Target ball center fitting method and device based on long time series point cloud joint optimization

Abstract

This invention discloses a target sphere center fitting method based on long-term time-series point cloud joint global optimization, applicable to long-term time-series lidar monitoring of geological disasters in high and steep mountainous areas. It acquires three-dimensional point cloud data obtained from scanning a fixed spherical target under different time series, and segments the point cloud at each time phase into target sphere point clouds. A long-term time-series joint global optimization model objective function is constructed, fusing data fitting terms and temporal smoothing constraint terms. The data fitting term employs a robust estimation function to suppress the influence of outliers in the point cloud, while the temporal smoothing term introduces physical constraints by penalizing abrupt changes in the sphere center coordinates of adjacent time phases. The Levenburg-Marquardt algorithm is used to solve the joint global optimization model, outputting the optimal sphere center coordinate time series. This invention effectively overcomes the problem of uneven quality in single-time-phase point clouds by jointly optimizing all time-series observation data and introducing temporal constraints, significantly improving the temporal consistency, accuracy, and robustness of sphere center coordinate fitting.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional laser scanning data processing technology, specifically to a target sphere center fitting method and device based on long-term time-series point cloud joint optimization, which is applicable to scenarios requiring long-term tracking of target point coordinates, such as monitoring and deformation analysis. Background Technology

[0002] Traditional geological hazard investigation and monitoring mainly rely on manual ground patrols and simple monitoring equipment. However, when faced with steep canyons and densely vegetated high-altitude slopes, manual methods are not only inefficient and extremely risky, but also fail to detect hidden deformation signs beneath the surface or under vegetation cover, resulting in numerous "monitoring blind spots." To solve the problems of "where are the hidden dangers" and "when will the disaster occur," remote sensing technology, especially lidar (LiDAR) technology, has become a revolutionary means for the early identification and monitoring of geological hazards. LiDAR actively emits laser pulses and receives echoes, enabling it to quickly acquire dense three-dimensional point cloud data of the ground surface. Its core technological advantage lies in its ability to penetrate vegetation, removing surface vegetation cover and obtaining a high-precision digital elevation model (DEM) of the real surface, thus clearly revealing the micro-topographic features of hazard development such as surface cracks, mounds, and cavities. In recent years, through a combination of airborne (including drones and helicopters) and ground-based three-dimensional laser scanning, lidar has been successfully applied to the identification of high-altitude hidden geological hazards, achieving "CT scan-like" fine-grained detection of mountains.

[0003] As geological disaster prevention and control work shifts from "hazard identification" to "risk early warning," long-term, continuous time-series monitoring of specific hazard points to understand their deformation processes and trends becomes crucial. This means that it is necessary to conduct long-term, continuous time-series monitoring at different time points (t1, t2, ..., t...). n Repeated scanning of the same area yields long-term point cloud data, and comparative analysis allows for precise quantification of surface or specific target displacement changes. For example... Figure 2 (a) and Figure 2 As shown in (b), the same target sphere is scanned at different time phases, resulting in variations in point cloud integrity and noise. Therefore, in long-term monitoring, a fundamental and crucial step is to accurately register point clouds from multiple time phases to the same global coordinate system. However, in steep mountainous environments, lidar scanning faces significant challenges:

[0004] 1. Limited site deployment: The monitoring area is often difficult to access, the selection of scanning sites is limited, and the scanning angle and position of different time phases are difficult to completely repeat.

[0005] 2. Lack of stable features: The terrain is complex and varied, lacking stable and permanent feature points such as building corners and streetlights that are relied upon in traditional registration.

[0006] 3. Differences in point cloud characteristics: Point clouds at different times may have significant differences in density and integrity due to factors such as flight trajectory, weather conditions, and vegetation phenology. This can lead to registration methods based on the characteristics of the point cloud itself (such as the ICP algorithm) being prone to failure or producing large errors.

[0007] To address the aforementioned registration challenges, deploying artificial targets and using their geometric centers as stable control points has become the preferred solution for high-precision long-term point cloud registration. Among these, spherical targets, due to their unique advantage of rotational symmetry (their center point position remains unchanged from any direction of observation), have been proven in theory and practice to be one of the most ideal target forms. The core process of existing technologies typically involves: scanning the target sphere separately at each monitoring phase, segmenting the spherical point set from the point cloud, and then independently calculating the 3D coordinates of the sphere's center defined by the point cloud data at that phase using a spherical fitting algorithm (such as the least squares method). Finally, these sphere center coordinates calculated at different phases are used as "corresponding points" to solve for the optimal spatial transformation (rotation and translation matrices) to complete the registration of the entire point cloud scene. However, this two-step method of "independent fitting followed by registration" reveals significant limitations in long-term monitoring scenarios:

[0008] 1. Error accumulation and propagation: The sphere center coordinate fitting error of each time phase (originating from point cloud noise, occlusion, and uneven distribution) will be directly propagated and affect the final registration accuracy, and may be amplified in time series superposition.

[0009] 2. Failure to utilize temporal constraints: Treating the fitting of each time phase as an independent event ignores the strong temporal invariance constraint that "all time phases observe the same physical location of the fixed sphere center". When the point cloud quality is poor in a certain time phase (such as due to temporary occlusion causing incomplete spherical point cloud), the reliability of the independent fitting results drops sharply, forming "abnormal jump points" in the time series.

[0010] 3. Weak anti-interference ability: Traditional least squares fitting algorithms are very sensitive to outliers in point clouds (such as temporary pollutant reflections on the surface of a target sphere or interference reflections from nearby objects), which can easily cause the fitting center to deviate from the true center of the sphere.

[0011] Therefore, in the specific application context of long-term lidar monitoring of geological disasters in high and steep mountainous areas, developing a more accurate and robust spherical point cloud center coordinate fitting method that can overcome the limitations of the traditional two-step method is of urgent technical demand and important application value for improving the accuracy and reliability of deformation monitoring data, thereby achieving effective early warning of geological disasters. Summary of the Invention

[0012] This invention aims to address the problems of low accuracy in fitting target sphere center coordinates and poor temporal consistency in long-term lidar monitoring of geological disasters in high and steep mountainous areas due to the uneven quality of single-phase point clouds. This invention abandons the traditional approach of independently fitting each phase point cloud and instead constructs a spatiotemporal joint overall optimization model. This model treats all phases of the target sphere point cloud data over a long time series as a whole, while introducing physical constraints for "smooth temporal changes in sphere center coordinates" and robust estimation mechanisms to jointly calculate the globally optimal sphere center coordinate sequence.

[0013] The above-mentioned objectives of the present invention are achieved through the following technical means:

[0014] The target sphere center fitting method based on long-time-series point cloud joint optimization includes the following steps: Step 1: Acquisition and preprocessing of long-term target sphere point cloud data; Step 2: Construct the objective function of the long-term joint global optimization model ; Step 3: Based on the preprocessed long-term target sphere point cloud data, with the objective function... To optimize the objective, a joint global optimization model is solved to obtain the optimal time series of sphere center coordinates.

[0015] The acquisition and preprocessing of the long-time target sphere point cloud data are based on the following steps: Step 1.1: Deploy monitoring equipment at fixed locations within the monitoring area. A target ball, and at different times The monitoring area was repeatedly scanned using a 3D lidar to obtain... Three-dimensional point cloud dataset of each phase ,in, The phase number, The maximum number of the time phase; Step 1.2: Process the 3D point cloud dataset. Point cloud data for each time phase Segment the point cloud subset belonging to each target sphere. ,in , Number the target ball. The total number of target balls. For phase The first scanned The first target ball A three-dimensional point, Number the three-dimensional points of the target sphere. For phase The first scanned The total number of three-dimensional points of a target sphere; Step 1.3: Record each subset of the point cloud. Corresponding time phase The specific scanning time, for each time phase, and for each target sphere's point cloud subset. Independent initial spherical fitting is performed to obtain the initial fitted spheres for each target sphere at each time phase. The initial center coordinates of the fitted spheres are: The initial center radius of the fitted sphere Constrained to a preset nominal radius, the initial center coordinates of the same target sphere at various time phases. The initial center coordinate sequence of the target sphere .

[0016] The point cloud subsets belonging to each target sphere are segmented. Includes the following steps: Based on the normal vector consistency, curvature features, and prior spatial information of the target sphere placement positions of the 3D point cloud, a region growing clustering algorithm is used to automatically segment the point cloud subsets belonging to each target sphere. .

[0017] The process of obtaining the initial fitted spheres for each target sphere at each time phase includes the following steps: using the traditional least squares method to fit the point cloud subsets of each time phase and each target sphere. Perform independent initial spherical fitting to obtain the initial fitted spheres for each target sphere at each time phase.

[0018] The objective function of the long-term joint overall optimization model Based on the following formula: ; in, For the first The first target ball The corresponding iterative center coordinates of the fitted sphere. For the first The first target ball The iteration radius of the corresponding fitted sphere, For the number of iterations, For the iterative baseline radius, The fitted sphere is the initial fitted sphere. For the iterative thermal expansion coefficient, and The first Shi Xiang Ji Di Phase of time Number the three-dimensional points of the target sphere. For phase The first scanned The total number of three-dimensional points of a target sphere. For phase The first scanned The first target ball A three-dimensional point, The maximum number of the time phase. Number the target ball. The phase number; For phase The first scanned The first target ball Three-dimensional points To its corresponding phase iteration sphere center coordinates The Euclidean distance; For phase The first scanned The first target ball Three-dimensional points The geometric distance residual to the ideal sphere; For the first In the nth iteration, the 1st The first target ball Temporal Iteration Sphere Center Coordinates To the The first target ball Temporal Iteration Sphere Center Coordinates The Euclidean distance; It is a robust function. As a scale factor, These are the smoothing weighting coefficients.

[0019] The output of the optimal sphere center coordinate time series is based on the following steps: Step 3.1: For the target sphere to be optimized, determine its initial center coordinate sequence. Initial reference radius and initial thermal expansion coefficient As the initial values ​​for the optimization variables during iteration, where, Set to the preset nominal radius. Set to 0; Step 3.2: Optimize the objective function of the current target ball based on the optimization variables. Perform iterative optimization and calculate the objective function. The gradients of all optimization variables are calculated, and the values ​​of the optimization variables are updated. Step 3.3: The iteration terminates when the preset iteration termination condition is met. Step 3.4: After the iteration terminates, output the final optimized sequence of sphere center coordinates. Optimal reference radius and the optimal coefficient of thermal expansion. ; Step 3.5: Traverse all target spheres, and repeat steps 3.1 to 3.4 for the remaining target spheres to obtain the time series sequence of all optimal sphere center coordinates. .

[0020] The iterative optimization includes the following steps: The Levenburg-Marquardt algorithm is used to evaluate the objective function of the current target ball. Perform iterative optimization.

[0021] The preset iteration termination condition is based on the following steps:

[0022] objective function The relative rate of decrease of the value is less than a preset threshold, or the norm of the vector change of the optimization variable is less than a preset threshold, or the number of iterations... The preset maximum value has been reached.

[0023] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the above-described target sphere center fitting method based on long-term point cloud joint global optimization.

[0024] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described target sphere center fitting method based on long-term time-series point cloud joint global optimization.

[0025] A computer program product includes a computer program that, when executed by a processor, implements the steps of the target sphere center fitting method based on long-term time-series point cloud joint global optimization.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. From “independent” to “joint”: Incorporating observation data from multiple time points into a unified model, and using data from all time phases to jointly constrain the sphere center coordinates of each time phase, significantly improving the overall accuracy and consistency of the sphere center coordinate sequence.

[0028] 2. From "static" to "dynamic": Not only are the center coordinates of the target ball fitted, but also the time-series variation model of the target ball's radius is established to more realistically reflect the physical deformation of the target ball in the long-term field environment, thereby improving the physical accuracy and fitting precision of the model.

[0029] 3. From “fragile” to “robust”: By incorporating robust estimation and temporal smoothing constraints, the algorithm is made highly resistant to gross errors (such as occlusion and noise) and anomalous scanning conditions in single-phase point clouds, ensuring the stability of the output results. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention;

[0031] Figure 2 This is a schematic diagram of long-term point cloud data, where (a) is the point cloud data of the target sphere in the first time phase, and (b) is the point cloud data of the second time phase (showing that the same target sphere is scanned in different time phases, and the point cloud integrity and noise may be different). Detailed Implementation

[0032] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0033] Example 1:

[0034] This embodiment demonstrates the application of the method described in this invention in long-term monitoring of the stability of a steep slope on the bank of a large reservoir in southwestern China. The slope is composed of loose deposits and exhibits obvious signs of creep deformation, requiring millimeter-level displacement monitoring. During the monitoring period, the reservoir water level fluctuated periodically, and the ambient temperature changed significantly.

[0035] like Figure 1 As shown, the target sphere center fitting method based on long-term point cloud joint optimization specifically includes the following steps: Step 1: Acquisition and preprocessing of long-term target sphere point 3D cloud data.

[0036] Specifically, the process of acquiring and preprocessing long-term target sphere 3D point cloud data is as follows: Step 1.1: Deploy monitoring equipment at fixed locations within the monitoring area. A target ball, and at different times The monitoring area was repeatedly scanned using a 3D lidar to obtain... Three-dimensional point cloud dataset of each phase ,in, The phase number, The maximum number of the time phase; Specifically, four bedrock points with relatively stable geological conditions and good visibility are selected on the slope, and four of them are firmly set up (i.e., in this embodiment, ...). A high-strength PVC target sphere with a diameter of 14cm was used to form a monitoring baseline network. A RIEGLVZ-2000 ground-based three-dimensional laser scanner was used to scan at three characteristic time points (referred to as time phases): July 11, 2024 (pre-flood low water level period), December 27, 2024 (post-flood stable water level period), and September 15, 2025 (the following year's high water level period). , , In this embodiment, that is, The slope area containing all target spheres was repeatedly scanned. During scanning, the completeness and uniform density of the target sphere point cloud were ensured, ultimately obtaining three-dimensional point cloud datasets for three time phases. .

[0037] Step 1.2: Process the 3D point cloud dataset. Each phase in 3D point cloud data Based on the consistency of normal vectors, curvature features, and prior spatial information of target sphere placement in 3D point clouds, a region growing clustering algorithm is used to automatically segment the point cloud subsets belonging to each target sphere. ,in , Number the target ball. The total number of target balls. For phase The first scanned The first target ball A three-dimensional point, Number the three-dimensional points of the target sphere. For phase The first scanned The total number of three-dimensional points of a target sphere.

[0038] Step 1.3: Record each subset of the point cloud. Corresponding time phase The specific scanning time was determined using the traditional least squares method for each time phase and each target sphere's point cloud subset. Independent initial spherical fitting is performed to obtain the initial fitted spheres for each target sphere at each time phase. A nominal radius of 0.07m is used as a strong constraint, and the initial center coordinates of the fitted spheres are... The initial radius of the fitted sphere Equal to 0.07m. Initial center coordinates of the same target sphere at various time phases. The initial center coordinate sequence of the target sphere (Defined in the global coordinate system).

[0039] Step 2: Construct the objective function of the long-term joint global optimization model .

[0040] The objective function of the long-term joint global optimization model Based on the following formula: ; Indicates the first The target ball in the first The objective function at the next iteration.

[0041] Define optimization variables: Optimization variables include the iterative center coordinates of the fitted sphere. Iteration baseline radius Based on iteration and coefficient of thermal expansion .

[0042] Detailed explanation of data fitting terms: The core data fitting term aims to make the fitted sphere best match the actual observed point cloud at all time phases.

[0043] In subsequent steps, the initial fitted sphere is iteratively optimized, the th... The first target ball The corresponding iterative center coordinates of the fitted sphere are: , No. The first target ball The corresponding iteration radius of the fitted sphere is Considering the thermal expansion and contraction effect of the target sphere material, the definition is... , For the iterative baseline radius, For the iterative thermal expansion coefficient, For the number of iterations, The fitted sphere is the initial fitted sphere.

[0044] For phase The first scanned The first target ball Three-dimensional points To its corresponding phase iteration sphere center The Euclidean distance.

[0045] For phase The first scanned The first target ball Three-dimensional points To the ideal sphere (with With the center as the center, The geometric distance residual of a standard sphere (with radius ).

[0046] It is a robust function (the Huber function is used in this embodiment). When the geometric distance residual When the value is small, it behaves similarly to least squares; when the geometric distance residual exceeds a certain threshold, it reduces the value of the least squares method. The first target ball Three-dimensional points The weights are adjusted to effectively suppress the negative impact of outliers in the 3D point cloud (such as noise points generated by snow accumulation on the sphere during the December 2024 scan) on the fitting results. This is the scaling factor used to normalize the residuals.

[0047] Detailed explanation of time series smoothing term: For time-series smoothing of data; This item penalizes adjacent temporal center coordinates. The large displacements between them introduce prior knowledge of the relatively stable physical position of the target sphere, improving the temporal consistency and noise resistance of the sphere center coordinate sequence.

[0048] For the first In the nth iteration, the 1st The first target ball Temporal Iteration Sphere Center Coordinates To the The first target ball Temporal Iteration Sphere Center Coordinates The Euclidean distance; These are smoothing weights used to balance data fitting accuracy and temporal smoothness. The larger the value, the more the algorithm tends to believe that the center of the sphere is stable, and the smoother the output coordinate sequence.

[0049] Step 3: Solve the long-term joint global optimization model and output the optimal sphere center coordinate time series.

[0050] Specifically, the solution process for the long-term joint global optimization model is as follows: Step 3.1, Iterative Initialization. For the target ball to be optimized (taking target ball number 1 as an example), its initial center coordinate sequence is... Initial reference radius and initial thermal expansion coefficient As the initial value for iterative optimization, where, Assuming a nominal radius of 0.07m, Set it to 0.

[0051] Step 3.2, Iterative Optimization. The Levenberg-Marquardt algorithm is used to optimize the objective function of the current target ball. Iterative optimization. During the iteration process, the algorithm automatically calculates the objective function. Regarding all optimization variables (time-series images) , , The gradient (Jacobi matrix) of the target ball is calculated, and the optimization variable values ​​are updated to optimize the objective function of the current (target ball 1). The value of decreases. Robustness function In each iteration, the number of the current (number 1) target ball will be determined based on its position. Three-dimensional points The geometric distance residuals are automatically weighted to achieve automatic suppression of gross point clouds.

[0052] Step 3.3, Convergence Criterion. The iteration terminates when any of the following termination conditions are met: objective function The relative rate of decrease of the value is less than a preset threshold (e.g., 1e-6), or the norm of the vector change of the optimization variable is less than a preset threshold, or the number of iterations... The preset maximum value has been reached.

[0053] Step 3.4: Output Results. After the iteration terminates, output the final optimized sequence of sphere center coordinates. Optimal reference radius and the optimal coefficient of thermal expansion. .

[0054] Step 3.5: Traverse all target spheres. Repeat steps 3.1 to 3.4 for target spheres 2, 3, and 4 to obtain a high-precision, time-consistent optimal time series sequence of the center coordinates of all target spheres after joint optimization. .

[0055] After obtaining the optimal sphere center coordinate time series sequence, this embodiment further provides displacement analysis and application based on the optimal sphere center coordinate time series sequence, including the following steps: Step 4: Calculate the displacement time series; Using the optimal center coordinates of the target spheres at the initial time as a reference, the three-dimensional displacement of each target sphere relative to the initial time phase is calculated in all subsequent time phases, resulting in a displacement-time series. For the first A target ball, in time phase displacement , For the first A target ball in time phase The optimal coordinates of the sphere's center. For the first The initial optimal center coordinates of each target sphere; for example, the displacement of target sphere 1 in September 2025 relative to July 2024 is... .

[0056] Step 5: Deformation feature extraction and analysis application; Based on displacement time series, deformation feature extraction and analysis are performed to provide reliable data support for disaster early warning. The specific steps include: Step 5.1: Perform linear or nonlinear fitting on the displacement time series to obtain the deformation rate of each target ball in key directions (such as vertical elevation direction, along slope dip, and along slope direction). Step 5.2: Combine the displacement vectors of all target spheres and generate a two-dimensional or three-dimensional deformation field on the surface of the monitoring area through spatial interpolation and other methods to intuitively display the spatial distribution of deformation. Step 5.3: Generate displacement time series curves, output the visualization results of the time series target sphere point cloud, and form a standardized monitoring and analysis report.

[0057] Even with minor rain interference in the December 2024 scan data, the sphere center coordinates of that time phase were effectively constrained to a reasonable temporal trajectory after optimization using the method of this invention. The temporal consistency of the sphere center coordinate sequence was improved, which more realistically reflects the small and continuous deformation trend of the slope under reservoir water level changes and temperature changes, providing a more reliable data basis for slope stability assessment and early warning.

[0058] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods.

[0059] Example 2:

[0060] In this embodiment, a computer device is also provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in Embodiment 1 above.

[0061] Example 3:

[0062] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps in Embodiment 1 above.

[0063] Example 4:

[0064] In this embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in Embodiment 1 described above.

[0065] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A target ball center fitting method based on long time series point cloud joint optimization, characterized in that, Includes the following steps: Step 1: Acquisition and preprocessing of long-term target sphere point cloud data; Step 2, constructing the objective function of the long-term joint overall optimization model ; Step 3, based on the pre-processed long time series target ball point cloud data, taking the objective function as the optimization target, solving the joint global optimization model to obtain the optimal ball center coordinate time series.

2. The long time series point cloud joint optimization based target sphere center fitting method according to claim 1, characterized in that, The acquisition and preprocessing of the long-time target sphere point cloud data are based on the following steps: Step 1.

1. Setting up a target ball at a fixed position of the monitoring area and repeatedly scanning the monitoring area with a three-dimensional laser radar at different time phases ​​​​​​ Step 1.2: Process the 3D point cloud dataset. Point cloud data for each time phase Segment the point cloud subset belonging to each target sphere. ,in , Number the target ball. The total number of target balls. For phase The first scanned The first target ball A three-dimensional point, Number the three-dimensional points of the target sphere. For phase The first scanned The total number of three-dimensional points of a target sphere; Step 1.3: Record each subset of the point cloud. Corresponding time phase The specific scanning time, for each time phase, and for each target sphere's point cloud subset. Independent initial spherical fitting is performed to obtain the initial fitted spheres for each target sphere at each time phase. The initial center coordinates of the fitted spheres are: The initial center radius of the fitted sphere Constrained to a preset nominal radius, the initial center coordinates of the same target sphere at various time phases. The initial center coordinate sequence of the target sphere .

3. The target sphere center fitting method based on long-term point cloud joint optimization according to claim 2, characterized in that, The point cloud subsets belonging to each target sphere are segmented. Includes the following steps: Based on the normal vector consistency, curvature features, and prior spatial information of the target sphere placement positions of the 3D point cloud, a region growing clustering algorithm is used to automatically segment the point cloud subsets belonging to each target sphere. .

4. The target sphere center fitting method based on long-term point cloud joint optimization according to claim 3, characterized in that, The process of obtaining the initial fitted spheres for each target sphere at each time phase includes the following steps: using the traditional least squares method to fit the point cloud subsets of each time phase and each target sphere. Perform independent initial spherical fitting to obtain the initial fitted spheres for each target sphere at each time phase.

5. The target sphere center fitting method based on long-term point cloud joint optimization according to claim 2, characterized in that, The objective function of the long-term joint overall optimization model Based on the following formula: ； in, For the first The first target ball The corresponding iterative center coordinates of the fitted sphere. For the first The first target ball The iteration radius of the corresponding fitted sphere. For the number of iterations, For the iterative baseline radius, The fitted sphere is the initial fitted sphere. For the iterative thermal expansion coefficient, and The first Shi Xiang Ji Di Phase of time Number the three-dimensional points of the target sphere. For phase The first scanned The total number of three-dimensional points of a target sphere. For phase The first scanned The first target ball A three-dimensional point, The maximum number of the time phase. Number the target ball. The phase number; For phase The first scanned The first target ball Three-dimensional points To its corresponding phase iteration sphere center coordinates The Euclidean distance; For phase The first scanned The first target ball Three-dimensional points The geometric distance residual to the ideal sphere; For the first In the nth iteration, the 1st The first target ball Temporal Iteration Sphere Center Coordinates To the The first target ball Temporal Iteration Sphere Center Coordinates The Euclidean distance; It is a robust function. As a scale factor, These are the smoothing weighting coefficients.

6. The target sphere center fitting method based on long-term point cloud joint optimization according to claim 2, characterized in that, The output of the optimal sphere center coordinate time series is based on the following steps: Step 3.1: For the target sphere to be optimized, determine its initial center coordinate sequence. Initial reference radius and initial thermal expansion coefficient As the initial values ​​for the optimization variables during iteration, where, Set to the preset nominal radius. Set to 0; Step 3.2: Optimize the objective function of the current target ball based on the optimization variables. Perform iterative optimization and calculate the objective function. The gradients of all optimization variables are calculated, and the values ​​of the optimization variables are updated. Step 3.3: The iteration terminates when the preset iteration termination condition is met. Step 3.4: After the iteration terminates, output the final optimized sequence of sphere center coordinates. Optimal reference radius and the optimal coefficient of thermal expansion. ; Step 3.5: Traverse all target spheres, and repeat steps 3.1 to 3.4 for the remaining target spheres to obtain the time series sequence of all optimal sphere center coordinates. .

7. The target sphere center fitting method based on long-term point cloud joint optimization according to claim 6, characterized in that, The iterative optimization includes the following steps: The Levenburg-Marquardt algorithm is used to evaluate the objective function of the current target ball. Perform iterative optimization.

8. The target sphere center fitting method based on long-term point cloud joint optimization according to claim 7, characterized in that, The preset iteration termination condition is based on the following steps: objective function The relative rate of decrease of the value is less than a preset threshold, or the norm of the vector change of the optimization variable is less than a preset threshold, or the number of iterations... The preset maximum value has been reached.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the target sphere center fitting method based on long-term point cloud joint optimization as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the target sphere center fitting method based on long-term point cloud joint optimization as described in any one of claims 1 to 8.

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