Robust three-dimensional reconstruction method based on weighted local curved surface approximation

Abstract

The invention belongs to the technical field of point cloud data reconstruction, and particularly relates to a robust three-dimensional reconstruction method based on weighted local curved surface approximation. The method comprises the following steps: firstly, preprocessing input three-dimensional point cloud data, constructing a neighborhood relationship, and fitting a local curved surface in a local neighborhood of each point through a least square method; secondly, calculating the influence weight based on the neighborhood information of the point, and calculating the position of a final curved surface point by adopting a weighted average method so as to optimize the geometric accuracy of a local curved surface; then, screening and removing abnormal points by using an abnormal weight elimination strategy based on a mean square error, reducing noise interference, and improving stability and robustness of curved surface reconstruction; and finally, through weighted average, the precision of overall curved surface fitting is improved, so that the reconstructed curved surface can more accurately fit the original point cloud data, and the reconstruction precision of the point cloud data is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of point cloud data reconstruction, and in particular relates to a robust three-dimensional reconstruction method based on weighted local surface approximation. Background Art

[0002] Point cloud data reconstruction is a core technology in the fields of computer vision, 3D modeling, and digital geometric reconstruction. It plays an important role in many applications such as autonomous driving, virtual reality, 3D printing, cultural heritage protection, industrial inspection, and medical imaging. Point cloud data is usually acquired by laser radar (LiDAR), structured light scanning, stereo vision system, or depth camera. Its essence is discretely sampled 3D coordinate points used to describe the geometric structure of objects. However, due to factors such as measurement errors, environmental noise, point cloud sparsity, and occlusion, how to accurately reconstruct 3D surfaces from these high-dimensional, sparse, and noisy point cloud data has become an important research direction in the fields of computer graphics and computational geometry.

[0003] Traditional 3D reconstruction methods mainly rely on geometric modeling and optimization techniques, which construct clear mathematical models to fit point cloud data to generate continuous and smooth surfaces. In addition, global fitting methods aim to fit the surface of point cloud data through accurate mathematical models. These methods can process point cloud data to a certain extent, but they often face several problems. First, triangulation is sensitive to noise, especially for point cloud data containing noise and outliers, which may cause the generated mesh to be non-smooth or self-intersecting. Second, point cloud data in reality is often unevenly distributed, especially in areas with complex geometries or rich details. Traditional meshing methods find it difficult to accurately capture local features. Summary of the invention

[0004] In order to overcome the problems in the prior art, the present invention proposes a robust three-dimensional reconstruction method based on weighted local surface approximation.

[0005] The technical solution of the present invention to solve the above technical problems is as follows: A robust 3D reconstruction method based on weighted local surface approximation comprises the following steps: Subdividing the original triangular mesh in the point cloud three-dimensional space into a plurality of small triangles; wherein the vertices of the plurality of small triangles include point cloud data points and generated vertices; Based on the weighted average method of triangle area, the normal vector of the generated vertex is calculated; based on the neighborhood points of the generated vertex, a fitting surface is constructed, and the intersection point between the motion trajectory of the generated vertex along the normal vector and the fitting surface is calculated; Calculate the distance between the neighborhood point of the generated vertex and the intersection point, and determine the influence weight of the neighborhood point of the generated vertex on the generated vertex according to the distance; screen and remove abnormal neighborhood points based on the abnormal influence weight elimination strategy of the mean square error; Based on the positions of neighborhood points and their influence weights, the final coordinates of the generated vertices are calculated by weighted averaging to generate a refined point cloud reconstruction model.

[0006] Furthermore, the original triangular mesh in the point cloud three-dimensional space is subdivided into multiple small triangles, including: evenly dividing each edge of the original triangle and generating new segmentation points on each edge; forming a new boundary relationship between the boundary of the original triangle and the newly added segmentation points, and then constructing a regular grid structure inside the original triangle, divided into multiple small triangles.

[0007] Furthermore, based on the weighted average method of the triangle area, the normal vector of the generated vertex is calculated, specifically including: Get the normal vectors of the three vertices of the original triangle; Determine the three small triangles formed by the generated vertices and obtain the areas of the three sub-triangles; Based on the normal vectors of the three vertices of the original triangle and the areas of the three sub-triangles, a vertex normal vector is generated by weighted calculation: and the generated vertex normal vector is normalized to obtain the normalized generated vertex normal vector.

[0008] Furthermore, the step of constructing a fitting surface based on the neighborhood points of the generated vertex and calculating the intersection point between the motion trajectory of the generated vertex along the normal vector and the fitting surface specifically includes: Construct a set of neighborhood points for generating vertices; for each neighborhood point in the set of neighborhood points, construct a fitting surface equation, and represent the motion trajectory of the generated vertex along the normal vector through parameterization; The motion trajectory of the generated vertex is substituted into the surface equation, the intersection position of the motion trajectory of the generated vertex along the normal vector and the fitting surface is calculated, and the position of the generated vertex on the fitting surface is determined.

[0009] Furthermore, the calculating of the distance between the neighborhood point of the generated vertex and the intersection point, and determining the influence weight of the neighborhood point of the generated vertex on the generated vertex according to the distance, specifically includes: Calculate the influence radius of the neighborhood point of the generated vertex, where the influence radius is the distance from the neighborhood point of the generated vertex to its farthest first-order neighbor point; When the generated vertex is within the influence radius of the generated vertex's neighborhood point, the influence weight of the generated vertex's neighborhood point is the difference between the influence radius and the distance between the two points; if the generated vertex is outside the influence range of the generated vertex's neighborhood point, the influence weight is zero.

[0010] Furthermore, the abnormal influence weight elimination strategy based on mean square error screens and removes abnormal neighborhood points, specifically including: Calculate the average value of the influence weights of the neighborhood points, and calculate the mean square error based on the average value of the influence weights of the neighborhood points and the influence weights of the neighborhood points; Preset Threshold , if the difference between the influence weight of the generated vertex's neighborhood points and the average influence weight is greater than times the mean square error, it is considered that the influence weight of the neighborhood points of the generated vertex is unreasonable and the neighborhood points are removed.

[0011] Furthermore, the calculation of the final coordinates of the vertex based on the positions of the neighborhood points and their influence weights by weighted average method specifically includes: Generate the final position of the vertex : ; ; ; in, Represents the coordinates of the neighborhood points; Indicates the number of neighboring points; Represents the influence weight of each neighborhood point.

[0012] Compared with the prior art, the present invention has the following technical effects: (1) The present invention proposes a robust 3D reconstruction method based on weighted local surface approximation, which can effectively reduce the error accumulation in the global fitting method and improve the reconstruction accuracy of the local surface, making it more suitable for point cloud data with complex surface structures.

[0013] (2) The present invention further optimizes the surface structure by refining the reconstructed fitting surface, so that the reconstruction result is more accurately close to the real three-dimensional shape, and to a certain extent alleviates the problem of local structure loss caused by sparse data sampling or point cloud holes.

[0014] (3) The present invention proposes a mechanism for eliminating unreasonable weights based on mean square error screening. When calculating the point cloud weights, abnormal points are adaptively eliminated to reduce the interference of noise points on the surface fitting results, thereby improving the stability of reconstruction and ensuring the reliability of surface reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0016] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 The rendering result of the original point cloud and the rendering result after reconstruction by the method of the present invention are shown; Figure 3 This is the rendering result before reconstruction; Figure 4 This is a rendering result diagram of the present invention. DETAILED DESCRIPTION

[0017] In order to further explain the technical means and effects taken by the present invention to achieve the predetermined invention purpose, the specific implementation methods, structures, features and effects of the technical solutions proposed by the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments. The specific features, structures or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by technicians in the technical field of the present invention.

[0018] Starting from the complex geometric features of point cloud data, this embodiment proposes a robust 3D reconstruction method based on weighted local surface approximation. This method enhances the reconstruction accuracy by combining the weighted local surface approximation method with the local fitting optimization strategy, weighted neighborhood point influence calculation, and abnormal point removal mechanism. Combined with the weighted calculation of normal vectors, it ensures that the reconstructed surface of the point cloud data is smoother and conforms to the actual geometric form. On this basis, the normal vector weighting method is introduced to weight the normal vector according to the area of ​​each small triangle, so that the normal vector can smoothly transition in the subdivided grid, avoiding the problem of normal vector inconsistency caused by local errors, thereby improving the accuracy and robustness of the reconstructed model.

[0019] In addition, in order to better handle the local complexity and geometric details in the point cloud data, this embodiment proposes a method for calculating the intersection of the fitting surface and the generated vertex. This method further refines the position of the generated vertex by solving the intersection of the generated vertex and the fitting surface of the point cloud data point. This method can effectively avoid the problem of the generated vertex deviating from the real geometric surface and improve the accuracy of point cloud reconstruction. In order to deal with the noise and irregularity in the point cloud data, an outlier removal mechanism is also designed, which uses the mean square error algorithm to identify and remove outliers, thereby ensuring that each point in the reconstruction process makes a positive contribution to the precise positioning of the generated vertex.

[0020] By combining triangle subdivision, normal vector weighting and fitting surface intersection calculation, a high-precision and robust point cloud reconstruction method is proposed. This method can not only process point clouds with complex shapes and large-scale data, but also cope with point cloud data sets with large noise, significantly improving the accuracy and stability of the point cloud reconstruction model. After a large number of experimental verifications, this embodiment greatly improves the robustness of the algorithm while improving the accuracy of point cloud data, and provides an effective solution for the refined reconstruction of point cloud data.

[0021] In one embodiment of the present invention, referring to Figure 1 , a robust 3D reconstruction method based on weighted local surface approximation is provided, comprising the following steps: Step 100: subdividing the original triangular mesh in the point cloud three-dimensional space into a plurality of small triangles; wherein the vertices of the plurality of small triangles include point cloud data points and generated vertices; Step 200: Calculate and generate the normal vector of the vertex based on the weighted average method of the triangle area; Step 300: construct a fitting surface based on the neighborhood points of the generated vertex, and calculate the intersection point between the motion trajectory of the generated vertex along the normal vector and the fitting surface; Step 400: Calculate the distance between the neighborhood point of the generated vertex and the intersection point, and determine the influence weight of the neighborhood point of the generated vertex on the generated vertex according to the distance; Step 500: Screen and remove abnormal neighborhood points based on the abnormal influence weight elimination strategy of the mean square error; Step 600: Based on the positions of the neighborhood points and their influence weights, the final coordinates of the generated vertices are calculated by weighted averaging to generate a refined point cloud reconstruction model.

[0022] The following is a detailed explanation of each of the above steps: Step 100: Connect the 3D point cloud data into a triangular mesh, i.e., the original triangular mesh, and subdivide the original triangular mesh into a plurality of small triangles, wherein the vertices of the plurality of small triangles include the original point cloud data and the generated vertices. The mesh generated after subdivision has a higher resolution, which helps to capture the details of the point cloud data and provides a more accurate basis for surface reconstruction.

[0023] The discrete point set is connected into a triangular mesh, i.e., the original triangular mesh, by the triangulation algorithm. The original triangular mesh is subdivided. First, each edge of the original triangle is evenly divided. Specifically, each edge of the original triangle is divided into five equal parts according to the proportion, so that four new segmentation points are generated on each edge; next, the original triangle is further divided into 25 small triangles by connecting the vertices. Specifically, a new boundary relationship is formed between the boundary of the original triangle and the newly added segmentation points, and then a regular grid structure is constructed inside the original triangle. Through this operation, each segmentation point of the three edges of the original triangle will form a new connection relationship with other segmentation points and the original vertices of the triangle, and form a vertex set containing 21 vertices, which are composed of the three original point cloud data points of the original triangle, the subnodes generated by the uniform segmentation of the boundary, and the new vertices generated by the topological connection between the segmentation points. Among them, the 21 vertices include 3 original point cloud data points and 18 generated vertices.

[0024] The subdivided mesh has a higher resolution and finer structure, and can better capture the local geometric details in the point cloud data. The subdivision operation increases the density of the mesh, so that the surface shape can be restored more accurately in the subsequent interpolation and reconstruction process. By increasing the number of small triangles, a more regular mesh can be obtained, avoiding the geometric irregularities that may be caused by the original triangular mesh. This process enables subsequent steps such as normal vector calculation, interpolation, and outlier removal to be performed on a finer and more uniform mesh, thereby ensuring the accuracy and robustness of the reconstruction results. Subdivision not only optimizes the local calculation accuracy, but also provides a more suitable mesh structure for the processing of complex geometric shapes, avoiding the error accumulation caused by coarse meshes.

[0025] Step 200: Calculate the normal vector of the generated vertex based on the weighted average method of the triangle area. The normal vector of each small triangle is assigned different weights according to its area, and finally a smooth normal vector of the generated vertex is obtained. This method ensures the stability of the normal vector and avoids the influence of local errors on the reconstruction results.

[0026] The calculation of the normal vector of the generated vertex adopts the weighted average method based on the area of ​​the triangle. First, the three small triangles formed by the generated vertex are determined, and the normal vector of the generated vertex is calculated according to the area and normal direction of each small triangle. The normal vector of each small triangle is assigned different weights according to its area, and the normal vector of the final generated vertex is obtained by weighted average. The advantage of this is that it can avoid the excessive influence of the normal vector of a single small triangle on the result, and avoid the jump or inconsistency of the normal vector. Due to the possible noise and irregularity in the point cloud data, directly using the normal vector of a single triangle may lead to uneven calculation results. Therefore, by weighted averaging the normal vectors of multiple triangles, the normal vector is effectively smoothed and the consistency of the geometric surface is ensured. The normal vector calculated by this method can better reflect the changes in the geometric structure around the generated vertex, thereby providing more stable and consistent direction information for subsequent interpolation calculations. Overall, this weighted normal vector calculation method improves the accuracy of the normal vector while ensuring the smooth transition and geometric consistency of the surface.

[0027] Specifically, let the three vertices of the original triangle be , , , the normal vectors of the three vertices are , , ; and generate vertices Located in triangle At a certain position in the surface, the original triangle is divided into three sub-triangles: , , , corresponding to the area , , .

[0028] Generate vertices by weighted calculation of vertex normal vectors The normal vector As shown in formula (1): (1); in, , , Generating vertices exist , , The component of the normal vector in the direction.

[0029] Further normalization is performed to ensure that the calculated normal vector has the same direction and scale: (2); In the above formula, Represents the generated vertices after normalization The normal vector of .

[0030] Step 300: construct a fitting surface based on the neighborhood points of the generated vertex, and calculate the intersection between the motion trajectory of the generated vertex along the normal vector and the fitting surface. This method ensures that the generated vertex is accurately aligned with the point cloud data surface, thereby improving the accuracy and geometric consistency of point cloud reconstruction.

[0031] The present invention constructs a quadratic polynomial fitting surface for the neighborhood points, and generates the motion trajectory of the vertex along the normal vector through parameterization. By substituting the motion trajectory of the generated vertex along the normal vector into the equation of the fitting surface, the intersection of the generated vertex and the fitting surface along the normal vector direction is calculated. Quadratic polynomial fitting can effectively capture the local geometric features of point cloud data and provide accurate position correction for the generated vertices. In this way, the generated vertices can be accurately mapped to the fitting surface, avoiding the accumulation of errors caused by surface irregularities. The fitting surface can not only improve the positioning accuracy of the generated vertices, but also better adapt to the complex shapes and local changes in the point cloud data, and improve the accuracy and geometric consistency of the reconstructed model. In addition, the parameterized equation provides a flexible motion description, so that the method can be optimized according to different data distributions, improving the adaptability and computational efficiency of the algorithm.

[0032] In this step, the original triangle vertices in the point cloud data are , , and its first-order neighborhood point set, calculate the generated vertex The intersection between the trajectory of motion along the normal vector and the fitted surface where these points lie.

[0033] First, build a set of neighborhood points. , its neighborhood point set is: ,in For point , , The first-order neighboring points of .

[0034] for For each first-order neighboring point in , a fitting surface in the form of a quadratic polynomial is constructed for them. The polynomial equation is shown in formula (3): (3); Need to solve the generated vertex The intersection point between the trajectory of motion along the normal vector and the fitted surface.

[0035] Assume that the generated vertex The coordinates are , using parameterized form to represent the generated vertices Movement along the normal vector direction. Specifically, generate vertices The motion trajectory along the normal vector can be expressed by formula (4): (4); Substituting the above parameterized equation into the polynomial equation of the fitting surface (3), we can get a parameter The equation is: (5); Solve this equation to obtain the parameters Since we are interested in the positive direction along the normal vector, we choose The correct answer is the result, so the specific coordinates of the intersection point JD can be calculated , thereby determining the generated vertex The intersection point between the motion trajectory of the normal vector and the fitting surface is used to determine the position of the generated vertex on the fitting surface.

[0036] Step 400: Calculate the distance between the neighborhood point of the generated vertex and the intersection point obtained in step 300, and determine the influence weight of the neighborhood point of the generated vertex on the generated vertex according to the distance. By reasonably allocating weights, it is ensured that only the neighborhood points closely related to the generated vertex have a significant impact on the interpolation, thereby improving the reconstruction accuracy.

[0037] First, the Euclidean distance between the neighborhood point of the generated vertex and the intersection point obtained in step 300 is calculated, and then the influence range on the generated vertex is determined. Based on these distances, a weight is assigned to each point cloud data point, and the point cloud data point with a closer distance has a larger weight, while the point far away from the generated vertex has a smaller influence on the generated vertex. In this way, the point cloud data points that affect the position of the generated vertex can be effectively controlled, and the interference of the points far away from the generated vertex on the calculation results can be avoided. The calculation of the influence weight can better reflect the contribution of each point cloud data point in the process of generating vertex positioning, ensuring that when the weighted average calculation generates the vertex coordinates, the important neighborhood points will have a greater impact on the results, while the distant points are weakened. Through this weight distribution, the calculation of the generated vertex can more accurately reflect the local spatial distribution of the point cloud data, especially when the point cloud density is uneven or has a complex geometric shape, it can more stably generate a fine reconstructed surface. Overall, the reasonable distribution of the influence weight improves the accuracy of the interpolation and accelerates the calculation process, while avoiding the interference of irrelevant points, ensuring the high quality and accuracy of the generated vertices.

[0038] In this step, it is necessary to clearly define the influence range of the neighborhood points of the generated vertex and the weight distribution of the point cloud data points related to it.

[0039] For point (in , that is, generate vertices The influence radius of a point is defined as the neighborhood point set of the point, which is used to measure the scope of the point in the local geometric structure. The scope of influence, determine the point The distance to its farthest first-order neighbor is the point Maximum influence radius The formula is as follows: (6); in, Indicate point Its first-order neighboring points The Euclidean distance between .

[0040] Defining influence weights Let's quantify The impact on the intersection JD. The impact weight is related to the distance between the two points of the neighborhood point intersection and the impact range. The specific formula is as follows: (7); When the intersection point JD is at point Within the influence range, point The influence weight of is the difference between the influence radius and the distance between the intersection of the neighborhood points; if the intersection point JD is located at point If it is outside the influence range of , the point has no influence on the intersection point JD and its weight is zero.

[0041] Step 500: Based on the abnormal influence weight elimination strategy of the mean square error, screen and remove abnormal neighborhood points. This step effectively removes the negative impact of noise points and irregular points on the generated vertex interpolation, ensuring the stability and accuracy of the reconstruction results.

[0042] Outlier removal is to identify and remove those point cloud data points that have a negative impact on the interpolation results of the generated vertices through the mean square error. In this process, the mean and mean square error of all neighborhood points are first calculated, and then the ratio of the influence weight of each neighborhood point to the mean square error is used to determine whether it is an outlier. Outliers are usually caused by noise or measurement errors, and they may have a significant negative impact on the coordinate calculation of the generated vertices. Removing these outliers can effectively improve the smoothness and accuracy of the interpolation results and ensure that the reconstructed model is not disturbed by noise and errors. Through the MSE algorithm, the difference in the influence weight of each point in the point cloud data can be quantified, and then those points that deviate from the true geometric surface and affect the interpolation results can be identified. The practice of removing outliers can not only reduce the errors in the calculation, but also improve the stability of the entire reconstruction process. Especially when there are noise or outliers in the point cloud data, this process can significantly improve the quality of the final model. Through this outlier removal mechanism, the reconstruction results are more accurate and have higher geometric consistency, making the point cloud reconstruction process more robust.

[0043] Calculate the influence weight of each neighborhood point Then, use the mean square error To measure the difference in influence weights, the calculation formula is as follows: (8); in, To generate vertices The number of first-order neighboring points of ; is the average value of all neighborhood point weights, which is used as a reference value to measure the rationality of the weights. It provides a standard for weight rationality, which is used for subsequent weight elimination.

[0044] Set a threshold , which is used to measure the degree to which the weight deviates from the average value. If the influence weight of a neighborhood point The average of the impact weights The difference between times the mean square error, the weight is considered unreasonable and the point may be a noise point. Its influence on the neighborhood point is removed. The specific judgment criteria are as follows: (9); If a weight If the above conditions are met, the weight is considered abnormal and is removed in the subsequent fitting process. Once the unreasonable weights are removed, the local fitting surface can be recalculated based on the remaining reasonable weights. This process uses the remaining neighborhood points and their influence weights to refit the local surface of the point, which can more accurately reflect the generated vertices. The geometric relationship between the points and their neighborhood can improve the accuracy of the overall reconstruction.

[0045] Step 600: Based on the positions of the neighborhood points and their influence weights, the final coordinates of the generated vertices are calculated by weighted average method. This method effectively integrates the spatial information of the point cloud data, improves the accuracy of the generated vertices, and provides accurate vertex coordinates for the subsequent triangle mesh construction.

[0046] In the previous steps, outliers have been removed and the effective points that affect the generated vertices and the corresponding influence weights have been determined. In this step, the final coordinates of the generated vertices are calculated by the weighted average method. The calculation of each coordinate component takes into account the spatial position of the effective point and its influence weight information. Through weighted averaging, the position of the generated vertex can integrate the spatial information of the surrounding point cloud data points, reduce the influence of errors and noise, and ensure the accuracy of the generated vertex. The weighted average method can effectively integrate the information of multiple neighborhood points in the interpolation calculation, thereby improving the position accuracy and stability of the generated vertex. The resulting vertex coordinates can more accurately reflect the real surface of the point cloud data and provide more accurate vertex positions for subsequent mesh construction. Through this weighted average calculation, the reconstruction quality of the entire point cloud data has been significantly improved, and the generated triangular mesh is smoother, richer in details, and more in line with the actual geometric shape. This process makes the reconstruction of point cloud data show significant advantages in accuracy, robustness and detail retention, especially in complex geometric scenes, and can generate high-precision reconstruction models.

[0047] Generating Vertices The final position calculation of depends on the three vertices of the triangle in which it is located and the positions and influence weights of its first-order neighboring points. The calculated point positions will be located on the fitting surface of the triangle patch. Final location It can be calculated by formula (10): ; ; (10); in, represents the coordinates of the first-order neighborhood point, Indicate point The number of first-order neighboring points of .

[0048] The generated vertices are calculated by weighted average method The final position of can obtain a more accurate geometric description in the local area. When calculating the position of a point cloud, not only the original coordinates are considered, but also the geometric information of the neighborhood points. This method allows the shape of the local surface to better maintain the geometric characteristics of the original point cloud and avoid the error amplification problem caused by single-point calculation. Since the position of each point is obtained through weighted average optimization, the entire surface can maintain a high degree of smoothness. This method makes the fitting surface more consistent with the point cloud data. Since the weighted average method comprehensively considers the neighborhood points during calculation and filters out some possible abnormal points by influencing the weights, it can reduce the impact of noise on the final surface calculation to a certain extent, improve the stability of reconstruction, and make the reconstruction result closer to the real surface shape.

[0049] For the generated vertices, the coordinates will be solved according to the weighted average, and they will be connected according to the subdivided triangle topology to build a new mesh structure.

[0050] Table 1 Comparison of experimental results

[0051] Table 1 shows the comparison results of the method of the present invention and other methods using F-Score and CD-L1 as evaluation indicators. Other methods include: SPSR (Surface Piecewise Smooth Reconstruction), POCO (Point Cloud Optimization), NP (Neural Points), SAL (Shape Alignment Layer), SALD (Shape Alignment and Deformation), IGR (Implicit Geometric Regularization), DiGS (Differentiable Geometry Synthesis), SSP (Sparse Surface Prior). F-Score is the harmonic mean of precision and recall, which is used to comprehensively evaluate the accuracy and completeness of the reconstruction results. CD-L1 uses L1-norm to calculate the distance between two points, which is used to measure the average nearest neighbor distance between the reconstructed model and the true model.

[0052] Reference Figure 2 ,The experiment selected ten models with different complexity and rendered them respectively. ,The first and third rows show the rendering results of the original point cloud, ,and the second and fourth rows correspond to the rendering results after reconstruction ,by the method of the present invention. Figure 3Rendering before reconstruction, Figure 4 Rendering after reconstruction.

[0053] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A robust 3D reconstruction method based on weighted local surface approximation, characterized in that: The following steps are involved: Subdividing the original triangular mesh in the point cloud three-dimensional space into a plurality of small triangles; wherein the vertices of the plurality of small triangles include point cloud data points and generated vertices; Based on the weighted average method of triangle area, the normal vector of the generated vertex is calculated; based on the neighborhood points of the generated vertex, a fitting surface is constructed, and the intersection point between the motion trajectory of the generated vertex along the normal vector and the fitting surface is calculated; Calculate the distance between the neighborhood point of the generated vertex and the intersection point, and determine the influence weight of the neighborhood point of the generated vertex on the generated vertex according to the distance; screen and remove abnormal neighborhood points based on the abnormal influence weight elimination strategy of the mean square error; Based on the positions of neighborhood points and their influence weights, the final coordinates of the generated vertices are calculated by weighted averaging to generate a refined point cloud reconstruction model.

2. The robust 3D reconstruction method based on weighted local surface approximation according to claim 1, characterized in that: The method of subdividing the original triangular mesh in the point cloud three-dimensional space into multiple small triangles includes: evenly dividing each edge of the original triangle and generating new segmentation points on each edge; forming a new boundary relationship between the boundary of the original triangle and the new segmentation points, and then constructing a regular grid structure inside the original triangle, which is divided into multiple small triangles.

3. The robust 3D reconstruction method based on weighted local surface approximation according to claim 1, characterized in that: Based on the weighted average method of triangle area, the normal vector of the generated vertex is calculated, including: Get the normal vectors of the three vertices of the original triangle; Determine the three small triangles formed by the generated vertices and obtain the areas of the three sub-triangles; Based on the normal vectors of the three vertices of the original triangle and the areas of the three sub-triangles, a vertex normal vector is generated by weighted calculation: and the generated vertex normal vector is normalized to obtain the normalized generated vertex normal vector.

4. The robust 3D reconstruction method based on weighted local surface approximation according to claim 1, characterized in that: The step of constructing a fitting surface based on the neighborhood points of the generated vertex and calculating the intersection point between the motion trajectory of the generated vertex along the normal vector and the fitting surface specifically includes: Construct a set of neighborhood points for generating vertices; for each neighborhood point in the set of neighborhood points, construct a fitting surface equation, and represent the motion trajectory of the generated vertex along the normal vector through parameterization; The motion trajectory of the generated vertex is substituted into the surface equation, the intersection position of the motion trajectory of the generated vertex along the normal vector and the fitting surface is calculated, and the position of the generated vertex on the fitting surface is determined.

5. The robust 3D reconstruction method based on weighted local surface approximation according to claim 4, characterized in that: The calculating the distance between the neighborhood point of the generated vertex and the intersection point, and determining the influence weight of the neighborhood point of the generated vertex on the generated vertex according to the distance specifically includes: Calculate the influence radius of the neighborhood point of the generated vertex, where the influence radius is the distance from the neighborhood point of the generated vertex to its farthest first-order neighbor point; When the generated vertex is within the influence radius of the generated vertex's neighborhood point, the influence weight of the generated vertex's neighborhood point is the difference between the influence radius and the distance between the two points; if the generated vertex is outside the influence range of the generated vertex's neighborhood point, the influence weight is zero.

6. The robust 3D reconstruction method based on weighted local surface approximation according to claim 5, characterized in that: The abnormal influence weight elimination strategy based on mean square error screens and removes abnormal neighborhood points, specifically including: Calculate the average value of the influence weights of the neighborhood points, and calculate the mean square error based on the average value of the influence weights of the neighborhood points and the influence weights of the neighborhood points; Preset Threshold , if the difference between the influence weight of the generated vertex's neighborhood points and the average influence weight is greater than times the mean square error, it is considered that the influence weight of the neighborhood points of the generated vertex is unreasonable and the neighborhood points are removed.

7. The robust 3D reconstruction method based on weighted local surface approximation according to claim 1, characterized in that: The method of calculating the final coordinates of the vertex based on the positions of the neighborhood points and their influence weights by weighted average method specifically includes: Generate the final position of the vertex : ； ； ； in, Represents the coordinates of the neighborhood points; Indicates the number of neighboring points; Represents the influence weight of each neighborhood point.

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