumference of the fitted circle are found.

[0054] This embodiment directly parses the diameter value from the converged fitted circle parameters and defines it as the cross-sectional diameter at the slice location. The two-dimensional coordinates of the center determined from the fitted circle parameters are then transformed back to three-dimensional space and marked as the geometric center of the slice. To accurately determine the true growth position of non-upright or curved trunks, this embodiment obtains the coordinates of the bottom starting point of the trunk's central axis as the zero-point reference for measurement. This embodiment uses numerical integration or the cumulative chord length method to calculate the length of the curved path from the bottom starting point along the curved trunk's central axis to the geometric center of the current slice. This curved path length is strictly defined as the slice height. This physical quantity effectively eliminates the vertical projection error caused by trunk tilting or bending, thus truly reflecting the trunk growth characteristics of the standing tree.

[0055] After calculating a single slice, this embodiment iterates through all generated trunk point cloud slices, extracting the corresponding cross-sectional diameter and calculated slice height for each slice, forming multiple sets of one-to-one diameter-height data pairs. Based on a preset data structure standard, this embodiment combines and encapsulates all diameter-height data pairs with the tree height values ​​of the previously calculated clean trunk point cloud. Specifically, this embodiment constructs a high-density diameter-height observation dataset containing a tree height constant and a multi-row, two-column observation matrix. This dataset, in a structured form, completely stores the fine geometric morphology information of the target standing tree from root to tip, providing complete and high-precision numerical input for subsequent automated inversion of model parameters using the variable parameter taper equation.

[0056] Furthermore, the specific implementation process of step 500 is as follows:

[0057] This embodiment first selects a variable-parameter taper equation suitable for the target tree species as the basic mathematical model based on the standards and specifications in the field of forest measurement and monitoring. This aims to solve the problem that traditional fixed-parameter equations cannot flexibly adapt to changes in the trunk shape of different standing trees. This embodiment defines the relative tree height ratio as a key independent variable in the model. This ratio is obtained by calculating the quotient of the current slice height and the tree height value, and is used to unify standing trees of different absolute heights into a standardized dimensionless numerical range. Simultaneously, this embodiment introduces the ratio of diameter at breast height (DBH) value to tree height value as a height-to-diameter ratio factor, using it as a shape constraint variable to characterize the overall slenderness of the trunk, thereby enabling the constructed model to perceive the macroscopic morphological differences of individual trees.

[0058] This embodiment constructs a power function nonlinear framework containing a base term and an exponential term to specifically characterize the variation of trunk diameter with height. The base term is defined as a geometric decay function of the relative height of the trunk, specifically the ratio of the distance from the treetop to the slice to the distance from the treetop to the diameter at breast height (DBH). This base term establishes the fundamental geometric trend of the trunk diameter gradually decreasing from the base to the top. This embodiment further constructs a dynamic exponential expression as the exponential term of the power function. This exponential term is not a fixed constant but a complex polynomial composed of different power terms of the relative tree height ratio and a height-to-diameter ratio factor. Its function is to finely adjust the concavity and convexity of different parts of the trunk, characterizing the dynamic adjustment law of the trunk shape with height.

[0059] This embodiment defines a vector of undetermined shape parameters as the core variable controlling the aforementioned dynamic exponential expression. This vector contains multiple scalar elements to be inverted. In this embodiment, these scalar elements are respectively used as constant term coefficients, quarter-power term coefficients, half-power term coefficients, and height-to-diameter ratio adjustment term coefficients, which are linearly weighted and combined with the corresponding power terms of the relative tree height ratio and the height-to-diameter ratio factor. Through this parameterized construction method, this embodiment successfully establishes an automatic inversion mathematical model for timber taper parameters, using the vector of undetermined shape parameters as independent variables, the relative tree height ratio and the height-to-diameter ratio factor as inputs, and the cross-sectional diameter as the output. This provides a complete theoretical equation for subsequently solving for the optimal trunk shape parameters using numerical optimization algorithms.

[0060] Furthermore, the expression for the variable parameter taper equation model is as follows:

[0061] ;

[0062] The diameter of the cross-section of the tree trunk at any slice height; This refers to the diameter at breast height (DBH) of the tree trunk. This represents the tree height. This represents the absolute height of the current slice from the root collar of the tree trunk. This is the ratio of relative tree heights. These are the elements in the vector of shape parameters to be determined.

[0063] Specifically, this embodiment constructs and employs a variable-parameter taper equation model to quantitatively describe the trunk shape of standing trees. The model uses the cross-sectional diameter of the trunk at any slice height as the prediction target quantity. This physical quantity originates from the results of circle fitting calculations on the point cloud slices in the preceding steps, and its function is to reflect the thickness of the trunk at different height positions. The model uses the trunk's diameter at breast height (DBH) as a basic scaling factor. This value refers to the diameter of the trunk at a standard DBH position and is typically input into the model as a known quantity. The model introduces the tree height value as a constraint boundary for the vertical scale. This value represents the total length from the trunk root collar to the treetop tip. To describe positional changes, the model defines the absolute height of the current slice from the trunk root collar and calculates the relative tree height ratio accordingly. This ratio is the quotient of the absolute height and the tree height value, used to normalize the height information. The core of the model lies in the elements in the vector of undetermined shape parameters. These elements are a set of mathematical coefficients that need to be determined through inversion calculation. They serve as weighting factors in the exponential term to adjust the model's ability to fit the degree of trunk curvature and the rate of change of taper under different tree species and growth environments. Specifically, they include constant term coefficients and adjustment coefficients associated with different powers of relative tree height, which together determine the specific shape of the taper curve.

[0064] Furthermore, the specific implementation process of step 600 is as follows:

[0065] This embodiment first traverses the high-density diameter and height observation dataset generated in the preceding steps, reading the stored tree height values ​​and the corresponding diameter at breast height (DBH) values ​​for each cross-section. For each slice location, this embodiment uses division to calculate the ratio of the slice height to the tree height value, thus obtaining a normalized relative tree height ratio. Simultaneously, it calculates the ratio of the DBH value to the tree height value to generate the height-to-diameter ratio factor. These two ratios will serve as known inputs for subsequent model calculations. Based on this, this embodiment constructs a nonlinear function framework according to the preset taper equation mathematical form. This framework includes a base term describing geometric decay and an exponential term describing trunk shape adjustment, establishing the fundamental mathematical structure for diameter variation with height.

[0066] This embodiment substitutes the calculated relative tree height ratio and height-to-diameter ratio factor into the exponential term of the nonlinear function framework, and introduces an undetermined shape parameter vector as the set of independent variables to be solved. Each independent element in this undetermined shape parameter vector is used as a weighting coefficient, and linearly combined with different powers of the relative tree height ratio and the height-to-diameter ratio factor to generate a dynamic exponential expression containing undetermined coefficients. This embodiment further substitutes the diameter at breast height (DBH) value, tree height value, slice height, and this dynamic exponential expression into the nonlinear function framework, and derives a symbolic expression for diameter prediction regarding the undetermined shape parameter vector through symbolic computation. This expression establishes a direct functional relationship between the model parameters and the theoretical diameter value, where the base term represents the geometric decay law of the relative height change of the trunk; and the exponential term represents the dynamic adjustment law of the trunk shape with height change.

[0067] This embodiment performs the objective function construction step of model inversion. First, it extracts the true cross-sectional diameter corresponding to each slice from the high-density diameter and height observation dataset. This embodiment calculates the numerical difference between the true cross-sectional diameter and the aforementioned diameter prediction symbolic expression, obtaining a single-point residual term representing the single-point prediction error. To eliminate the influence of positive and negative error cancellation and highlight the weight of large error terms, this embodiment squares the single-point residual terms at all slice locations and sums all the squared results. This embodiment ultimately generates a residual sum of squares objective function with the undetermined shape parameter vector as the only variable. This function transforms the morphological fitting problem in physical space into a numerical optimization problem of finding the minimum value of a function in mathematical space.

[0068] Furthermore, the notation for diameter prediction is as follows:

[0069] ;

[0070] The expression for the objective function of the residual sum of squares is:

[0071] ;

[0072] in, Let be the height of the i-th slice, and N be the total number of slices; Given a vector of shape parameters to be determined, Let be the theoretically predicted diameter at the i-th slice position. Let be the diameter of the cross section of the tree trunk at the height of the i-th slice.

[0073] Specifically, this embodiment constructs a diameter prediction symbolic expression to calculate the theoretical predicted diameter at a certain slice position. This parameter characterizes the ideal geometric diameter of the trunk at that specific height, derived by the model under the control of a given undetermined shape parameter vector. In this calculation process, this embodiment defines the slice height of the first slice as the axial path distance from the center of the slice to the starting point at the bottom of the trunk, and defines the total number of slices as the statistical total number of slices obtained after slicing the entire standing tree. Subsequently, this embodiment constructs a residual sum of squares objective function, which is an optimization objective expression with the undetermined shape parameter vector as the sole independent variable.

[0074] Specifically, in this embodiment, the cross-sectional diameter of the tree trunk at a certain slice height is obtained as the actual observed value. The numerical deviation between the actual observed value and the corresponding theoretical predicted diameter is calculated. The deviation is squared to eliminate the influence of positive and negative signs and amplify the weight of larger errors. Finally, the squared deviation values ​​at all slice positions are summed to obtain the residual sum of squares, which quantitatively represents the degree of fit between the overall model prediction accuracy and the actual observation data.

[0075] Furthermore, the specific implementation process of step 700 is as follows:

[0076] This embodiment utilizes a nonlinear least squares solver to iteratively optimize the aforementioned residual sum of squares objective function, aiming to find the parameter combination that minimizes the deviation between the observed data and the model prediction. First, this embodiment sets initial iteration values ​​for the undetermined shape parameter vector, constructs the initial parameter vector, and inputs it into the solver. During each iteration, this embodiment uses differential calculus to calculate the first-order partial derivative matrix of the residual sum of squares objective function with respect to the undetermined shape parameter vector, i.e., the Jacobian matrix, which indicates the direction of the fastest decrease in function value. Based on the Jacobian matrix, this embodiment constructs an incremental normal equation, solves this equation using the Gauss-Newton method or the Levenberg-Marquardt algorithm to obtain the parameter update increment, and uses this increment to correct the current parameter vector. This embodiment repeats the above calculation and update process, continuously minimizing the function value of the objective function until the decrease in function value or the change in parameters between two adjacent iterations is less than a preset convergence tolerance. At this point, this embodiment stops iterating and locks the finally converged parameter vector as the optimal shape parameter vector.

[0077] This embodiment uses the obtained optimal shape parameter vector to backtest the model's fitting effect. The optimal shape parameter vector is substituted back into the variable parameter taper equation model, and the relative tree height ratio from the high-density diameter-to-height observation dataset is used as the input variable. The theoretical diameter value corresponding to each slice position is calculated one by one, and all theoretical diameter values ​​are connected in height order to form a predicted taper curve. Subsequently, this embodiment extracts the corresponding actual cross-sectional diameter from the observation dataset, uses statistical methods to calculate the difference between the actual cross-sectional diameter and the theoretical diameter value, and generates an accuracy evaluation index. Specifically, this embodiment calculates the coefficient of determination to characterize the model's ability to explain data variability, and calculates the standard deviation of the estimated values ​​to quantify the dispersion of the prediction error, thereby comprehensively evaluating whether the model parameters obtained through inversion can truly reflect the trunk shape characteristics of the target standing trees.

[0078] This embodiment concludes with a rigorous model validity determination and parameter output procedure. It invokes preset accuracy acceptance criteria, including a first threshold corresponding to the coefficients of determination and a second threshold corresponding to the standard deviation of the estimated values. The embodiment logically compares the calculated accuracy evaluation index with these thresholds. If and only if the coefficients of determination are greater than the first threshold and the standard deviation of the estimated values ​​is less than the second threshold, the embodiment determines the current model inversion result to be valid. Under this premise, the embodiment analyzes the optimal shape parameter vector, extracting the element values ​​representing constant term coefficients, power term adjustment coefficients, and height-to-diameter ratio adjustment coefficients. These values ​​are then mapped to specific parameter symbols of the standard taper equation, ultimately outputting them as parameters of the variable parameter taper equation model specific to the target standing tree.

[0079] Specifically, the first threshold set in this embodiment is derived from the general standard for measuring the goodness of fit of nonlinear regression models in statistics and the specific requirements for the accuracy of volumetric models in forestry survey planning and design specifications. Its value is typically set to a floating-point number between 0.90 and 0.95. For example, in a preferred application scenario of this embodiment, to ensure that the inversion model can explain more than 90% of the stem variation data, the first threshold is specifically set to 0.9. The second threshold set in this embodiment is derived from the ranging accuracy limit of the lidar equipment and the inherent noise level introduced by the surface roughness of the standing trees. Its value is typically set to a physical quantity between 1.0 cm and 2.0 cm. For example, to meet the accurate calculation requirements of commercial timber yield, the second threshold is specifically set to 1.5 cm. This embodiment, through the joint constraint of the above dual thresholds, ensures that the output model parameters are both statistically significant and meet the high-precision standards for practical engineering applications in terms of physical error.

[0080] Furthermore, the expression for the incremental normal equation is:

[0081] ;

[0082] Where J is the Jacobian matrix of the residual sum of squares objective function with respect to the undetermined shape parameter vector; It is the transpose of the Jacobian matrix; The damping coefficient; It is the identity matrix; Update the parameter vector increment for the current iteration step; r is the residual vector consisting of single-point residual terms for all slice positions.

[0083] Specifically, in this embodiment, the coefficient matrix of the linear equation system is constructed as the core component on the left side of the equation. This coefficient matrix is ​​composed of two parts: the first part is the matrix product of the transpose of the Jacobian matrix and the Jacobian matrix itself, used to approximate the second-order curvature information of the objective function; the second part is the product of the damping coefficient and the identity matrix. The damping coefficient is a non-negative scalar parameter used for dynamic trade-offs between gradient descent and Gauss-Newton methods, controlling the step size and direction of iteration to ensure the stability of the algorithm at different convergence stages. The identity matrix is ​​a standard square matrix with all diagonal elements being one and all other elements being zero. This embodiment also constructs a constant vector on the right side of the equation, obtained by multiplying the transpose of the Jacobian matrix and the residual vector. The residual vector is a column vector composed of the sequentially arranged single-point residual terms of all slice positions, representing the overall deviation distribution between the current model predictions and the actual observations.

[0084] This embodiment solves the constructed system of linear equations to parse the parameter vector update increment for the current iteration step. This increment directly quantifies the magnitude and direction of the value that the undetermined shape parameter vector needs to be adjusted in the current step, thereby driving the model parameters to gradually approach the optimal solution.

[0085] Furthermore, this embodiment first establishes a one-to-one mapping between the theoretical diameter values ​​output by the model calculation and the corresponding slice heights, aiming to transform discrete numerical results into positional information in geometric space. This embodiment traverses each calculation node, using the slice height values ​​at the same height position as the independent variable on the horizontal axis and the corresponding theoretical diameter values ​​as the dependent variable on the vertical axis, encapsulating each data pair into a standard two-dimensional coordinate point structure. Through this data structuring process, this embodiment transforms the abstract model parameter inversion results into a discrete set of theoretical coordinate points distributed in a two-dimensional plane coordinate system, providing fundamental geometric data support for subsequent morphological reconstruction.

[0086] This embodiment performs a rigorous topological sorting operation on the generated discrete set of theoretical coordinate points to establish the correct geometric connection order. Specifically, this embodiment selects the numerical value of the slice height as the unique sorting key and uses the quicksort algorithm to sort all coordinate points in ascending order. Through this step, this embodiment reorganizes the scattered points that might have been out of order during calculation or storage into an ordered sequence of points that monotonically increases in the height direction. This monotonicity ensures that the subsequently constructed curves physically conform to the natural law of unidirectional growth of a tree trunk from the root to the tip, effectively avoiding logical errors such as curve reversals or self-intersections.

[0087] This embodiment utilizes a cubic spline interpolation algorithm to make the arranged ordered points continuous, simulating the smooth and continuous biological characteristics of a tree trunk surface. A cubic polynomial function is constructed between adjacent coordinate points, and constraints are applied to ensure the continuity of the first and second derivatives at the nodes. This results in a smooth geometric trajectory that smoothly passes through all theoretical coordinate points without abrupt changes at the connections. Ultimately, this embodiment defines this smooth geometric trajectory generated through mathematical interpolation as a predicted taper curve. This curve intuitively and quantitatively represents the theoretical trend of the target standing tree's cross-sectional diameter gradually decreasing with increasing height, under the control of the current optimal shape parameter vector.

[0088] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0089] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An automatic inversion method for timber taper parameters based on ground-based lidar and deep learning, characterized in that, include: The original three-dimensional laser point cloud of the target tree is obtained based on a preset multi-station scanning scheme, and the original three-dimensional laser point cloud is semantically segmented to obtain a clean tree trunk point cloud containing only the tree trunk surface. Calculate the tree height value of the clean tree trunk point cloud; The clean tree trunk point cloud is extracted by axial skeletonization to obtain the central axis of the tree trunk, and the clean tree trunk point cloud is sliced ​​along the central axis of the tree trunk at a preset slice interval to obtain multiple tree trunk point cloud slices at different heights. Geometric center localization and circle fitting calculation are performed on each of the tree trunk point cloud slices to obtain the corresponding cross-sectional diameter and slice height. All the cross-sectional diameters, slice heights and tree height values ​​are combined to obtain a high-density diameter-height observation dataset. A variable parameter taper equation model was constructed that incorporates the relative tree height ratio; Substitute the high-density diameter-height observation dataset into the variable parameter taper equation model, and construct the residual sum of squares objective function to characterize the deviation between the observed and predicted values, using the undetermined shape parameter vector as the independent variable. The objective function of residual sum of squares is solved iteratively using a nonlinear least squares algorithm to obtain the optimal shape parameter vector. A predicted taper curve is then generated based on the optimal shape parameter vector. When the accuracy evaluation index of the predicted taper curve meets a preset threshold, the parameters of the variable parameter taper equation model of the target standing tree are output.

2. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 1, characterized in that, The method involves acquiring the original 3D laser point cloud of the target standing tree based on a preset multi-station scanning scheme, and performing semantic segmentation on the original 3D laser point cloud to obtain a clean tree trunk point cloud containing only the tree trunk surface, including: Multiple lidar scanning stations with overlapping fields of view are deployed around the target standing tree to obtain single-station lidar point clouds from multiple perspectives. A point cloud registration algorithm is then used to unify all the single-station lidar point clouds into the same coordinate system to obtain a registered point cloud set. The registered point cloud set is subjected to denoising preprocessing and data fusion operations to obtain the original three-dimensional laser point cloud; A semantic segmentation network based on a point cloud deep learning architecture is constructed, and the semantic segmentation network is trained under supervision using a point cloud training set containing trunk labels and non-trunk labels to obtain a trained trunk semantic recognition model. The original 3D laser point cloud is input into the trained tree trunk semantic recognition model to extract the high-dimensional geometric features of the original 3D laser point cloud, and the category probability of each point cloud data point is calculated based on the high-dimensional geometric features. Each point cloud data point is assigned a semantic label based on the category probability; Based on the semantic tags, the point set marked as the trunk tag is extracted from the original 3D laser point cloud to obtain the preliminary trunk point cloud; The preliminary tree trunk point cloud is subjected to statistical outlier removal processing to obtain a clean tree trunk point cloud that only contains the tree trunk surface; The expression for the tree trunk semantic recognition model is: ； in, Given a point cloud Output the probability distribution of each point belonging to the trunk category; The input is the high-dimensional geometric feature matrix of the original 3D laser point cloud data; For parameters The nonlinear mapping function of deep neural networks; is the set of weights and bias parameters learned through training in the network; Softmax is the normalized exponential function; Predictive semantic labels for point cloud data points.

3. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 1, characterized in that, The formula for calculating the tree height value of the clean tree trunk point cloud is as follows: ； in, The tree height value of the clean tree trunk point cloud obtained from the calculation; The top of the tree; This is the starting position of the root collar.

4. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 1, characterized in that, The clean tree trunk point cloud is subjected to axial skeletonization extraction to obtain the central axis of the tree trunk. Then, the clean tree trunk point cloud is sliced ​​along the central axis at a preset slicing interval to obtain multiple tree trunk point cloud slices at different heights, including: The clean tree trunk point cloud is roughly divided into equal-interval layers along the Z-axis of the global coordinate system to obtain multiple initial layer subsets; Calculate the geometric centroid of each initial layered subset to obtain a layered centroid point set, and use the cubic B-spline interpolation algorithm to perform spatial curve fitting on the layered centroid point set to obtain a three-dimensional curve that runs through the interior of the clean tree trunk point cloud. Mark the three-dimensional curve as the central axis of the tree trunk. Based on the preset slice spacing, equidistant diffuse sampling is performed on the central axis of the tree trunk to obtain a series of orderly arranged axis sampling nodes; Calculate the tangent vector of each axis sampling node on the central axis of the tree trunk, and construct a local normal plane that passes through the axis sampling node and is perpendicular to the tangent vector based on the tangent vector; Using the local normal plane as a reference, a preset slice thickness threshold is set. All point cloud data points located on both sides of the local normal plane and at a distance less than the slice thickness threshold are retrieved and extracted from the clean tree trunk point cloud. The set of extracted point cloud data points is defined as the tree trunk point cloud slice at the current height.

5. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 1, characterized in that, The geometric center is located and a circle is fitted to each of the tree trunk point cloud slices to obtain the corresponding cross-sectional diameter and slice height. All the cross-sectional diameters, slice heights, and tree height values ​​are combined to obtain a high-density diameter-height observation dataset, including: Construct a local projection plane for each of the tree trunk point cloud slices; Projecting all three-dimensional point cloud data points within the tree trunk point cloud slice onto the local projection plane yields a set of two-dimensional projection points. The least squares circle fitting algorithm is used to perform iterative regression calculations on the two-dimensional projection point set to obtain the fitting circle parameters that minimize the sum of squared distance errors. The diameter value in the fitted circle parameters is extracted as the cross-sectional diameter, and the center coordinates in the fitted circle parameters are marked as the geometric center of the slice. Obtain the coordinates of the bottom starting point of the tree trunk central axis, calculate the length of the curved path from the bottom starting point along the tree trunk central axis to the geometric center, and define the length of the curved path as the slice height; Traverse all the tree trunk point cloud slices, extract the corresponding cross-sectional diameter and slice height to form multiple sets of diameter-height data pairs, and encapsulate all the diameter-height data pairs and the tree height value according to a preset data structure to obtain the high-density diameter-height observation dataset.

6. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 1, characterized in that, The expression for the variable parameter slope equation model is: ； The diameter of the cross-section of the tree trunk at any slice height; This refers to the diameter at breast height (DBH) of the tree trunk. This represents the tree height. This represents the absolute height of the current slice from the root collar of the tree trunk. This is the ratio of relative tree heights. These are the elements in the vector of shape parameters to be determined.

7. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 6, characterized in that, The step of substituting the high-density diameter-height observation dataset into the variable parameter taper equation model, using the undetermined shape parameter vector as the independent variable, and constructing a residual sum of squares objective function representing the deviation between observed and predicted values ​​includes: Traverse the high-density diameter-height observation dataset to extract the tree height value and the diameter at breast height value corresponding to the cross-section diameter; Calculate the ratio of the height of each slice to the tree height value to obtain the relative tree height ratio, and calculate the ratio of the diameter at breast height (DBH) value to the tree height value to obtain the height-to-diameter ratio factor; Construct a nonlinear function framework that includes a base term and an exponential term; The relative tree height ratio and the height-to-diameter ratio factor are substituted into the exponential term as known quantities, and each element in the vector of undetermined shape parameters is used as a weighting coefficient to linearly combine with the polynomial of the relative tree height ratio to generate a dynamic exponential expression containing undetermined coefficients. Substituting the diameter at breast height (DBH) value, the tree height value, the slice height, and the dynamic exponential expression into the nonlinear function framework, a diameter prediction symbolic expression for the undetermined shape parameter vector is generated; The difference between the cross-sectional diameter and the diameter prediction symbolic expression in the high-density diameter-height observation dataset is calculated to obtain a single-point residual term. The single-point residual terms at all slice locations are squared and summed to generate the residual sum of squares objective function with the undetermined shape parameter vector as the only variable. The notation for diameter prediction is: ； The expression for the objective function of the residual sum of squares is: ； in, Let be the height of the i-th slice, and N be the total number of slices; Given a vector of shape parameters to be determined, Let be the theoretically predicted diameter at the i-th slice position. Let be the diameter of the cross section of the tree trunk at the height of the i-th slice.

8. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 7, characterized in that, The base term represents the geometric decay law of the relative height change of the tree trunk; the exponential term represents the dynamic adjustment law of the trunk shape with height change.

9. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 1, characterized in that, The method involves iteratively solving the objective function of the residual sum of squares using a nonlinear least squares algorithm to obtain an optimal shape parameter vector. A predicted taper curve is then generated based on this optimal shape parameter vector. When the accuracy evaluation index of the predicted taper curve meets a preset threshold, the parameters of the variable parameter taper equation model for the target standing tree are output, including: Set the initial iteration values ​​for the vector of shape parameters to be determined; An initial parameter vector is constructed based on the initial iterative values, and the initial parameter vector and the objective function of the residual sum of squares are input into the nonlinear least squares solver. The Jacobian matrix of the residual sum of squares objective function with respect to the undetermined shape parameter vector is calculated using the nonlinear least squares solver. Based on the Jacobian matrix, an incremental normal equation is constructed. The initial parameter vector is iteratively updated to minimize the function value of the residual sum of squares objective function until the decrease in the function value is less than the preset convergence tolerance. The finally converged parameter vector is locked as the optimal shape parameter vector. Substitute the optimal shape parameter vector back into the variable parameter taper equation model, and use the relative tree height ratio in the high-density diameter-height observation dataset as the input variable to calculate the theoretical diameter value corresponding to each slice position. The predicted taper curve is constructed based on the theoretical diameter values ​​at all slice locations; Extract the true cross-sectional diameter from the high-density diameter-height observation dataset; Calculate the statistical difference between the actual cross-sectional diameter and the theoretical diameter to obtain the accuracy evaluation index, including the coefficient of determination and the standard deviation of the estimated value. The accuracy evaluation index is compared with the preset accuracy acceptance threshold. If the coefficient of determination is greater than the first threshold and the standard deviation of the estimated value is less than the second threshold, the model inversion is deemed effective. The values ​​of each element in the optimal shape parameter vector are extracted and output as parameters of the variable parameter taper equation model of the target standing tree. The expression for the incremental normal equation is: ； Where J is the Jacobian matrix of the residual sum of squares objective function with respect to the undetermined shape parameter vector; It is the transpose of the Jacobian matrix; The damping coefficient; It is the identity matrix; Update the parameter vector increment for the current iteration step; r is the residual vector consisting of single-point residual terms for all slice positions.

10. The automatic inversion method for timber taper parameters based on ground-based lidar and deep learning according to claim 9, characterized in that, The predicted taper curve is constructed based on the theoretical diameter values ​​for all slice locations, including: Establish a one-to-one mapping relationship between the theoretical diameter value and the slice height; Based on the one-to-one mapping relationship, each corresponding theoretical diameter value and slice height are encapsulated into a two-dimensional coordinate point to obtain a discrete set of theoretical coordinate points. Based on the numerical value of the slice height, the discrete set of theoretical coordinate points is sorted in ascending order to obtain an ordered sequence of points that monotonically increases in the height direction; The ordered point sequence is made continuous using a cubic spline interpolation algorithm to construct a smooth geometric trajectory connecting all the theoretical coordinate points; The smooth geometric trajectory is defined as the predicted taper curve.

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