Quadratic surface fitting method, model training method, model reasoning method and equipment

Abstract

The embodiment of the invention provides a quadric surface fitting method, a model training method, a model reasoning method and equipment, and relates to the technical field of computer vision, and the quadric surface fitting method comprises the steps: determining a local PCA coordinate system corresponding to a local curved surface where a target point is located through a PCA method; and then, converting a Mongolian equation corresponding to a local curved surface where the target point is located into a local PCA coordinate system to obtain an implicit curved surface equation. Then, solving the implicit curved surface equation according to the position information of the target point cloud block in the local PCA coordinate system, and obtaining the value of an item to be solved; and finally, according to the value of the item to be solved, obtaining a differential characteristic parameter of the local curved surface. According to the technical scheme, the quadric surface fitting precision can be improved, and more accurate differential characteristic parameters can be obtained.

Description

Technical Field

[0001] This application relates to the field of computer vision technology, and in particular to a quadratic surface fitting method, a model training method, a model inference method, and an apparatus. Background Technology

[0002] In 3D processing of target objects (such as objects perceived by LiDAR, objects in virtual reality scenes, etc.) (e.g., surface reconstruction, rendering, remeshing), a key process is fitting a quadratic surface based on point cloud data to obtain the differential properties of the quadratic surface, such as normal vectors and curvature. The accuracy of this quadratic surface fitting directly affects the refinement of the output results in the 3D processing. For example, when the accuracy of the fitted normal vectors and curvature is high, the rendering results can present richer surface details of the target object. Therefore, it is necessary to provide a method that can accurately achieve quadratic surface fitting. Summary of the Invention

[0003] In view of this, embodiments of this application provide a quadratic surface fitting method, a model training method, a model inference method, and an apparatus to at least partially solve the above-mentioned problems.

[0004] According to a first aspect of the embodiments of this application, a quadratic surface fitting method is provided, comprising: using principal component analysis (PCA) to determine the local principal component analysis coordinate system corresponding to the local surface where a target point is located; the target point is any point in the point cloud data of a target object; transforming the Monge-type equation corresponding to the local surface where the target point is located to the local principal component analysis coordinate system to obtain an implicit surface equation; the implicit surface equation includes a term to be solved, and the implicit surface equation is used to describe the local surface; solving the implicit surface equation based on the position information of the target point cloud block in the local principal component analysis coordinate system to obtain the value of the term to be solved; the target point cloud block includes the target point and multiple points adjacent to the target point; obtaining the differential characteristic parameters of the local surface based on the value of the term to be solved, and the differential characteristic parameters are used to realize the three-dimensional processing of the target object.

[0005] According to a second aspect of the embodiments of this application, a model training method is provided, comprising: determining sample point cloud blocks based on a pre-generated training dataset; the training dataset including multiple different quadratic surfaces; the sample point cloud blocks including data of points corresponding to local surfaces of any quadratic surface; inputting the sample point cloud blocks into a neural network model to be trained, so that the neural network model to be trained obtains initial differential feature parameters of the local surfaces by executing the method as described in the first aspect; constructing a loss function based on the initial differential feature parameters and the actual differential feature parameters of the local surfaces in the training dataset; and updating the model parameters of the neural network model to be trained based on the loss function to obtain a trained neural network model.

[0006] According to a third aspect of the embodiments of this application, a model inference method is provided, comprising: inputting a target point cloud block into a neural network model; the neural network model being trained based on the method described in the second aspect; the target point cloud block including a target point and a plurality of points adjacent to the target point; the target point being any point in the point cloud data of a target object; the neural network model obtaining differential feature parameters of the local surface where the target point is located by executing the method described in the first aspect, the differential feature parameters being used to realize three-dimensional processing of the target object.

[0007] According to a fourth aspect of the embodiments of this application, an electronic device is provided, comprising: a computer storage medium configured to store computer program instructions for performing the methods described in the first, second, and third aspects.

[0008] According to a fifth aspect of the embodiments of this application, a computer storage medium is provided, wherein at least one piece of program code is stored in the computer storage medium, the program code being loaded and executed by a processor to implement the methods described in the first, second and third aspects.

[0009] According to a sixth aspect of the embodiments of this application, a computer program product is provided, including computer instructions that instruct a computing device to perform operations corresponding to the methods described in the first, second, and third aspects above.

[0010] In the above technical solution, the Monge-type equation is transformed to a local PCA coordinate system to obtain an implicit expression of the Monge-type equation, namely the implicit surface equation. Then, a quadratic surface is fitted based on this implicit surface equation. Since the quadratic surface fitting is based on the implicit expression of the Monge-type equation, and given the absence of model error in the Monge-type equation, the above solution can fit a close approximation of the true surface. The errors in the normal vector and curvature of this close approximation are small compared to the normal vector and curvature of the true surface. In other words, the above technical solution can improve the accuracy of the quadratic surface fitting results, making the differential characteristic parameters of the fitted quadratic surface closer to the actual differential characteristic parameters. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0012] Figure 1 This is a schematic diagram illustrating the application scenarios of the differential characteristic parameters provided in the embodiments of this application; Figure 2 A flowchart of a quadratic surface fitting method provided in an embodiment of this application; Figure 3 This is a schematic diagram illustrating the quadratic curve fitting effect provided in an embodiment of this application; Figure 4 This is a flowchart of a model training method provided in an embodiment of this application. Detailed Implementation

[0013] To enable those skilled in the art to better understand the technical solutions in the embodiments of this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of this application.

[0014] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. The singular forms “a,” “the,” and “the” used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0015] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0016] It should also be noted that the terms "first, second, and third" used in the embodiments of this application are only used to distinguish similar objects and do not represent a specific order of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0017] Furthermore, in the embodiments of this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0018] To facilitate understanding of the technical solutions of the embodiments of this application, the relevant technologies of the embodiments of this application are described below. The following relevant technologies are optional solutions and can be combined with the technical solutions of the embodiments of this application in any way, and they all fall within the protection scope of the embodiments of this application.

[0019] Currently, 3D scanning and measurement technology has applications in numerous technical fields. It can be used to acquire raw point cloud data of a target object, which can then be used to fit a quadratic surface to the target object, obtaining its surface differential features. These features are then used for subsequent 3D processing and 3D feature analysis of the target object.

[0020] For example, in the field of autonomous driving, point cloud data of target objects such as obstacles in the environment can be collected using LiDAR or depth sensors. The collected point cloud data can be used to fit quadratic surfaces of the target objects in the environment to obtain differential surface features. These differential surface features can then be used to achieve 3D reconstruction of obstacles in the environment. For example, curvature features can be used to distinguish between flat ground, curved road boundaries, or sharp object edges, thereby improving the safety and accuracy of autonomous driving processes. Alternatively, the differential surface features can also be used to achieve lightweight semantic annotation of point cloud data, facilitating the reuse of these features in different decision-making scenarios.

[0021] For example, in the fields of virtual reality and augmented reality, the surface differential features of a target object in a real scene can be obtained from the point cloud data of the real scene. These surface differential features can be used to render a virtual display image corresponding to the real scene and blend it with the virtual object for display.

[0022] For example, in the field of medical imaging technology, point cloud data can be used to fit a quadratic surface to a lesion to obtain its surface differential features. These surface differential features can be used, for example, for occlusal analysis in dental scans, hemodynamic simulation in cardiovascular models, and fit assessment of orthopedic implants. Exemplarily, in one possible application scenario, a smooth anatomical surface at the lesion can be reconstructed from noisy scan data based on surface differential features, thereby facilitating accurate analysis and diagnosis of the lesion. Alternatively, in other application scenarios, surface differential features may be used only for medical complex analysis calculations (such as stress analysis) rather than directly for three-dimensional reconstruction.

[0023] Alternatively, in the field of cultural heritage digitization, quadratic surface fitting based on point cloud data can be used to extract differential features from the surface of cultural relics and detect curvature anomalies in damaged areas. In this application scenario, the differential features obtained from quadratic surface fitting can not only achieve 3D reconstruction of cultural relics but also enable digital archiving of them—that is, storing only parameters without performing reconstruction. Or, in the fields of scanning metrology and quality control, quadratic surface fitting based on point cloud data can be used for tolerance inspection of industrial parts, reverse engineering geometric verification, and infrastructure deformation monitoring. In this case, the differential feature parameters of the fitted surface can be used for geometric measurement and analysis of parts, or to generate 3D models of parts.

[0024] In the process of fitting a quadratic surface based on point cloud data to obtain its differential properties, the fitting accuracy of the quadratic surface will affect the fineness of the output results in subsequent 3D processing. For ease of understanding, Figure 1 A schematic diagram is given showing the rendering results obtained from 3D rendering based on surface differential features of different accuracies. For example... Figure 1 As shown, when the surface differential features obtained by fitting a quadratic surface based on point cloud data do not contain accurate normal information, the resulting rendering cannot reflect the surface texture features of the target object; when the surface differential features obtained by fitting a quadratic surface based on point cloud data contain accurate normal information, the resulting rendering will present the fine surface details of the target object. It should be understood that... Figure 1 The illustrations shown are merely illustrative of the rendering effect and are intended to help understand the embodiments of this application. They are not based on actual rendering results obtained using real rendering tools.

[0025] However, current technical solutions cannot achieve accurate fitting of the quadratic surface of the target object.

[0026] To address the aforementioned issues, this application provides a quadratic surface fitting method. This method can be used to fit an implicit surface of a target object based on point cloud data. The local positions of each point on this implicit surface closely approximate the corresponding positions of the target object. Specifically, "closely approximate" means that the normals of the local positions of each point on the implicit surface are close to the actual normals of the corresponding positions on the target object, and the curvature of the local positions of each point on the implicit surface is close to the actual curvature of the corresponding positions on the target object.

[0027] Based on the quadratic surface fitting method provided in this application, the fitting accuracy of the quadratic surface of the target object can be improved, resulting in more accurate differential feature parameters of the quadratic surface of the target object. Therefore, in the fields of autonomous driving, virtual reality, medical imaging, archaeology, and cultural relic restoration, it can improve the processing accuracy of 3D reconstruction, rendering, remeshing, and other 3D processing operations on different types of target objects.

[0028] The specific implementation of the quadratic surface fitting method provided in the embodiments of this application will be described below with reference to the relevant accompanying drawings.

[0029] Figure 2 This is a flowchart illustrating a quadratic surface fitting method provided in an embodiment of this application. Figure 2 As shown, the quadratic surface fitting method provided in this application embodiment may include the following method flow: 101. Using the principal component analysis (PCA) method, determine the local principal component analysis coordinate system corresponding to the local surface where the target point is located.

[0030] In this embodiment, multiple points adjacent to the target point can be determined. The target point can be any point in the point cloud data of the target object. The multiple points adjacent to the target point can be, for example, the K nearest neighbors of the target point. The target point and its multiple adjacent points can form a target point cloud block. The target point cloud block can be translated so that the target point is located at the origin. Based on the distance between the farthest neighbor among the K nearest neighbors and the target point, the distances between each neighboring point and the target point are normalized to obtain a normalized target point cloud block. Then, Principal Component Analysis (PCA) can be applied to the normalized target point cloud block to obtain the local principal component analysis coordinate system corresponding to the local surface where the target point is located, hereinafter referred to as the "local PCA coordinate system".

[0031] 102. Transform the Monge-type equation corresponding to the local surface where the target point is located to the local principal component analysis coordinate system to obtain the implicit surface equation.

[0032] Based on the principles of differential geometry, any quadratic surface corresponding to a local part of a target object can be expressed as the following Monge form equation: (1) in, and These are the two principal curvatures of the quadratic surface corresponding to the local area of ​​the target object. Indicates the target point is at Coordinate values ​​along the axis, Indicates the target point is at Coordinate values ​​along the axis, Indicates the target point is at The coordinate values ​​along the axis.

[0033] In other words, the Monge form equation is an explicit representation of the quadratic surface of the target object. The Monge form equation can accurately characterize the local geometry in an analytical sense, and its second-order expansion is consistent with the quadratic surface at that point.

[0034] However, directly solving the Monge-type equations based on pure point cloud data is not feasible because constructing the Monge-type equations requires coefficients. and And the normal to the target point and and The Monge coordinate system is formed by the directions of the principal curvatures, and these data depend on the differential characteristic parameters of the quadratic surface we are trying to fit, thus forming a cyclic dependency.

[0035] For the reasons stated above, in this embodiment of the application, the Monge-type equation corresponding to the local surface where the target point is located can be transformed to the local PCA coordinate system to obtain the implicit surface equation. The obtained implicit surface equation contains a term to be solved, which is based on the Monge-type equation... and The transformation yields an implicit surface equation, which is an implicit representation of the quadratic surface of the target object and can be used to describe local surfaces.

[0036] The specific conversion method from Monge-type equations to implicit surface equations is explained below.

[0037] First, let the target point cloud block normalized to the local PCA coordinate system be... ,set up For the target point cloud block in the Monge coordinate system The coordinates of the midpoint, where, This indicates the position information of the target point in the world coordinate system. Let represent the two principal directions at the target point in the world coordinate system and the surface normal vector, respectively. Then, the Monge-type equation can be transformed into: (2) in , for one A diagonal matrix, whose two principal curvatures are related to the Monge form equation. and related; It is a column vector, corresponding to the direction of the target point in the Monge coordinate system.

[0038] For simplicity, you can use This represents the coordinates of the target point cloud patch in the local PCA coordinate system. Therefore:

[0039] in, Let be the rotation matrix from the Monge coordinate system to the local PCA coordinate system, and we have:

[0040] in, is the basis matrix of the local PCA coordinate system, and its columns are the principal directions of the local PCA coordinate system in the world coordinate system.

[0041] Finally, after transforming the Monge-type equations to the local PCA coordinate system, the implicit surface equations are obtained as follows: (3) in Represents the second-order coefficient matrix. This represents the first-order coefficient vector. Furthermore, As a structural identity, this holds because of the rotation of the unit vector. It will not change The length.

[0042] 103. Solve the implicit surface equation based on the position information of the target point cloud block in the local principal component analysis coordinate system to obtain the value of the term to be solved.

[0043] In this embodiment, the position information of the target point cloud block in the local PCA coordinate system can be corrected to obtain the corrected position information of each point in the target point cloud block; then, the implicit surface equation can be solved based on the corrected position information of each point to obtain the value of the term to be solved. Specifically, correcting the position information of the target point cloud block in the local PCA coordinate system includes: using a target neural network model to determine the position offset corresponding to each point in the target point cloud block; and correcting the position information of the target point cloud block in the local PCA coordinate system based on the position offset.

[0044] The specific method for solving the implicit surface equation can be based on the weighted least squares (WLSQ) method.

[0045] First, using the weighted least squares method, an objective function can be established for the unsolved terms in the implicit surface equation based on the position information of the target point cloud patch in the local PCA coordinate system. Then, by minimizing this objective function, the values ​​of the unsolved terms in the implicit surface equation can be obtained.

[0046] The establishment of the objective function will be explained below.

[0047] In this embodiment, the position information and weight information of each point in the target point cloud in the local PCA coordinate system can be substituted into the aforementioned implicit surface equation to obtain a multivariate equation containing multiple equations. Then, using the weighted least squares method, an objective function for the unsolved terms in the implicit surface equation can be constructed based on the aforementioned multivariate equation containing multiple equations. The weight information corresponding to each point is related to the distance from each point to the target point in the feature space. The closer the feature to the target point, the larger the corresponding weight value; conversely, the farther away, the smaller the corresponding weight value.

[0048] In one specific implementation, due to 3D scanning errors, the obtained point cloud data carries noise, and its position information cannot represent the true local position information of the target object. Therefore, to improve the fitting accuracy of the weighted least squares method, in this embodiment, the position information of the target point cloud block in the local PCA coordinate system can be corrected to obtain the corrected position information of each point in the target point cloud block. Then, the weighted least squares method can be used to establish an objective function for the unsolved terms in the implicit surface equation based on the corrected position information of each point. Specifically, correcting the position information of the target point cloud block in the local PCA coordinate system can be achieved by using a target neural network model to determine the position offset corresponding to each point in the target point cloud block, and then correcting the position information of the target point cloud block in the local PCA coordinate system based on the position offset to obtain the corrected position information of each point in the target point cloud block.

[0049] Furthermore, in this embodiment, the weight values ​​corresponding to each point can also be obtained using a target neural network model. Specifically, the target neural network model can be used to determine the position offset and weight value corresponding to each point in the target point cloud. The position offset and weight information corresponding to each point are correlated with the differential feature parameters of the local quadratic surface of the target object. Based on this, in this embodiment, the above-mentioned target neural network model can be trained, for example, based on the actual differential feature parameters of the surface of a real sample object. The specific model training process will be described in subsequent embodiments. Then, the position information of each point in the local PCA coordinate system can be corrected according to the position offset corresponding to each point to obtain the corrected position information. Finally, based on the corrected position information of each point and the weight value of each point, the weighted least squares method can be used to establish the objective function for the unsolved term in the implicit surface equation as follows: (4) in, , where represents the coefficients of the implicit surface equation to be solved. Corresponding to the implicit surface equation (Formula 3) above , represents the second-order coefficient matrix of the implicit surface equation. Corresponding to the implicit surface equation (Formula 3) above , represents the first-order coefficient vector of the implicit surface equation. The coefficients are first-order and satisfy the following constraints: . The satisfied constraints can be used to force the gradient at the target point to be a unit vector, which is consistent with the implicit surface equations mentioned above. Maintain consistency. , , These represent the corrected axis coordinates of each point. This represents the weight value corresponding to each point.

[0050] The following explains the specific implementation method of obtaining the value of the term to be solved in the implicit surface equation by minimizing the above objective function.

[0051] In this embodiment, the process of minimizing the objective function can be transformed into a Rayleigh quotient problem. Then, by solving the Rayleigh quotient problem, the value of the term to be solved in the implicit surface equation can be obtained. The specific derivation process is explained below.

[0052] First, the objective function (Equation 4) and its corresponding constraints can be rewritten in matrix form, then we have: satisfy: (5) in, , is a diagonal matrix. It is a symmetric matrix: (6) The objective function in matrix form (Equation 5) simplifies to a standard generalized Rayleigh quotient, the optimal solution of which is given by the generalized eigenvector corresponding to the minimum eigenvalue, and the minimum algebraic fitting error is equal to that eigenvalue. Specifically, the solution satisfies: (7) in It is the smallest generalized eigenvalue.

[0053] However, due to Since the matrix is ​​not full-rank, directly solving the generalized eigenvalue problem may be numerically unstable. Therefore, the generalized Rayleigh quotient problem can be transformed into a standard Rayleigh quotient problem, which can be solved by... Efficiently solve the eigenvalues ​​of the matrix. and By dividing the data into blocks, we can obtain: (8) make Rewrite the first row of formula (7) in block matrix form: (9) Formula (9) can be solved as follows:

[0054] in It is a pseudo-inverse matrix. Let The optimal solution of formula (7) is:

[0055] because It is The matrix is ​​used; therefore, the objective function is simplified to a standard Rayleigh quotient problem. Optimal solution. It corresponds to the smallest eigenvalue The normalized eigenvectors can be obtained by... We can perform eigenvalue decomposition for efficient solution. Therefore, the unsolved terms in the implicit surface equation can be obtained as follows: (12) In the above technical solution, by transforming the process of minimizing the objective function into a Rayleigh quotient problem, the efficiency of solving the objective function can be improved, the consumption of computational resources can be reduced, and thus the execution efficiency of the quadratic surface fitting process can be improved.

[0056] 104. Based on the value of the term to be solved, the differential characteristic parameters of the local surface are obtained.

[0057] Specifically, based on the coefficients of the implicit surface equation obtained by solving, the differential characteristic parameters of the local surface, including the normal vector, Gaussian curvature, and mean curvature, can be calculated using preset formulas. The obtained differential characteristic parameters can be used to realize the three-dimensional processing of the target object, such as 3D reconstruction and rendering, to meet the needs of different application scenarios.

[0058] In the above technical solution, the Monge-type equation is transformed to the local PCA coordinate system to obtain the implicit expression of the Monge-type equation, namely the implicit surface equation. Then, a quadratic surface is fitted based on the implicit surface equation. Since the quadratic surface fitting is based on the implicit expression of the Monge-type equation, it benefits from the characteristic that the Monge-type equation has no model error. Figure 3 As shown in 3A, the above-described scheme in the embodiments of this application can fit a closely spaced surface of the real surface, and the normal vector and curvature of the closely spaced surface are closer to the normal vector and curvature of the real surface.

[0059] In contrast, traditional methods of surface fitting based on predefined surface functions in a local PCA coordinate system introduce model errors because real-world surfaces may not conform to such strict functional forms. Therefore, the predefined surface functions themselves introduce model errors. Figure 3 As shown in 3B, the method can only guarantee that as many data points as possible fall on the fitted surface, but cannot obtain the close surface of the real surface. That is, it cannot guarantee that the normal vector and curvature of the fitted local quadratic surface are close to the normal vector and curvature of the real surface.

[0060] This application also provides a model inference method. In this application embodiment, the above-mentioned quadratic surface fitting method can be implemented based on a neural network model.

[0061] Specifically, the model inference method provided in this application includes: First, the target point cloud block is input into the neural network model. The target point cloud block includes the target point and multiple points adjacent to the target point. The target point is any point in the point cloud data of the target object.

[0062] Furthermore, the neural network model can obtain the differential feature parameters of the local surface where the target point is located by performing the aforementioned quadratic surface fitting method. The differential feature parameters can be used to realize the three-dimensional processing of the target object.

[0063] The training method for the above neural network model will be explained below. Figure 4 A flowchart of the model training method provided in the embodiments of this application is given, such as... Figure 4 As shown, the model training method provided in this application embodiment may include: 201. Determine sample point cloud blocks based on a pre-generated training dataset.

[0064] In this embodiment, the pre-generated training dataset may include multiple different quadratic surfaces. The training dataset can provide precise reference normals, principal curvatures, and principal directions derived from precise computer-aided design (CAD) geometry for each quadratic surface. Sample point cloud blocks may include data corresponding to points on a local surface of any quadratic surface included in the training dataset.

[0065] 202. Input the sample point cloud block into the neural network model to be trained so that the neural network model to be trained can obtain the initial differential feature parameters of the local surface by performing a quadratic surface fitting method.

[0066] 203. Construct a loss function based on the initial differential feature parameters and the actual differential feature parameters of the local surfaces in the training dataset.

[0067] 204. Update the model parameters of the neural network model to be trained based on the loss function to obtain the trained neural network model.

[0068] For any iteration in the model training process, the neural network model to be trained can execute the quadratic surface fitting method described in the above embodiments once to infer the normal, mean curvature, and Gaussian curvature of the fitted quadratic surface. Then, the actual differential feature parameters of the local surfaces in the pre-generated training dataset can be used as supervision information to calculate the loss function of the quadratic surface coefficients, normal, Gaussian curvature, and mean curvature. Subsequently, backpropagation can be performed based on the calculation results of the loss function to update the model parameters, resulting in the iterative neural network model. Through multiple iterations, the model accuracy can be gradually improved.

[0069] This application also provides an electronic device, which can be of any form and is not limited thereto. The electronic device provided in this application may include a computer storage medium configured to store computer program instructions for executing the quadratic surface fitting method provided in this application.

[0070] This application also provides a computer program product, including computer instructions that instruct a computing device to perform an operation corresponding to any of the methods in the above-described plurality of method embodiments. It should be noted that, depending on implementation needs, the various components / steps described in the embodiments of this application can be broken down into more components / steps, or two or more components / steps or parts of the operations of components / steps can be combined into new components / steps to achieve the purpose of the embodiments of this application.

[0071] This application also provides a computer-readable storage medium in which the methods described in this application embodiment can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as CDROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code downloaded over a network that is originally stored in a remote recording medium or a non-transitory machine-readable medium and will be stored in a local recording medium. Thus, the methods described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses code used to implement the methods shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for executing the methods shown herein.

[0072] Those skilled in the art will recognize that the units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the embodiments of this application.

[0073] It should be noted that, in this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0074] Furthermore, it should be noted that the user-related information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to sample data used for training the model, data used for analysis, stored data, displayed data, etc.) involved in the embodiments of this application are all information and data authorized by the user or fully authorized by all parties. Moreover, the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions, and corresponding operation entry points are provided for users to choose to authorize or refuse.

[0075] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0076] The methods disclosed in the several method embodiments provided in this application can be arbitrarily combined without conflict to obtain new method embodiments.

[0077] The features disclosed in the several product embodiments provided in this application can be arbitrarily combined without conflict to obtain new product embodiments.

[0078] The features disclosed in the several method or device embodiments provided in this application can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0079] The above embodiments are only used to illustrate the embodiments of this application, and are not intended to limit the embodiments of this application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the embodiments of this application. Therefore, all equivalent technical solutions also fall within the scope of the embodiments of this application, and the patent protection scope of the embodiments of this application should be defined by the claims.

Claims

1. A quadratic surface fitting method, comprising: Using the principal component analysis (PCA) method, the local principal component analysis coordinate system corresponding to the local surface where the target point is located is determined; the target point is any point in the point cloud data of the target object. The Monge-type equation corresponding to the local surface where the target point is located is transformed to the local principal component analysis coordinate system to obtain the implicit surface equation; the implicit surface equation contains terms to be solved and is used to describe the local surface; The implicit surface equation is solved based on the position information of the target point cloud block in the local principal component analysis coordinate system to obtain the value of the term to be solved; the target point cloud block includes the target point and multiple points adjacent to the target point; Based on the value of the term to be solved, the differential characteristic parameters of the local surface are obtained.

2. The method according to claim 1, wherein, The implicit surface equation is solved based on the position information of the target point cloud block in the local principal component analysis coordinate system to obtain the value of the term to be solved, including: The position information of the target point cloud block in the local principal component analysis coordinate system is corrected to obtain the corrected position information of each point in the target point cloud block; Based on the corrected position information of each point, the implicit surface equation is solved to obtain the value of the term to be solved.

3. The method according to claim 2, wherein, Correcting the position information of the target point cloud block in the local principal component analysis coordinate system includes: Using a target neural network model, determine the position offset of each point in the target point cloud block; Based on the position offset, the position information of the target point cloud block in the local principal component analysis coordinate system is corrected.

4. The method according to claim 2, wherein, Based on the corrected position information of each point, the implicit surface equation is solved to obtain the value of the term to be solved, including: Using the weighted least squares (WLSQ) method, an objective function is established for the terms to be solved in the implicit surface equation based on the corrected position information of each point. The value of the term to be solved is obtained by minimizing the objective function.

5. The method according to claim 4, wherein, The value of the term to be solved is obtained by minimizing the objective function, including: The process of minimizing the objective function is transformed into a Rayleigh quotient problem; The value of the term to be solved is obtained by solving the Rayleigh quotient problem.

6. The method according to claim 4, wherein, The method further includes: Using a target neural network model, determine the weight value corresponding to each point in the target point cloud block; Using the weighted least squares (WLSQ) method, based on the corrected position information of each point, an objective function is established for the unsolved terms in the implicit surface equation; including: Using the weighted least squares (WLSQ) method, an objective function is established for the terms to be solved in the implicit surface equation based on the corrected position information of each point and the weight values.

7. The method according to claim 1, wherein, The differential characteristic parameters include the normal vector, Gaussian curvature, and mean curvature.

8. A model training method, comprising: Determine sample point cloud blocks based on a pre-generated training dataset; The training dataset includes multiple different quadratic surfaces; The sample point cloud block includes data of points corresponding to the local surface of any quadratic surface; The sample point cloud block is input into the neural network model to be trained, so that the neural network model to be trained obtains the initial differential feature parameters of the local surface by executing the method as described in any one of claims 1-7. A loss function is constructed based on the initial differential feature parameters and the actual differential feature parameters of the local surface in the training dataset; The model parameters of the neural network model to be trained are updated based on the loss function to obtain the trained neural network model.

9. A model reasoning method, comprising: The target point cloud block is input into a neural network model; the neural network model is trained based on the method described in claim 8. The target point cloud block includes a target point and multiple points adjacent to the target point; the target point is any point in the point cloud data of the target object; The neural network model obtains differential feature parameters of the local surface where the target point is located by executing the method described in any one of claims 1-7. The differential feature parameters are used to realize the three-dimensional processing of the target object.

10. An electronic device, comprising: A computer storage medium configured to store computer program instructions for performing the method as described in any one of claims 1 to 9.

11. A computer storage medium storing at least one piece of program code, the program code being loaded and executed by a processor to implement the method as described in any one of claims 1 to 9.

Images