3DGS linear point cloud length calculation method based on Kalman filtering

Abstract

The application relates to the technical field of computer vision and image understanding, and discloses a 3DGS linear point cloud length calculation method based on Kalman filtering, which comprises the following steps: reconstructing length calculation into a method of dynamic integration of a virtual measurement probe along an information field; under the Kalman filtering framework, equivalent length elements and direction confidence degrees contained in a 3DGS point covariance matrix are decoded, multi-point information is fused to update a probe state containing accumulated length, and then eigenvalue spectrum and a historical state sequence are utilized to adaptively constrain path generation logic; the application is free from dependence on point cloud geometric topology integrity, a measurement process can maintain logical continuity in a data sparse or interrupted area, and an inherent topology perception and historical self-consistency constraint mechanism ensure adaptability and reliability of the method in complex path and long distance measurement, thereby providing an effective path for real-time three-dimensional linear structure understanding at a resource-limited edge end.

Description

Technical Field

[0001] This invention relates to a method for calculating the length of 3DGS linear point clouds based on Kalman filtering, belonging to the field of computer vision and image technology. Background Technology

[0002] Currently, when using 3D Gaussian spherical point clouds for 3D reconstruction and geometric measurement of linear structures such as power cables, industrial pipelines, or biological blood vessels, a commonly used approach under current technological conditions is based on high-precision geometric topology reconstruction. This approach typically focuses on constructing a continuous and explicit 3D spatial path from discrete and often noisy point cloud data through complex denoising, segmentation, interpolation, and connection algorithms, and then calculating the length of this path by accumulation. This technical approach can provide effective results in offline analysis scenarios with ideal data quality and sufficient computing resources.

[0003] However, with the rapid development of automated inspection, embedded diagnostics, and IoT applications, the industry has placed far higher demands on the real-time performance of measurement processes, the economic efficiency of deployment costs, and the reliability under imperfect data. Against this backdrop, the aforementioned geometric reconstruction-based approach, with its high computational cost in pursuit of perfect geometric shape and stringent reliance on data quality, has gradually shifted from an acceptable technical compromise in the industry to a limiting factor in specific application scenarios, such as edge computing or real-time processing.

[0004] Analysis reveals that this inherent limitation stems primarily from a fundamental inversion of its technical approach: unnecessarily escalating a problem of measuring macroscopic one-dimensional information into a problem of perfectly reconstructing microscopic three-dimensional geometry. Specifically, existing technologies suffer from the following shortcomings: they are overly dependent on the integrity of the point cloud's geometric topology. When point clouds exhibit widespread local deficiencies or sparsity due to occlusion, reflection, or high-speed scanning, the geometric connection chain breaks, leading to significant measurement deviations or failures. The majority of computational resources are consumed in the intermediate reconstruction stage, rather than the final length measurement target. This resource mismatch is unacceptable for edge devices with limited computing power and power consumption, hindering the real-time deployment and large-scale application of this type of measurement technology in scenarios such as drones or portable probes. Therefore, the technical problem this invention aims to solve is to abandon the traditional path of high computational cost in geometric reconstruction and create a new method that can accurately understand and calculate the length of linear structures directly from imperfect 3DGS point cloud data in a highly fault-tolerant manner. Summary of the Invention

[0005] This invention provides a method for calculating the length of 3DGS linear point clouds based on Kalman filtering. Its main purpose is to solve the problem of accurately calculating the length of linear structures directly from imperfect 3DGS point clouds in a highly fault-tolerant manner by abandoning geometric reconstruction paths.

[0006] To achieve the above objectives, this invention provides a method for calculating the length of a 3DGS linear point cloud based on Kalman filtering, comprising the following steps: Step a, calculate the length of the linear point cloud and reconstruct it into a method of dynamic integration along the information field formed by a virtual measurement probe along the point cloud. The information field is composed of the local geometric and orientation information of each 3DGS point in the 3DGS point cloud. Step b, define the Kalman state of the virtual measurement probe, which includes the accumulated path length component, position component, and orientation component; Step c: Within the Kalman filter framework, the prediction and correction loop is iteratively executed to update the Kalman state. The correction process includes obtaining the covariance matrix of 3DGS points located in the neighborhood of the predicted position of the virtual measurement probe, and decoding the equivalent length element and orientation confidence represented by each point from the covariance matrix; and forming a fused observation vector to correct the virtual measurement probe state by weighted fusion of the equivalent length element, position, and orientation of the 3DGS points, where the weight values ​​used for weighted fusion depend on the orientation confidence. Furthermore, the execution of the correction loop is also subject to the joint constraints of the following two mechanisms: first, using the eigenvalue spectrum distribution of the covariance matrix to evaluate the uncertainty of the local topology, thereby adaptively adjusting the path generation logic; second, applying a self-consistency constraint to the current correction based on a sliding window containing historical states. Step d: When the loop terminates, the accumulated path length component in the virtual measurement probe state is used as the calculated length of the linear point cloud.

[0007] Preferably, the magnitude of the direction confidence is positively correlated with the ratio of the first principal eigenvalue of the covariance matrix to the sum of the remaining eigenvalues; the magnitude of the equivalent length element is determined by the square root of the first principal eigenvalue of the covariance matrix, which reflects the spatial extension of the 3DGS point in the principal direction.

[0008] Preferably, the weight values ​​used in the weighted fusion also depend on the distance between the respective positions of the 3DGS points and the predicted positions of the virtual measurement probe, and on the angle between the respective directions of the 3DGS points and the predicted directions of the virtual measurement probe.

[0009] Preferably, the method of adaptively adjusting the path generation logic using the eigenvalue spectrum distribution of the covariance matrix includes: calculating the eigenvalue spectrum entropy, which characterizes the degree of balance of the eigenvalue spectrum distribution of the fused covariance matrix, based on the fused covariance matrix formed by fusing 3DGS point information in the neighborhood. ; Eigenvalue spectral entropy The calculation satisfies: ,in, For the first fusion covariance matrix eigenvalues The normalized proportion of the sum of all eigenvalues; then, the calculated eigenvalue spectral entropy. The path generation logic is compared with an entropy threshold, and based on the comparison result, it dynamically switches between a path generation logic dominated by directional components and a path generation logic that prioritizes multi-directional spatial exploration.

[0010] Preferably, when the eigenvalue spectral entropy When the entropy threshold is not less than the specified threshold, the path generation logic that prioritizes multi-directional spatial exploration includes: pausing the prediction based on the directional components of the virtual measurement probe at the previous moment; starting from the current position of the virtual measurement probe, issuing multiple parallel virtual sub-probes into the planar sector defined by the first two principal eigenvectors of the fused covariance matrix; and selecting the eigenvalue spectral entropy that enables the next state to be optimized. The preferred path for the virtual sub-probe with the largest decrease is determined by a method that constrains the current correction based on a sliding window containing historical states. This method includes: maintaining a sliding window that stores the N most recent corrected historical states of the virtual measurement probe, where N is an integer greater than 1; and performing self-consistent pre-calibration on the position or orientation components of the fused observation vector based on a local path trend jointly defined by the historical states within the sliding window before correcting the predicted virtual measurement probe state using the fused observation vector.

[0011] Preferably, the local path trend is a historical self-consistency curve obtained by polynomial fitting of the position components of N historical states within the sliding window; the self-consistency pre-calibration is to perform a weighted average of the position components in the fused observation vector to the projection point of that position on the historical self-consistency curve; and to perform a weighted average of the direction components in the fused observation vector to the tangent direction of the historical self-consistency curve at that projection point.

[0012] Preferably, the termination condition of the loop is that a 3DGS point is not acquired consecutively within a predetermined number of times in the neighborhood of the predicted position of the virtual measurement probe.

[0013] Preferably, when no 3DGS point is acquired in the neighborhood of the predicted location of the virtual measurement probe, the correction step is skipped, and the state of the virtual measurement probe is updated only according to its prediction model to maintain the logical continuity of the path in the data interruption area of ​​the 3DGS point cloud.

[0014] Preferably, the weight values ​​used in the weighted fusion are also modulated by a dynamic weighting factor. The magnitude of the dynamic weighting factor is inversely proportional to the dispersion of the virtual measurement probe’s most recent N historical directional components, so as to reduce the weight of the current observation information when the dispersion of the historical directional components increases.

[0015] Compared with the prior art, the beneficial effects of the present invention are: 1. The method employed in this invention decodes the covariance matrix inherent in each three-dimensional Gaussian spherical point into a directional confidence level that directly characterizes the significance of its linear features and an equivalent length element that reflects its spatial extension in the principal direction, thereby changing the way point cloud information is utilized. It no longer treats the point cloud as a geometric node that requires laborious connection, but rather as a non-uniform field carrying its own mass and length information. The virtual measurement probe performs weighted fusion and dynamic integration of the effective information in this field within the Kalman filter framework. This processing method frees the measurement process from dependence on the geometric topological integrity of the point cloud. When encountering local data loss caused by occlusion or high-speed scanning, which is common in the real world, the probe can still smoothly flow through the data vacuum area based on its inherent motion model and established directional beliefs, thereby ensuring the continuity of path understanding and the global effectiveness of length calculation without sacrificing inspection efficiency.

[0016] 2. This invention further elevates the utilization of covariance matrix information from single-dimensional directional extraction to real-time quantitative perception of local topological uncertainties. By introducing the eigenvalue spectral entropy as a metric, the method itself gains a self-awareness capability. When the virtual measurement probe reaches a sharp corner or intersection of the path, the natural increase in this entropy value becomes a clear internal signal, triggering the path generation logic to automatically switch from an efficient directional inertia mode to a more cautious spatial diffusion exploration mode. This mechanism, which adaptively adjusts its behavior based on the inherent structural complexity of the data, enables this method to exhibit structural adaptability that surpasses conventional filtering algorithms when facing complex paths, avoiding path interruptions or errors caused by rigid logic.

[0017] 3. This invention also avoids the long-distance drift problem caused by error accumulation in traditional Kalman filters by constructing a sliding window calibration mechanism based on historical state self-consistency. This mechanism transforms the path segment verified by the probe into a historical template for constraining the current decision. Before each update iteration, the newly acquired observation information is pre-calibrated using this template, thereby organically unifying the local smoothness and global consistency of the path. This closed-loop design, which utilizes the information byproducts generated by the method itself for self-supervision and correction, not only avoids the additional costs brought about by introducing external sensors or more complex motion models, but also ensures that the final calculated path length is based on a more stable and reliable measurement process with memory capabilities and self-correction. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a method for calculating the length of a 3DGS linear point cloud based on Kalman filtering, according to the present invention. Figure 2 This is a schematic diagram illustrating the variation of the eigenvalue spectral entropy with path position according to the present invention; Figure 3 This is a schematic diagram illustrating the data flow and collaborative relationships between the various functional modules of this invention.

[0019] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0021] The present invention discloses a 3DGS linear point cloud length calculation method based on Kalman filtering. The core of its technical solution lies in reconstructing the length calculation of the linear point cloud into a method of dynamic integration along the information field formed by a virtual measurement probe along the point cloud. This process mainly includes the construction of the information field, iterative updating of the virtual measurement probe state based on the Kalman filtering framework, and the final output of the length component. In a specific implementation scenario, such as using a drone to perform 3D scanning of power transmission cables or industrial pipelines, the acquired 3DGS point cloud data often exhibits local sparseness and data interruptions due to factors such as occlusion, high-speed movement, or material reflection. Faced with such imperfect source data, this method first defines the local geometric and directional information carried by each 3DGS point as a non-uniform information field. A virtual measurement probe, configured with accumulated path length components, 3D position components, and travel direction components, is initialized at a known endpoint of the linear point cloud. The stable operation of the Kalman filter framework is based on the reasonable initialization of its core covariance matrix. This initialization procedure binds the initial values ​​of each matrix to measurable physical quantities or statistical priors. Among them, the measurement noise covariance matrix... It is used to quantify the uncertainty of a single observation data, and its diagonal element values ​​are taken from the single-point measurement accuracy specified in the technical specifications of the 3DGS scanning equipment. The square of, that is Alternatively, it can be taken from the sample variance of the residual sequence obtained after linear fitting of a small segment of flat point cloud; process noise covariance matrix. It is used to characterize the unpredictable perturbation of the probe's motion model between two iterations, and its diagonal element values ​​are set as the estimated maximum physical deviation of the linear structure under test within a unit step. The square of, Smaller values ​​are used for rigid pipes and larger values ​​are used for flexible cables; State estimation covariance matrix The confidence level, used to characterize the initial state of the probe, is set to a diagonal element that is positive. diagonal matrix , here Let be a non-informative prior constant, such as 1000, and The identity matrix is ​​set so that the filter can accept the observation data to the greatest extent during the first iteration, thereby achieving rapid convergence of the state.

[0022] The Kalman state evolution of the virtual measurement probe follows an iterative prediction and correction loop within a Kalman filtering framework. In each iteration, the system first predicts the probe's theoretical position at the next moment based on its current state, particularly its orientation components. When point cloud data is interrupted or sparse, this prediction step updates the state based on its inherent motion model, maintaining the logical continuity of the path. Next, the system searches within a preset neighborhood space centered on the predicted position to obtain one or more 3DGS points as the observation basis for this state correction. In the correction phase, the system obtains the covariance matrix from the 3DGS points located in the neighborhood of the virtual measurement probe's predicted position and decodes the equivalent length element and orientation confidence represented by each point from the covariance matrix. Specifically, for each 3DGS point in the neighborhood, the system performs eigenvalue decomposition on its 3D Gaussian covariance matrix. Given the local anisotropy of the linear structure, its first principal eigenvalue... It is significantly larger than the other eigenvalues. and The sum; based on this, the square root of the first principal eigenvalue. It is used to determine an equivalent length element, the physical meaning of which lies in quantifying the spatial extension of the 3DGS point in its principal direction. Meanwhile, The proportion relative to the sum of the remaining eigenvalues ​​is used to define a directional confidence level, the magnitude of which is positively correlated with this proportion, to characterize the significance of the linear feature of the point. Furthermore, the system forms a fused observation vector to correct the virtual measurement probe state by weighted fusion of the equivalent length element, position, and direction indicated by the first principal feature vector of the 3DGS point. The weight values ​​used in the weighted fusion are deterministically designed as a function, whose input variables include at least: the aforementioned directional confidence level, the distance between the position of each 3DGS point and the predicted position of the virtual measurement probe, and the angle between the direction of each 3DGS point and the predicted direction of the virtual measurement probe. Thus, 3DGS points with more significant linear features, closer spatial positions, and smaller directional deviations will be given higher influence in the correction process.

[0023] In the weighted fusion process, the fused observation vector used to correct the state of the virtual measurement probe is the 3DGS point in each neighborhood. The corresponding fusion weight value It is obtained through a deterministic numerical calibration procedure, which begins with the dimensionless processing of each physical influence factor, including the Euclidean distance between the 3DGS point and the probe prediction location. Transform into distance factor ,in, The neighborhood search radius is the angle between the direction vector of this point and the probe prediction direction. Transform into angle factor The confidence factor is defined as the confidence level of the direction representing the significance of the linear feature of the point, as determined by the covariance matrix decoding. Subsequently, a weighted index is constructed. Adjusted product weight function model Among them, the weight index These weighting indices are used to determine the relative contributions of spatial proximity, directional consistency, and observation data reliability, respectively. Ultimately, the values ​​of these weighting indices are determined using a grid search algorithm on a reference 3DGS point cloud dataset with true length values ​​within a predefined numerical space, such as... The optimal solution is obtained iteratively with the sole optimization objective of minimizing the absolute error between the final calculated length and the true length. To address the challenge of determining paths in topologically complex regions such as intersections, forks, or sharp corners, this method integrates an adaptive path generation logic. This logic first fuses 3DGS point information within the neighborhood to form a fused covariance matrix, and then calculates an eigenvalue spectral entropy based on this matrix. Its calculation follows the formula ,in, The first digit of the fusion covariance matrix eigenvalues The entropy value is the normalized proportion of the sum of all eigenvalues. Used to assess the uncertainty of local topology, the entropy value remains low when the probe travels along a straight path, but increases significantly when it reaches an intersection. The system will then calculate... Compared with a preset entropy threshold, if If the value is not less than this threshold, the system dynamically switches from a path generation logic dominated by directional components to a path generation logic that prioritizes multi-directional spatial exploration. Under this exploration logic, the system pauses predictions based on the directional components from the previous time step and instead starts from the current position, sending out multiple parallel virtual sub-probes into the planar sector defined by the first two principal eigenvectors of the fused covariance matrix, and selecting the eigenvalue spectral entropy that enables the next state. The sub-probe path with the largest descent is used as a continuation of the main path.

[0024] Furthermore, to suppress the cumulative drift that may occur during long-distance iterations, the system also employs a self-consistency constraint mechanism based on a sliding window of historical states. This mechanism maintains a window that stores the most recent virtual measurement probe data. A sliding window with corrected historical state, in which For integers greater than 1, before using the fused observation vector for correction, the system first defines a local path trend based on the historical states within the sliding window, and pre-calibrates the fused observation vector accordingly. In a specific implementation, this local path trend is determined by analyzing the historical states within the window. A historical consistency curve is obtained by polynomial fitting of the position components of each historical state. Pre-calibration involves weighted averaging of the position components in the fused observation vector to their projection points on this curve, and weighted averaging of their direction components to the tangent direction of the curve at those projection points. Furthermore, the weights used in the weighted fusion are modulated by a dynamic weighting factor, the magnitude of which is closest to the virtual measurement probe. The dispersion of each historical direction component is inversely proportional to the current observation information, so as to reduce the weight of the current observation information when the dispersion of the historical direction component increases. The prediction and correction cycle continues. When a predetermined number of times a 3DGS point is not acquired in the neighborhood of the predicted position of the virtual measurement probe, the cycle terminates. At this time, the accumulated path length component finally recorded in the virtual measurement probe state is output as the calculated length of the linear point cloud.

[0025] Example 1: In an online monitoring operation of a process pipeline in a large chemical plant area, partially covered by insulation and exhibiting surface corrosion, the technical solution of this invention is deployed on a mobile scanning terminal. The 3DGS point cloud data collected by this terminal shows positional noise due to corrosion in the straight section of the pipeline, and at a complex node consisting of valves, support structures, and another accompanying pipeline, it exhibits data occlusion and topological ambiguity. When the virtual measurement probe travels along the straight section of the pipeline, although the individual 3DGS points constituting the information field experience continuous positional disturbances due to surface corrosion, the self-consistency constraint mechanism based on the historical state sliding window continues to play a stabilizing role during this stage. This mechanism, through recent... Polynomial fitting is performed on the position components of the corrected historical state to maintain a historical self-consistency curve representing the local path trend. In each correction cycle, the newly acquired fused observation vector with noise is pre-calibrated onto this historical self-consistency curve. In this way, the drift caused by single-point observation noise is effectively suppressed, thereby ensuring the directional consistency of the probe measurement in long-distance straight segments. As the probe approaches the complex node, 3DGS points belonging to the main pipe, support structure, and adjacent accompanying pipes begin to appear simultaneously in the neighborhood of its predicted position. The shape of the local information field changes from anisotropy to isotropy, causing the eigenvalue spectrum distribution of the fused covariance matrix formed by fusing neighborhood point cloud information to tend to be balanced, and its eigenvalue spectrum entropy The calculated value then rises accordingly and exceeds the preset entropy threshold. This change immediately triggers the adaptive adjustment of the system path generation logic, switching from the efficient advancement logic dominated by the directional component to a prudent decision-making logic that prioritizes multi-directional spatial exploration.

[0026] Under this decision-making logic, the system suspends prediction in a single direction and instead sends out multiple parallel virtual sub-probes from the current position into the planar sector defined by the first two principal eigenvectors of the fused covariance matrix. At this point, the aforementioned self-consistency constraint mechanism and the current adaptive path generation logic work closely together. The local path trend defined by the historical self-consistency curve provides a deterministic constraint for the evaluation of these parallel virtual sub-probes, effectively narrowing the exploration space. Ultimately, the continuation path chosen by the system is the one that not only maximizes the eigenvalue spectral entropy of the next state... The virtual sub-probe path exhibits the largest decrease and best matches the trend indicated by the historical self-consistency curve. The inherent synergy of this mechanism allows the system to rapidly integrate on simple paths without human intervention, and to make decisions on complex paths based on both historical and future information. This ensures the correct continuation of the main pipeline path without path interruption or erroneous jumps to accompanying pipelines. Ultimately, the virtual measurement probe logically and continuously traverses a mixed region containing noise, obstructions, and topological ambiguities, and outputs the accumulated path length component of the pipeline upon reaching the predetermined endpoint. The entire measurement process does not rely on an explicit and complete reconstruction of the pipeline geometry model.

[0027] Example 2: To quantitatively verify the effectiveness and robustness of the method of the present invention when facing technical challenges such as incomplete point cloud data and complex path topology, a comparative experimental environment based on computer simulation was built. This environment can generate 3DGS point cloud data with precise geometric parameters and known reference lengths, and can programmatically introduce specific defects. A conventional method based on point cloud skeleton extraction and path integration was used as the comparative method in this experiment. During the experimental parameter setting stage, the eigenvalue spectral entropy discrimination threshold, i.e., the entropy threshold, and the size of the historical state sliding window in the method of the present invention were determined. All settings were configured through a deterministic calibration process. The entropy threshold was set to balance the detection sensitivity to complex path topologies with the immunity to point cloud noise. To this end, a standard 3DGS point cloud sample library containing straight lines, smooth curves, corners at different angles, and intersection nodes was first established. The eigenvalue spectral entropy of each type of topology in the sample library was then calculated. Statistical analysis was performed to obtain the numerical distribution range, and then a value that could distinguish between simple and complex topologies with minimal classification error rate was selected, such as 0.7, as the entropy threshold for this experiment; similarly, the sliding window size... The setting aims to balance the ability to remember long-term path trends with the response speed to local path changes. Its value is related to the expected range of change in path curvature. In this experiment, for a general industrial scenario, the setting is... The value is 15; a total of four test cases were designed for the experiment, all based on a smooth curve model with a baseline length of 100.0m. Table 1 shows the experimental data records.

[0028] Table 1: Comparison of length calculation results for the two methods under different test cases.

[0029]

[0030] Under the complete data conditions of use case A, the measurement errors of both methods are at a low level (see Table 1). In use case B, a continuous data interruption of 20% length is introduced in the middle of the curve. The comparative method deviates significantly from its calculation results because it cannot construct a complete geometric topology connection. However, the virtual measurement probe in the method of this invention automatically switches its state update to a mode that relies solely on the prediction model after entering the data interruption area, maintaining the logical continuity of the path. Its final length calculation error is still within 1%. In use case C, when the path reaches a 90° corner, the local eigenvalue spectral entropy calculated by the method of this invention... When the instantaneous value exceeds the set entropy threshold, it triggers the adaptive path generation logic, enabling the path to turn correctly. In contrast, the comparison method, due to its inherent tendency to smooth out paths, creates shortcuts at corners, leading to an underestimation of the length. For the Y-shaped branching path in use case D, the method of this invention not only senses the existence of nodes through entropy value changes but also selects a branch that is more consistent with the path trend before entering the node as the continuation path through the historical state self-consistency constraint mechanism, thereby obtaining a measurement result close to the baseline length. In contrast, the comparison method produces a large error because it cannot handle this topological ambiguity point.

[0031] Example 3: This example combines Figures 1 to 3 This section explains the method for calculating the length of 3DGS linear point clouds based on Kalman filtering, as follows: Figure 1As shown, the process begins with inputting 3DGS linear point cloud data that may contain sparse, interrupted, or noisy elements. An initialization step constructs a virtual measurement probe and defines a Kalman state, which includes three core components: accumulated length, position, and orientation. Subsequently, an iterative loop based on a Kalman filter framework is entered. Within the loop, a prediction step is first executed, predicting the new state based on the motion model and the current orientation. This is followed by a correction step, updating the probe state by fusing neighborhood point cloud information. During this iteration, a parallel self-consistent constraint mechanism based on a historical state sliding window continuously runs. This mechanism uses local path trends to pre-calibrate the observation vector to suppress drift and applies it to the correction step. Simultaneously, the output of the correction step is also fed back to the mechanism in the form of updated historical states, forming a dynamic constraint closed loop. At the same time, the system makes real-time judgments on whether the local topology is complex, based on the eigenvalue spectral entropy > threshold. If the judgment is yes, the adaptive path generation logic is triggered, switching the path generation to a multi-directional spatial exploration mode to handle corners or forks, and applying the adjusted logic to the prediction step. The termination condition of the iterative loop is that no valid 3DGS point is obtained in the neighborhood for N consecutive times. If the condition is not met, the loop continues; if the condition is met, the loop terminates and enters the output stage. Finally, the accumulated path length in the final state of the virtual measurement probe is extracted as the calculated length of the linear structure.

[0032] like Figure 2 As shown in the figure, the horizontal axis represents the path position (m), and the vertical axis represents the eigenvalue spectral entropy. The figure contains two curves, where the solid line represents the eigenvalue spectral entropy calculated in real time along the path. The dynamic value is represented by the dashed line, which represents the preset entropy threshold. As can be seen from the graph, on most path segments... The value remains at a low level, below the entropy threshold, but around 50 meters and 80 meters, the value shows significant peaks and exceeds the entropy threshold.

[0033] like Figure 3As shown, the entire system acquires D1: 3DGS point cloud data from the 3DGS scanning system. Neighborhood point cloud data is fed into the 1.0 decoding neighborhood point cloud information module, where it is processed to generate a fused observation vector. Simultaneously, the neighborhood point cloud data is also fed into the 4.0 adaptive path adjustment logic module. After performing logical judgments, this module sends a path generation logic switching signal to the 2.0 iterative probe state update module and also participates in the final length calculation. Module 2.0 is the iteration core; it receives the fused observation vector and simultaneously receives self-consistency pre-calibration information from the 3.0 self-consistency constraint execution module, updating the D2: Kalman probe state. The updated calibrated state is fed into the D3: historical state sliding window to form a historical state sequence, which is then used by module 3.0 to execute the next self-consistency constraint. Module 2.0 outputs the updated state to D2, and D2 feeds back the current state containing the updated information and the prediction to module 2.0 for the next iteration, finally outputting the calculation results to the application.

[0034] Example 4: In an application for length measurement of flexible linear structures with complex three-dimensional morphology, such as vascular networks in living organisms or compact cable bundles inside industrial robots, the key internal mechanism of the method of this invention is deterministically triggered and regulated when faced with drastic changes in path curvature and topological complexity. During the initialization or periodic self-calibration phase, the method dynamically optimizes the polynomial fitting model used to construct the historical self-consistency curve. Within the current historical state sliding window, the system uses first-order, second-order, and third-order polynomials in parallel to optimize the curve. The system fits the model to each historical position component and calculates an evaluation index of the Bayesian information criterion for each fitting result. This index penalizes the complexity of the model to prevent overfitting. The system finally selects the order with the best score under this criterion as the model used to generate the historical self-consistency curve in the current iteration cycle. Thus, when the virtual measurement probe travels along a straight line segment, the model automatically decreases to the first order, while when it enters a smooth curve segment, it automatically increases to the second or third order to ensure a good fit.

[0035] When the virtual measurement probe moves from a smooth curve segment into a continuous, high-curvature serpentine path, the most recent data stored in the sliding window... The historical directional components exhibit high discreteness. The system quantifies this degree of discreteness by calculating this... The trace of the covariance matrix formed by the three-dimensional direction vectors yields a scalar discreteness. This dispersion It is then substituted into the exponential decay function To generate dynamic weighting factors ,in It is a positive constant; when the path is smooth and the dispersion is... When approaching zero, Approaching 1 allows the historical self-consistency constraint to play a major role, while when entering this serpentine path, the dispersion... When it increases, This approach zero, thus automatically reducing the influence of unreliable historical path trends on current state correction, and instead relying more on real-time observation information decoded from current neighborhood 3DGS points; simultaneously, at each sharp turn in the serpentine path, the topological ambiguity of the local point cloud leads to eigenvalue spectral entropy. When the value exceeds a preset entropy threshold, a path generation logic prioritizing multi-directional spatial exploration is triggered. Under this logic, the system generates a sector with a 120-degree angle, based on the plane defined by the first two principal eigenvectors of the fused covariance matrix, with the current probe position as the origin. Within this sector, five parallel virtual sub-probes are generated at 30-degree angular intervals. For each virtual sub-probe, the system performs a forward simulation to predict its hypothetical position at the next time step. Based on the neighborhood information of this hypothetical position, the system pre-calculates the eigenvalue spectral entropy of the next state if this path is selected. The system's final selection enables The path of the virtual sub-probe with the smallest value is taken as the actual continuation direction of the main path in the current iteration cycle. Through the synergistic effect of the above mechanisms, this method can adaptively adjust the complexity of its internal model and the trust weight of different information sources without pre-tuning parameters for specific path shapes. Thus, it maintains the logical continuity of the measurement and the reliability of the final result on continuous complex paths containing multiple shape combinations.

[0036] Example 5: Before applying the method of the present invention to a new type of test object or deploying it in a new environment with different point cloud density characteristics, the system executes a standardized pre-calibration procedure to set the core operating parameters. The procedure first acquires a typical 3DGS point cloud sample of the test object. The system establishes a statistical baseline for subsequent measurement tasks by analyzing the average point density and spatial distribution variance of the sample point cloud. The neighborhood search radius used for the correction step is set to be inversely proportional to the cube root of the average point density. The number of consecutive no-observation iterations in the loop termination condition is set to match the maximum expected data gap calculated from the point cloud spatial distribution variance, thereby adapting the core parameters to the characteristics of the data itself.

[0037] After parameter calibration is completed, when the length calculation task is officially started, the system executes an automated initial point localization process. This process performs a fast, low-resolution traversal of the global point cloud, and identifies regions with significant linear features, i.e., regions where the first principal eigenvalue is much larger than the other eigenvalues, by calculating the eigenvalue distribution of the covariance matrix of the point set in the local region. Among all regions that meet the linear feature, the system selects the region with the most significant feature as a candidate, and locates the 3DGS point at the endpoint along the direction of its principal eigenvector within the candidate region. The position of this point and the principal eigenvector are then used to initialize the initial position and orientation components of the virtual measurement probe, thereby starting the subsequent iterative calculation process.

[0038] Example 6: In the task of high-precision geometric measurement of structural components used for engineering acceptance or billing, the method of the present invention performs a final system calibration and initial state verification procedure before being put into operation. This procedure utilizes a linear structural standard component with known geometric truth values. A reference 3DGS point cloud is generated by scanning the standard component. The system first calculates the covariance of the observation noise based on the deviation of each point in the reference point cloud from its corresponding position in the geometric truth model, and uses this as the measurement noise covariance matrix in the Kalman filter framework. The system then sets a value, and subsequently runs a virtual measurement probe on the reference point cloud, analyzing the residual sequence between the predicted state and the true value. Based on the statistical characteristics of this residual sequence, it analyzes the process noise covariance matrix. Perform iterative adjustments until the filter output achieves optimal consistency with the true value.

[0039] After setting the core parameters of the Kalman filter, the system executes an automated initial point localization process on the actual point cloud data of the object under test. Once a candidate initial state, including initial position and orientation, is determined, the system does not immediately begin global measurement. Instead, it initiates a bootstrapping verification step that lasts for several iterations. In this step, the virtual measurement probe only travels a short distance near the candidate initial point, while the system simultaneously evaluates the quality of this initial path segment. The evaluation metrics include the average eigenvalue spectral entropy of this path segment. Whether the initial state is consistently below the stability threshold set during the system calibration phase, and whether the fitting residual of the initial historical self-consistency curve constructed from the path segment is within the allowable range, the initial state is only confirmed as valid when all evaluation indicators meet the aforementioned baseline requirements, and a complete length calculation is then carried out from this point. If any indicator is not met, the current candidate initial point is discarded, and the system will automatically return to the initial point positioning process and search for the next candidate initial point on the point cloud data excluding the discarded points.

[0040] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for calculating the length of a 3DGS linear point cloud based on Kalman filtering, characterized in that, Includes the following steps: Step a, calculate the length of the linear point cloud and reconstruct it into a method of dynamic integration along the information field formed by a virtual measurement probe along the point cloud. The information field is composed of the local geometric and orientation information of each 3DGS point in the 3DGS point cloud. Step b, define the Kalman state of the virtual measurement probe, which includes the accumulated path length component, position component, and orientation component; Step c: Within the Kalman filter framework, the prediction and correction loop is iteratively executed to update the Kalman state. The correction process includes obtaining the covariance matrix of 3DGS points located in the neighborhood of the predicted position of the virtual measurement probe, and decoding the equivalent length element and orientation confidence represented by each point from the covariance matrix; and forming a fused observation vector to correct the virtual measurement probe state by weighted fusion of the equivalent length element, position, and orientation of the 3DGS points, where the weight values ​​used for weighted fusion depend on the orientation confidence. Furthermore, the execution of the correction loop is also subject to the joint constraints of the following two mechanisms: first, using the eigenvalue spectrum distribution of the covariance matrix to evaluate the uncertainty of the local topology, thereby adaptively adjusting the path generation logic; second, applying a self-consistency constraint to the current correction based on a sliding window containing historical states. Step d: When the loop terminates, the accumulated path length component in the virtual measurement probe state is used as the calculated length of the linear point cloud.

2. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, The magnitude of the directional confidence is positively correlated with the ratio of the first principal eigenvalue of the covariance matrix to the sum of the remaining eigenvalues; the magnitude of the equivalent length element is determined by the square root of the first principal eigenvalue of the covariance matrix, which reflects the spatial extension of the 3DGS point in the principal direction.

3. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, The weight values ​​used in the weighted fusion also depend on the distance between the respective positions of the 3DGS points and the predicted positions of the virtual measurement probe, as well as the angle between the respective directions of the 3DGS points and the predicted directions of the virtual measurement probe.

4. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, The method of adaptively adjusting the path generation logic by utilizing the eigenvalue spectrum distribution of the covariance matrix includes: calculating the eigenvalue spectrum entropy, which characterizes the balance of the eigenvalue spectrum distribution of the fused covariance matrix, based on the fused covariance matrix formed by fusing information from 3DGS points in the neighborhood. ; Eigenvalue spectral entropy The calculation satisfies: ,in, For the first fusion covariance matrix eigenvalues The normalized proportion of the sum of all eigenvalues; then, the calculated eigenvalue spectral entropy. The path generation logic is compared with an entropy threshold, and based on the comparison result, it dynamically switches between a path generation logic dominated by directional components and a path generation logic that prioritizes multi-directional spatial exploration.

5. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 4, characterized in that, When the eigenvalue spectrum entropy When the entropy threshold is not less than the specified threshold, the path generation logic that prioritizes multi-directional spatial exploration includes: pausing the prediction based on the directional components of the virtual measurement probe at the previous moment; starting from the current position of the virtual measurement probe, issuing multiple parallel virtual sub-probes into the planar sector defined by the first two principal eigenvectors of the fused covariance matrix; and selecting the eigenvalue spectral entropy that enables the next state to be optimized. The path of the virtual sub-probe with the largest decrease is used as a continuation of the main path.

6. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, The method of constraining the current correction based on a sliding window containing historical states includes: maintaining a sliding window that stores the most recent N corrected historical states of the virtual measurement probe, where N is an integer greater than 1; before correcting the predicted virtual measurement probe state using the fused observation vector, performing a self-consistent pre-calibration on the position or orientation components in the fused observation vector based on a local path trend jointly defined by the historical states within the sliding window.

7. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 6, characterized in that, The local path trend is a historical self-consistency curve obtained by polynomial fitting of the position components of N historical states within a sliding window; the self-consistency pre-calibration is to perform a weighted average of the position components in the fused observation vector to the projection point of that position on the historical self-consistency curve; and to perform a weighted average of the direction components in the fused observation vector to the tangent direction of the historical self-consistency curve at that projection point.

8. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, The loop terminates when a predetermined number of consecutive attempts fail to acquire a 3DGS point within the neighborhood of the predicted location of the virtual measurement probe.

9. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, If no 3DGS point is acquired in the neighborhood of the predicted location of the virtual measurement probe, the correction step is skipped, and the state of the virtual measurement probe is updated only according to its prediction model to maintain the logical continuity of the path in the data interruption area of ​​the 3DGS point cloud.

10. The method for calculating the length of a 3DGS linear point cloud based on Kalman filtering according to claim 1, characterized in that, The weight values ​​used in the weighted fusion are also modulated by a dynamic weighting factor. The magnitude of this dynamic weighting factor is inversely proportional to the dispersion of the virtual measurement probe’s most recent N historical directional components, so as to reduce the weight of the current observation information when the dispersion of the historical directional components increases.

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