Polar coordinate scanning based gaussian mixture modeling method and apparatus

Abstract

The application provides a Gaussian mixture modeling method and device based on polar coordinate scanning, and relates to the technical field of artificial intelligence. The method comprises the following steps: converting a two-dimensional data point cloud into a polar coordinate data set based on a polar coordinate system; setting an initial angle step, combining the polar coordinate data set to perform scanning and one-dimensional Gaussian mixture model fitting, and obtaining radial distribution parameters of each scanning angle; determining a plurality of adjacent scanning continuous Gaussian components, and determining residual point distribution; iteratively optimizing the plurality of adjacent scanning continuous Gaussian components and a continuous angle range according to a residual test result, and generating a polar coordinate Gaussian mixture model. The technical problems of poor geometric invariance, weak interpretability, inability to adapt to data complexity, fixed sampling, and inability to effectively capture the continuity of radial distribution and the angle change characteristic in the prior art are solved. The technical effects of significantly improving the interpretability of Gaussian mixture modeling and realizing adaptive angle sampling and residual iterative optimization are achieved.

Description

Technical Field

[0001] This application relates to the field of artificial intelligence technology, and in particular to a Gaussian mixture modeling method and apparatus based on polar coordinate scanning. Background Technology

[0002] In fields such as artificial intelligence, machine learning, and computer vision, two-dimensional data distribution modeling is a core component of object detection, feature extraction, shape analysis, and pattern recognition. Gaussian mixture models (GMMs) are widely used in two-dimensional point cloud distribution, image feature distribution, and data clustering analysis due to their strong probabilistic interpretability and flexible fitting.

[0003] However, traditional two-dimensional Gaussian mixture models have significant drawbacks in practical applications: On the one hand, the model requires storing two-dimensional mean vectors and covariance matrices, resulting in a large number of parameters and high storage overhead, leading to poor model interpretability and difficulty in intuitively reflecting the geometric distribution characteristics of the data. On the other hand, traditional Gaussian mixture models lack rotation, translation, and scaling invariance; when the data undergoes geometric transformations, the model parameters and distribution structure change significantly, resulting in insufficient robustness.

[0004] Meanwhile, Gaussian components between adjacent angles are prone to breakage and mismatch, making it impossible to form a complete and unified two-dimensional distribution description, which is difficult to meet the modeling needs of high-precision, high-efficiency, and robust industrial inspection, medical imaging, autonomous driving and other scenarios.

[0005] Therefore, there is an urgent need for an efficient, interpretable, and naturally geometrically invariant two-dimensional data modeling method to achieve accurate characterization and lightweight representation of complex two-dimensional distributions. Summary of the Invention

[0006] This application provides a Gaussian mixture modeling method and apparatus based on polar coordinate scanning, which solves the technical problems of poor geometric invariance, weak interpretability, inability to adapt to data complexity, and fixed sampling that prevents effective capture of the continuity and angular variation characteristics of radial distribution in existing Gaussian mixture modeling technologies. It achieves significantly improved interpretability of Gaussian mixture modeling, enables adaptive angle sampling and residual iterative optimization, and efficiently and accurately completes the modeling of two-dimensional point cloud distributions.

[0007] This application provides a Gaussian mixture modeling method based on polar coordinate scanning. The method is applied to a Gaussian mixture modeling device based on polar coordinate scanning. The method includes: acquiring a two-dimensional data point cloud and establishing a polar coordinate system with the centroid of the two-dimensional data point cloud as the origin; converting the two-dimensional data point cloud into a polar coordinate dataset based on the polar coordinate system; setting an initial angle step size; performing scanning and fitting a one-dimensional Gaussian mixture model with the polar coordinate dataset to obtain radial distribution parameters for each scanning angle; performing cross-angle matching based on the radial distribution parameters for each scanning angle to determine multiple adjacent scan continuous Gaussian components, and determining a continuous angle range based on the multiple adjacent scan continuous Gaussian components; identifying uncovered data points based on the radial distribution parameters for each scanning angle based on the multiple adjacent scan continuous Gaussian components to determine the residual point distribution; determining whether the residual point distribution satisfies the iteration termination condition, obtaining the residual test result, and iteratively optimizing the multiple adjacent scan continuous Gaussian components and the continuous angle range based on the residual test result to generate a polar coordinate Gaussian mixture model.

[0008] This application also provides a Gaussian mixture modeling device based on polar coordinate scanning. The device includes: a point cloud conversion module for acquiring a two-dimensional point cloud, establishing a polar coordinate system with the centroid of the two-dimensional point cloud as the origin, and converting the two-dimensional point cloud into a polar coordinate dataset based on the polar coordinate system; a one-dimensional Gaussian fitting module for setting an initial angle step size, performing scanning and fitting with a one-dimensional Gaussian mixture model in conjunction with the polar coordinate dataset, and obtaining radial distribution parameters for each scanning angle; a cross-angle matching module for performing cross-angle matching based on the radial distribution parameters of each scanning angle, determining multiple adjacent scan continuous Gaussian components, and determining a continuous angle range based on the multiple adjacent scan continuous Gaussian components; a residual identification module for identifying uncovered data points on the radial distribution parameters of each scanning angle based on the multiple adjacent scan continuous Gaussian components, and determining the residual point distribution; and a residual iterative optimization module for determining whether the residual point distribution meets the iteration termination condition, obtaining residual test results, and iteratively optimizing the multiple adjacent scan continuous Gaussian components and the continuous angle range based on the residual test results to generate a polar coordinate Gaussian mixture model.

[0009] This application proposes a Gaussian mixture modeling method and apparatus based on polar coordinate scanning. It establishes a polar coordinate system with the centroid of a 2D point cloud as the origin, and converts the 2D point cloud into a polar coordinate dataset. The polar coordinate dataset is scanned according to an initial angle step size and fitted with a 1D Gaussian mixture model to obtain radial distribution parameters for each scanning angle. Cross-angle matching of the radial distribution parameters for each scanning angle determines multiple adjacent scan continuous Gaussian components, and a continuous angle range is determined based on these components. Uncovered data points are identified using these adjacent scan continuous Gaussian components to determine the residual point distribution. The residual point distribution is then checked to determine if it meets the iteration termination condition, and residual verification results are obtained. Based on these results, the multiple adjacent scan continuous Gaussian components and the continuous angle range are iteratively optimized to generate a polar coordinate Gaussian mixture model. This solves the technical problems of poor geometric invariance, weak interpretability, inability to adapt to data complexity, and fixed sampling in existing Gaussian mixture modeling, which fails to effectively capture the continuity of radial distribution and the characteristics of angle changes. It achieves significant improvements in the interpretability of Gaussian mixture modeling, enables adaptive angle sampling and residual iterative optimization, and efficiently and accurately completes the technical effect of two-dimensional data point cloud distribution modeling. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. Flowcharts are used in this application to illustrate the operations performed by the apparatus according to the embodiments of the present application. It should be understood that the preceding or following operations are not necessarily performed precisely in sequence. Instead, various steps can be processed in reverse order or simultaneously as needed. Furthermore, other operations can be added to these processes, or one or more steps can be removed from these processes.

[0011] Figure 1 A flowchart illustrating the Gaussian mixture modeling method based on polar coordinate scanning provided in this application.

[0012] Figure 2 A schematic diagram of the technical solution of the Gaussian mixture modeling method based on polar coordinate scanning provided in this application.

[0013] Figure 3 A schematic diagram illustrating the fitting of a scan to a one-dimensional Gaussian mixture model in the Gaussian mixture modeling method based on polar coordinate scanning provided in this application.

[0014] Figure 4 A schematic diagram illustrating the generation of a polar coordinate Gaussian mixture model in the Gaussian mixture modeling method based on polar coordinate scanning provided in this application.

[0015] Figure 5 A schematic diagram of the Gaussian mixture modeling device based on polar coordinate scanning provided in this application.

[0016] Figure labeling: Point cloud conversion module 1, one-dimensional Gaussian fitting module 2, cross-angle matching module 3, residual identification module 4, residual iterative optimization module 5. Detailed Implementation

[0017] The above description is merely an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are given below.

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description of this application will be provided in conjunction with the accompanying drawings. The described embodiments should not be considered as limitations on this application. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] In the following description, references to "some embodiments" describe a subset of all possible embodiments. However, it is understood that "some embodiments" may be the same or different subsets of all possible embodiments and may be combined with each other without conflict. The terms "first" and "second" are used merely to distinguish similar objects and do not represent a specific ordering of objects. The terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product, or server that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or modules not explicitly listed or inherent to these processes, methods, products, or apparatuses. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used herein is for the purpose of describing this application only.

[0020] This application provides a Gaussian mixture modeling method based on polar coordinate scanning, which is applied to a Gaussian mixture modeling device based on polar coordinate scanning, such as... Figure 1 As shown, the method includes: The overall technical solution flow of the Gaussian mixture modeling method based on polar coordinate scanning in this embodiment can be found in [reference needed]. Figure 1 Its core steps and data flow relationships can also be combined. Figure 2 The technical solution diagram shown is for reference. Figure 2 It clearly demonstrates the complete process from 2D point cloud input, through polar coordinate transformation, angle scanning and 1D GMM fitting, cross-angle matching, residual identification, to the final generation of a polar coordinate Gaussian mixture model.

[0021] Step A100: Obtain a two-dimensional point cloud and establish a polar coordinate system with the centroid of the two-dimensional point cloud as the origin. Based on this polar coordinate system, convert the two-dimensional point cloud into a polar coordinate dataset. Specifically, the two-dimensional point cloud is a set of discrete points of the modeling target in a Cartesian coordinate system. The modeling target can be an industrial part, a medical lesion, a road obstacle, etc. The two-dimensional point cloud can be a point cloud of a circular part in a two-dimensional image, a point cloud of a tumor region in a CT image, a point cloud of a road image acquired by a vehicle camera, etc. The two-dimensional point cloud can be represented as: X={(x1,y1),(x2,y2),...,(x... n ,y n )}. Where X is a two-dimensional point cloud, n is the total number of point clouds, and x n y n Let x and y be the x and y coordinates of the nth data point in the Cartesian coordinate system, respectively. Further, a polar coordinate system is established with the centroid (x0, y0) of the two-dimensional data point cloud as the origin. The polar radius r and polar angle θ are defined, where r is the Euclidean distance from the data point to the centroid, and θ is the angle between the data point and the polar axis, ranging from 0 to 360 degrees. Based on the existing polar coordinate transformation formula, each data point (x0, y0) in the two-dimensional data point cloud is transformed into a polar coordinate system. i ,y i ) convert them one by one to polar coordinate form (r i ,θ i x i Let y be the x-coordinate of the i-th data point in the Cartesian coordinate system. i Let r be the ordinate of the i-th data point in the Cartesian coordinate system. i θ i These are the polar radius and polar angle corresponding to the i-th data point, respectively.

[0022] The polar radius and polar angle of all data points in the 2D point cloud are normalized and stored to form a polar coordinate dataset, providing standard input for subsequent angle scanning and radial GMM fitting. The polar coordinate dataset can be represented as: P={(r1,θ1),(r2,θ2),...,(rn,θn)}. As a preferred implementation, the polar coordinate dataset can be corrected by principal axis rotation: the principal direction of the 2D point cloud is calculated, and the polar axis of the polar coordinate system is aligned with the principal direction of the data to eliminate overall rotational deviation and improve the continuity and modeling accuracy of subsequent cross-angle matching.

[0023] Step A200: Set an initial angle step size, perform scanning and fitting with a one-dimensional Gaussian mixture model using the polar coordinate dataset, and obtain radial distribution parameters for each scanning angle. Step A200 further includes steps A210 to A240. Step A210: Generate a scanning angle sequence based on the initial angle step size, and define the neighborhood range of each angle based on the scanning angle sequence; Step A220: Filter data points from the polar coordinate dataset that fall within the neighborhood range of each angle, obtaining a current scanning candidate point set; Step A230: Extract the radial distance of each data point in the current scanning candidate point set, obtaining a one-dimensional radial distance dataset; Step A240: Perform a one-dimensional Gaussian mixture model fitting on the one-dimensional radial distance dataset to generate the radial distribution parameters for each scanning angle.

[0024] Specifically, such as Figure 3 As shown, firstly, an initial angle step size is set, which can be configured to values ​​such as 10°, 5°, and 8°. Based on the initial angle step size, a scanning angle sequence covering 0° to 360° is generated at equal intervals starting from 0°. The scanning angle sequence includes multiple scanning angles. Furthermore, with each scanning angle as the center, the angle neighborhood range is defined as [θ]. i -Predetermined degree, θ i [+Predetermined degrees] to ensure smooth connection of adjacent angular neighborhoods and complete coverage of the 360° orientation. Furthermore, iterate through the polar coordinate dataset, determining whether the polar angle θ of each data point falls within the current scanning angle θ. i Within the corresponding angular neighborhood, data points that fall within the angular neighborhood of each polar corner are extracted to obtain the current scan candidate point set.

[0025] Polar angle information is extracted from the current scanned candidate point set, retaining only the polar radius r value corresponding to each data point. All polar radii r are then sequentially combined into a purely numerical one-dimensional radial distance dataset, providing standard input for subsequent one-dimensional Gaussian mixture model fitting. Furthermore, the EM algorithm or variational inference method is used to perform one-dimensional Gaussian mixture model fitting on the one-dimensional radial distance dataset, setting a maximum cluster number K. max To limit model complexity, the radial distribution parameters for each scanning angle are output after fitting. These parameters include the radial mean, radial standard deviation, and weights corresponding to the current scanning angle. The EM algorithm is a classic fitting algorithm that iteratively solves the latent variables and model parameters of a Gaussian mixture model using alternating expectation and maximization steps. The variational inference method is an efficient inference method for fast fitting and parameter estimation of Gaussian mixture models based on probabilistic approximation and information lower bound optimization.

[0026] Step A300: Perform cross-angle matching based on the radial distribution parameters of each scanning angle to determine multiple adjacent scan continuous Gaussian components, and determine the continuous angle range based on the multiple adjacent scan continuous Gaussian components. Step A300 further includes: Step A310, extracting a first parameter list corresponding to the current scanning angle and a second parameter list corresponding to the previous adjacent scanning angle based on the radial distribution parameters of each scanning angle; Step A320, performing similarity calculation based on the first parameter list and the second parameter list to obtain a similarity matrix; Step A330, processing the similarity matrix according to a matching algorithm to determine the optimal matching relationship of the Gaussian components; Step A340, generating the multiple adjacent scan continuous Gaussian components based on the optimal matching relationship of the Gaussian components.

[0027] Based on the fitted radial distribution parameters for each scanning angle, the radial mean, radial standard deviation, and weight corresponding to the current scanning angle are used to form a first parameter list. Simultaneously, the radial mean, radial standard deviation, and weight corresponding to the previous adjacent scanning angle are extracted to form a second parameter list. Then, a matching matrix M is initialized with the length of the second parameter list as the number of rows and the length of the first parameter list as the number of columns. Each Gaussian component in the second parameter list is traversed to form a component pair with each Gaussian component in the first parameter list. The component similarity is calculated based on the difference in radial means combined with variance weighting. The similarity calculation formula is: Similarity = exp (-|μ_{r,i-1}^j - μ_{r,i}^k| / σ_avg). Where μ_{r,i-1}^j is the radial mean of the j-th component in the second parameter list, μ_{r,i}^k is the radial mean of the k-th component in the first parameter list, and σ_avg is the average radial standard deviation of the two components. The similarity values ​​of all component pairs are filled into the matching matrix M to obtain the similarity matrix used for component matching.

[0028] Furthermore, the Hungarian algorithm or a greedy matching algorithm is used to solve for the optimal allocation of the similarity matrix. The component correspondence with the highest similarity and satisfying the continuity constraint is selected as the optimal matching relationship for the Gaussian components. Specifically, the Hungarian algorithm is used to find the globally optimal matching scheme in the similarity matrix. Through row / column reduction, label covering, and path augmentation iterative operations on the similarity matrix, it obtains the globally optimal allocation result with the largest sum of total similarities in polynomial time, ensuring that each previous angle component matches at most one current angle component, and each current angle component matches at most one previous angle component, obtaining the globally optimal matching relationship without conflict or omission. The greedy matching algorithm traverses the elements in the similarity matrix in descending order of similarity, selecting the component pair with the largest current similarity value that has not been matched for matching each time, until no further matching is possible. This improves computational efficiency while ensuring matching accuracy. Both algorithms output a unique optimal matching relationship for the Gaussian components. The successfully matched Gaussian components are marked as continuing components, the unmatched previous angle components are marked as dying components, and the unmatched current angle components are marked as new components. Subsequently, the continuous components that are successfully matched between adjacent angles are merged and smoothed to form multiple adjacent scan continuous Gaussian components that maintain consistent distribution characteristics across angles. At the same time, the starting and ending scan angles covered by the multiple adjacent scan continuous Gaussian components are marked as continuous angle ranges, thus completing the angular continuity modeling of the two-dimensional data distribution.

[0029] Step A400: Identify uncovered data points based on the radial distribution parameters of each scanning angle according to the multiple adjacent scan continuous Gaussian components, and determine the residual point distribution. First, based on the generated multiple adjacent scan continuous Gaussian components and their radial distribution parameters and continuous angle ranges, determine the affiliation of each data point in the polar coordinate dataset. That is, substitute the polar angle and polar radius of each data point into the probability density function of the corresponding continuous Gaussian component to calculate its posterior probability of belonging to the current continuous Gaussian component. If the probability is less than a preset probability threshold, it is determined that the data point is not effectively covered by any continuous Gaussian component. Subsequently, all uncovered data points are separated from the original polar coordinate dataset and aggregated to form a residual point set. Further, perform statistical and distribution feature calculations on the residual point set to obtain the number, spatial location, radial distribution, and angular distribution of residual points, forming a complete residual point distribution, which is used for subsequent residual information entropy calculation and iterative optimization to achieve accurate positioning and supplementary modeling of unmodeled areas.

[0030] Step A500: Determine whether the residual point distribution meets the iteration termination condition, obtain the residual test result, and perform iterative optimization on the multiple adjacent scan continuous Gaussian components and the continuous angle range based on the residual test result to generate a polar coordinate Gaussian mixture model.

[0031] Step A500 includes: Step A510: Calculate the total residual entropy of the residual point distribution; Step A520: Set the iteration termination condition, which includes an information entropy threshold; Step A530: If the total residual entropy is greater than or equal to the information entropy threshold, the residual test result is not satisfied; Step A540: If the total residual entropy is less than the information entropy threshold, the residual test result is satisfied.

[0032] Specifically, such as Figure 4 As shown, based on the radial distance and angular distribution characteristics of the residual point distribution, the probability distribution statistics of the residual point set are performed according to the angular interval or radial interval to obtain the distribution probability of the residual data in each interval. Then, the information entropy calculation formula H_residual = -Σ(p ×log2p ), calculate multiple information entropies. H_residual represents the information entropy, p This represents the probability distribution of residual data within each interval. Furthermore, multiple information entropies are summed to obtain the total residual entropy, which quantitatively characterizes the complexity, disorder, and information content of the residual distribution. A larger total residual entropy indicates a more complex residual point distribution and less sufficient current model coverage. A smaller total residual entropy indicates a smoother residual distribution and higher modeling accuracy. The information entropy threshold is designated as the iteration termination condition.

[0033] The information entropy threshold can be adaptively set based on modeling accuracy requirements, data scenario characteristics, and computational efficiency requirements. Then, the total residual entropy is compared with the information entropy threshold. If the total residual entropy is greater than or equal to the information entropy threshold, it is determined that the current model's fit to the data distribution is insufficient, the residuals contain a large amount of unmodeled effective information, and the residual test result does not meet the iteration termination condition, requiring adaptive adjustment of the angle step size and the next round of iterative modeling. If the total residual entropy is less than the information entropy threshold, it is determined that the residual distribution has become smooth, the current model has fully covered the target data distribution, and the residual test result meets the iteration termination condition.

[0034] Step A500 includes: Step A550, if the residual test result is not satisfied, perform adaptive angle step size adjustment according to the residual point distribution to obtain an optimized angle step size; Step A560, perform local fine-tuning modeling according to the optimized angle step size to obtain a local Gaussian component parameter set; Step A570, fuse the local Gaussian component parameter set, the multiple adjacent scan continuous Gaussian components, and the continuous angle range to obtain a polar coordinate Gaussian fusion model; Step A580, determine whether the polar coordinate Gaussian fusion model satisfies the iteration termination condition; Step A590, if the polar coordinate Gaussian fusion model satisfies the iteration termination condition, output the polar coordinate Gaussian fusion model as the polar coordinate Gaussian mixture model.

[0035] If the residual test result is unsatisfactory, it indicates that the current angle sampling is relatively sparse. Based on the dense areas and complexity of the residual point distribution, the initial angle step size is adaptively reduced. In local angle regions with concentrated residual points and high distribution complexity, the angle step size is increased to a finer optimized step size. In sparse residual regions, the original step size is maintained or appropriately increased, realizing a dynamic sampling strategy of "dense sampling in complex regions and coarse sampling in flat regions," so that the angle step size is adaptively matched with the data complexity. Subsequently, the angle scan, radial one-dimensional Gaussian mixture model fitting, and cross-angle component matching process are re-executed on the local angle range where the residual points are located using the optimized angle step size. Layered refinement fitting is performed on the insufficiently modeled residual regions to obtain a denser and more accurate local Gaussian component parameter set within the local region. The local Gaussian component parameter set includes the radial mean, radial standard deviation, weight, and corresponding continuous angle range of each refined scan angle.

[0036] Furthermore, the local Gaussian component parameter set is aligned with multiple adjacent scanned continuous Gaussian components and continuous angle ranges through parameter alignment, angle range connection, and component deduplication. Global and local components are then systematically stitched and smoothly fused according to angle intervals, maintaining the continuity and consistency of radial parameters and angle ranges to form a fully covered 360° and locally refined polar coordinate Gaussian fusion model. Subsequently, based on the polar coordinate Gaussian fusion model, the 2D data point cloud is re-covered, identifying newly uncovered data points and calculating the updated total residual entropy. This updated total residual entropy is compared with the information entropy threshold. If the updated total residual entropy is less than the information entropy threshold, the polar coordinate Gaussian fusion model meets the iteration termination condition, and the model is output as a polar coordinate Gaussian mixture model. This improves the accuracy and interpretability of Gaussian mixture modeling, enabling adaptive angle sampling and residual iterative optimization. The polar coordinate Gaussian mixture model includes centroid coordinates, optimized angle step size, radial parameters of each continuous Gaussian component, and angle range, and can be directly used for data distribution reconstruction, probability calculation, and target recognition.

[0037] Step A500 includes: Step A5100, if the residual test result is satisfactory, construct the polar coordinate Gaussian mixture model based on the multiple adjacent scan continuous Gaussian components and the continuous angle range.

[0038] Specifically, if the residual test result is satisfactory, it indicates that the continuous Gaussian components of multiple adjacent scans have fully covered the two-dimensional data point cloud, and the residual points are only a small amount of noise and do not contain effective modeling information. At this point, using the centroid as the origin and based on the continuous Gaussian components of multiple adjacent scans, the radial mean, radial standard deviation, weights, and corresponding continuous angle ranges of the continuous Gaussian components of multiple adjacent scans are regularized, sorted, and integrated to form a polar coordinate Gaussian mixture model. This polar coordinate Gaussian mixture model includes the centroid coordinates, initial angle step size, unique identifier of each continuous Gaussian component, angle coverage range, radial mean function, radial standard deviation function, and weighting function that vary with the angle.

[0039] Step A580 includes: Step A581, if the polar coordinate Gaussian fusion model does not meet the iteration termination condition, perform iterative optimization on the polar coordinate Gaussian fusion model according to the iteration termination condition.

[0040] Specifically, when the updated total residual entropy of the polar coordinate Gaussian fusion model is still greater than or equal to the information entropy threshold, it is determined that the polar coordinate Gaussian fusion model does not meet the iteration termination condition. At this time, the polar coordinate Gaussian fusion model is used as the current base model, and the data points not covered by the polar coordinate Gaussian fusion model are re-extracted to form an updated residual point distribution. The updated residual point distribution is used as the input data for a new round of iteration. The entire process of angle sequence generation, angle neighborhood filtering, radial distance extraction, one-dimensional Gaussian mixture model fitting, cross-angle component matching, residual point identification, total residual entropy calculation, adaptive angle step size adjustment, local fine modeling, and model parameter fusion is repeated. In each round of iteration, the angle sampling is continuously refined, the Gaussian component parameters are optimized, and the residual distribution is reduced until the updated model meets the iteration termination condition. Through multi-level iterative loops, the two-dimensional data point cloud is gradually approximated and accurately modeled, ensuring that the final output polar coordinate Gaussian mixture model has high fitting degree, strong geometric invariance, and good interpretability.

[0041] In summary, the Gaussian mixture modeling method based on polar coordinate scanning provided in this application has the following technical effects: By establishing a polar coordinate system with the centroid of the 2D point cloud as the origin, the 2D point cloud is converted into a polar coordinate dataset. The polar coordinate dataset is scanned and fitted with a 1D Gaussian mixture model according to an initial angle step size to obtain radial distribution parameters for each scan angle. Cross-angle matching of the radial distribution parameters for each scan angle is performed to determine multiple adjacent scan continuous Gaussian components, and the continuous angle range is determined based on these components. Uncovered data points are identified using these adjacent scan continuous Gaussian components to determine the residual point distribution. The iteration termination condition is checked to obtain residual verification results. Based on these results, the multiple adjacent scan continuous Gaussian components and the continuous angle range are iteratively optimized to generate a polar coordinate Gaussian mixture model. This solves the technical problems of poor geometric invariance, weak interpretability, inability to adapt to data complexity, and fixed sampling in existing Gaussian mixture modeling, which fails to effectively capture the continuity of radial distribution and the characteristics of angle changes. It achieves significant improvements in the interpretability of Gaussian mixture modeling, enables adaptive angle sampling and residual iterative optimization, and efficiently and accurately completes the technical effect of two-dimensional data point cloud distribution modeling.

[0042] Based on the Gaussian mixture modeling method based on polar coordinate scanning in the foregoing embodiments, and using the same inventive concept, this invention also provides a Gaussian mixture modeling apparatus based on polar coordinate scanning. Please refer to the appendix. Figure 5 The device includes: Point cloud conversion module 1 is used to acquire two-dimensional data point cloud, establish a polar coordinate system with the centroid of the two-dimensional data point cloud as the origin, and convert the two-dimensional data point cloud into a polar coordinate dataset based on the polar coordinate system. The one-dimensional Gaussian fitting module 2 is used to set the initial angle step size, combine the polar coordinate dataset to perform scanning and fitting with the one-dimensional Gaussian mixture model, and obtain the radial distribution parameters of each scanning angle. The cross-angle matching module 3 is used to perform cross-angle matching based on the radial distribution parameters of each scanning angle, determine multiple adjacent scanning continuous Gaussian components, and determine the continuous angle range based on the multiple adjacent scanning continuous Gaussian components. The residual identification module 4 is used to identify uncovered data points of the radial distribution parameters of each scanning angle based on the multiple adjacent scanning continuous Gaussian components, and to determine the residual point distribution. The residual iterative optimization module 5 is used to determine whether the residual point distribution meets the iteration termination condition, obtain the residual test result, and perform iterative optimization on the multiple adjacent scan continuous Gaussian components and the continuous angle range based on the residual test result to generate a polar coordinate Gaussian mixture model.

[0043] Furthermore, the one-dimensional Gaussian fitting module 2 is also used to: generate a scanning angle sequence based on the initial angle step size, and define the neighborhood range of each angle based on the scanning angle sequence; select data points from the polar coordinate dataset that fall within the neighborhood range of each angle to obtain the current scanning candidate point set; extract the radial distance of each data point in the current scanning candidate point set to obtain a one-dimensional radial distance dataset; and perform a one-dimensional Gaussian mixture model fitting on the one-dimensional radial distance dataset to generate the radial distribution parameters of each scanning angle.

[0044] Furthermore, the cross-angle matching module 3 is also used to: extract a first parameter list corresponding to the current scanning angle and a second parameter list corresponding to the previous adjacent scanning angle based on the radial distribution parameters of each scanning angle; perform similarity calculation based on the first parameter list and the second parameter list to obtain a similarity matrix; process the similarity matrix according to the matching algorithm to determine the optimal matching relationship of Gaussian components; and generate the multiple adjacent scanning continuous Gaussian components based on the optimal matching relationship of Gaussian components.

[0045] Furthermore, the residual iterative optimization module 5 is also used to: calculate the total residual entropy of the residual point distribution; set the iteration termination condition, the iteration termination condition including an information entropy threshold; if the total residual entropy is greater than or equal to the information entropy threshold, the residual test result is not satisfied; if the total residual entropy is less than the information entropy threshold, the residual test result is satisfied.

[0046] Furthermore, the residual iterative optimization module 5 is also used for: if the residual test result is not satisfied, performing adaptive angle step size adjustment according to the residual point distribution to obtain an optimized angle step size; performing local fine modeling according to the optimized angle step size to obtain a local Gaussian component parameter set; fusing the local Gaussian component parameter set, the multiple adjacent scan continuous Gaussian components, and the continuous angle range to obtain a polar coordinate Gaussian fusion model; determining whether the polar coordinate Gaussian fusion model satisfies the iteration termination condition; and if the polar coordinate Gaussian fusion model satisfies the iteration termination condition, outputting the polar coordinate Gaussian fusion model as the polar coordinate Gaussian mixture model.

[0047] Furthermore, the residual iterative optimization module 5 is also used to: if the residual test result is satisfactory, construct the polar coordinate Gaussian mixture model based on the multiple adjacent scan continuous Gaussian components and the continuous angle range.

[0048] Furthermore, the residual iterative optimization module 5 is also used for: If the polar coordinate Gaussian fusion model does not meet the iteration termination condition, the polar coordinate Gaussian fusion model is iteratively optimized according to the iteration termination condition.

[0049] The Gaussian mixture modeling device based on polar coordinate scanning provided in the embodiments of the present invention can execute the Gaussian mixture modeling method based on polar coordinate scanning provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the method.

[0050] To more clearly demonstrate the application value and implementation details of the technical solution of this application, the invention will be further described below in conjunction with specific application scenarios and parameter settings. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0051] Example 1: Point Cloud Modeling of Circular Parts for Industrial Inspection This embodiment applies the method of this application to point cloud modeling of circular parts in two-dimensional images, aiming to accurately identify the center and edges of the parts and achieve efficient and lightweight representation.

[0052] Specifically, a two-dimensional image containing the circular part to be detected is first acquired. A two-dimensional point cloud X is then obtained using edge detection and point cloud extraction techniques. A polar coordinate system is established with the centroid of this two-dimensional point cloud as the origin, and all data points are converted into a polar coordinate dataset P.

[0053] According to the method of this application, the initial angle step size is set to 10°, and a scanning angle sequence is generated. Within the neighborhood of each scanning angle, a candidate point set is screened and the radial distance is extracted, and a one-dimensional Gaussian mixture model is fitted. In this embodiment, considering that circular parts usually contain multiple clustered regions such as the center, inner edge, and outer edge in the radial direction, the maximum cluster number K~max~ is set to 3 to fully capture the hierarchical features of the radial distribution.

[0054] Subsequently, cross-angle matching is performed, and multiple adjacent scan continuous Gaussian components are identified by calculating the similarity of each Gaussian component between adjacent angles. For uncovered data points caused by part surface texture or local occlusion, they are identified as residual point distributions. The total residual entropy is calculated and it is determined whether it is less than the set information entropy threshold. If it is satisfied, the final polar coordinate Gaussian mixture model is output.

[0055] Experimental results show that this method successfully identifies and models the central region, internal contour, and external edge of a circular part. The model parameters only need to store the centroid coordinates, the radial mean, standard deviation, weights, and corresponding angle ranges of each continuous Gaussian component, with a storage overhead of only a few hundred bytes, greatly reducing the model complexity. Furthermore, based on the data distribution reconstruction of this model, its reconstruction accuracy is comparable to that of the traditional two-dimensional Gaussian mixture model, but it exhibits natural robustness in rotational and translational scenarios, verifying the efficiency and accuracy of this method in the field of industrial inspection.

[0056] Example 2: Point Cloud Modeling of Tumor Regions for Medical Imaging This embodiment applies the method of this application to point cloud modeling of tumor regions in computed tomography (CT) images, aiming to achieve adaptive and fine characterization of irregular lesion morphology and improve the sensitivity of medical image analysis.

[0057] First, tumor lesions within regions of interest (ROIs) are segmented from medical CT image sequences and converted into two-dimensional point clouds. A polar coordinate system is then established with the centroid of this point cloud as the origin. Since tumor morphology is typically irregular and has complex edges, high angular resolution is required to capture its morphological changes.

[0058] According to the method of this application, an initial angle step size of 5° is set to generate a denser sequence of scanning angles. A radial one-dimensional Gaussian mixture model is fitted for each angle direction to obtain the radial distribution parameters for each scanning angle. Through cross-angle matching, multiple continuous Gaussian components describing the morphology of the lesion are formed.

[0059] To accurately capture complex features such as spiculation and lobulation at the lesion edge, this embodiment strengthens the residual iterative optimization mechanism. The information entropy threshold in the iteration termination condition is set to 0.7. When the calculated total residual entropy is greater than or equal to 0.7, the current model is deemed to have insufficient coverage of the complex region at the lesion edge. Based on the adaptive optimization strategy of this method, the system automatically reduces the angle step size (e.g., to 2°) in angular regions with dense residual points, performing local refined modeling, generating a local Gaussian component parameter set, and fusing it with the global model.

[0060] The results show that, through residual iteration and adaptive sampling, the polar coordinate Gaussian mixture model generated by this method can adaptively focus on the complex structure of the lesion edge, accurately describing subtle changes in the lesion boundary with a higher parameter density, while smoothly describing the homogeneous region inside the lesion with a lower parameter density. This hierarchical and focused modeling approach effectively improves the detection sensitivity and segmentation accuracy of irregular tumor morphologies, providing a more robust data foundation for subsequent benign and malignant differentiation.

[0061] Example 3: Point Cloud Modeling of Road Lane Lines for Autonomous Driving This embodiment applies the method of this application to an autonomous driving scenario, processing road images captured by an onboard camera to achieve stable recognition and modeling of lane lines.

[0062] First, a semantic segmentation network is used to process road images captured by vehicle cameras, extracting pixels belonging to lane lines and transforming them into a vehicle coordinate system to form a two-dimensional point cloud representing lane lines. During actual driving, the shape of lane lines in the image changes with road curvature and vehicle movement, resulting in rotation and translation.

[0063] According to the method of this application, a polar coordinate system is established with the centroid of the lane line point cloud as the origin. Since lane lines usually present as extended line structures, an initial angular step size of 8° is set for scanning. A radial one-dimensional Gaussian mixture model is fitted in each angular direction, where the maximum cluster number is usually small (e.g., Kmax ~= 2), used to capture the inner and outer edges of the lane lines.

[0064] During iterative optimization, this method supports dynamic step size adjustment. When a vehicle is traveling on a straight road, the lane lines are straight and the total residual entropy is small, so the model maintains a large angle step size to ensure computational efficiency. When the vehicle enters a curve, the lane line curvature increases, the data distribution complexity increases, and the total residual entropy increases accordingly. At this time, based on the residual test results, this method automatically reduces the angle step size within the angle range corresponding to the curve, performing local fine-tuning modeling to accurately capture the curvature changes of the lane lines.

[0065] Experimental results show that the polar coordinate Gaussian mixture model generated by this method can stably and continuously identify and model lane lines in both straight and curved road scenarios. Since the modeling process is based on the data centroid and scans along the polar angle direction, the model naturally possesses rotation and translation invariance. Even if the vehicle experiences slight tilting or the lane lines shift in the image, this method can still maintain the model's consistency and robustness, significantly improving the autonomous driving system's adaptability to environmental changes.

[0066] Although this application makes various references to certain modules in the apparatus according to the embodiments of this application, any number of different modules can be used and run on user terminals and / or servers. The various units and modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy distinction between each other and are not intended to limit the scope of protection of this invention.

[0067] The specific embodiments described above do not constitute a limitation on the scope of protection of this application. Those skilled in the art should understand that various modifications, combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A Gaussian mixture modeling method based on polar coordinate scanning, characterized in that, The method includes: Two-dimensional point cloud data is acquired, and a polar coordinate system is established with the centroid of the two-dimensional point cloud data as the origin. Based on the polar coordinate system, the two-dimensional point cloud data is converted into a polar coordinate dataset. Set an initial angle step size, combine the polar coordinate dataset to perform scanning and fit with a one-dimensional Gaussian mixture model, and obtain the radial distribution parameters of each scanning angle; Cross-angle matching is performed based on the radial distribution parameters of each scanning angle to determine multiple consecutive Gaussian components of adjacent scans, and a continuous angle range is determined based on the multiple consecutive Gaussian components of adjacent scans. Based on the multiple adjacent scan continuous Gaussian components, the radial distribution parameters of each scan angle are used to identify uncovered data points and determine the residual point distribution. Determine whether the residual point distribution satisfies the iteration termination condition, obtain the residual test result, and perform iterative optimization on the multiple adjacent scan continuous Gaussian components and the continuous angle range based on the residual test result to generate a polar coordinate Gaussian mixture model.

2. The method as described in claim 1, characterized in that, An initial angle step size is set, and scanning is performed using the polar coordinate dataset, along with fitting to a one-dimensional Gaussian mixture model, to obtain radial distribution parameters for each scanning angle, including: Based on the initial angle step size, a scanning angle sequence is generated, and the neighborhood range of each angle is defined based on the scanning angle sequence; From the polar coordinate dataset, select data points whose polar corners fall within the neighborhood of each angle to obtain the current scan candidate point set; Extract the radial distance of each data point in the current scan candidate point set to obtain a one-dimensional radial distance dataset; A one-dimensional Gaussian mixture model is fitted to the one-dimensional radial distance dataset to generate radial distribution parameters for each scanning angle.

3. The method as described in claim 1, characterized in that, Based on the radial distribution parameters of each scanning angle, cross-angle matching is performed to determine multiple consecutive Gaussian components of adjacent scans, including: Based on the radial distribution parameters of each scanning angle, extract the first parameter list corresponding to the current scanning angle and the second parameter list corresponding to the previous adjacent scanning angle; A similarity matrix is ​​obtained by calculating the similarity based on the first parameter list and the second parameter list; The similarity matrix is ​​processed according to the matching algorithm to determine the optimal matching relationship of the Gaussian components; Based on the optimal matching relationship of the Gaussian components, the multiple adjacent scan continuous Gaussian components are generated.

4. The method as described in claim 1, characterized in that, Determine whether the residual point distribution satisfies the iteration termination condition and obtain the residual test results, including: Calculate the total residual entropy of the residual point distribution; The iteration termination condition is set, and the iteration termination condition includes an information entropy threshold. If the total residual entropy is greater than or equal to the information entropy threshold, the residual test result is not satisfied. If the total residual entropy is less than the information entropy threshold, the residual test result is satisfied.

5. The method as described in claim 1, characterized in that, Based on the residual test results, the continuous Gaussian components of the multiple adjacent scans and the continuous angle range are iteratively optimized to generate a polar coordinate Gaussian mixture model, including: If the residual test result is not satisfied, an adaptive angle step size adjustment is performed based on the residual point distribution to obtain the optimized angle step size. Local fine-grained modeling is performed based on the optimized angle step size to obtain the local Gaussian component parameter set; The local Gaussian component parameter set, the multiple adjacent scan continuous Gaussian components, and the continuous angle range are fused to obtain a polar coordinate Gaussian fusion model; Determine whether the polar coordinate Gaussian fusion model satisfies the iteration termination condition; If the polar coordinate Gaussian fusion model satisfies the iteration termination condition, the polar coordinate Gaussian fusion model is output as the polar coordinate Gaussian mixture model.

6. The method as described in claim 1, characterized in that, Based on the residual test results, the continuous Gaussian components of the multiple adjacent scans and the continuous angle range are iteratively optimized to generate a polar coordinate Gaussian mixture model, including: If the residual test result is satisfactory, the polar coordinate Gaussian mixture model is constructed based on the multiple adjacent scan continuous Gaussian components and the continuous angle range.

7. The method as described in claim 5, characterized in that, Determining whether the polar coordinate Gaussian fusion model satisfies the iteration termination condition includes: If the polar coordinate Gaussian fusion model does not meet the iteration termination condition, the polar coordinate Gaussian fusion model is iteratively optimized according to the iteration termination condition.

8. A Gaussian mixture modeling device based on polar coordinate scanning, characterized in that, The apparatus is used to implement the method according to any one of claims 1 to 7, the apparatus comprising: The point cloud conversion module is used to acquire two-dimensional data point cloud, establish a polar coordinate system with the centroid of the two-dimensional data point cloud as the origin, and convert the two-dimensional data point cloud into a polar coordinate dataset based on the polar coordinate system. The one-dimensional Gaussian fitting module is used to set the initial angle step size, combine the polar coordinate dataset to perform scanning and fitting with the one-dimensional Gaussian mixture model, and obtain the radial distribution parameters of each scanning angle. The cross-angle matching module is used to perform cross-angle matching based on the radial distribution parameters of each scanning angle, determine multiple adjacent scanning continuous Gaussian components, and determine the continuous angle range based on the multiple adjacent scanning continuous Gaussian components. The residual identification module is used to identify uncovered data points of the radial distribution parameters of each scanning angle based on the multiple adjacent scan continuous Gaussian components, and to determine the residual point distribution. The residual iterative optimization module is used to determine whether the residual point distribution meets the iteration termination condition, obtain the residual test result, and perform iterative optimization on the multiple adjacent scan continuous Gaussian components and the continuous angle range based on the residual test result to generate a polar coordinate Gaussian mixture model.

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