Robust 3D Reconstruction Method Based on Weighted Local Surface Approximation

Abstract

The present 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 surface approximation. The method includes: First, preprocess the input three-dimensional point cloud data, construct the neighborhood relationship, and fit the local surface in the local neighborhood of each point by the least squares method; Second, calculate its influence weight based on the neighborhood information of the point, and use the weighted average method to calculate the position of the final surface point to optimize the geometric accuracy of the local surface; Subsequently, use the outlier weight rejection strategy based on the mean square error to screen and remove the outlier points, reduce the noise interference, and improve the stability and robustness of the surface reconstruction; Finally, improve the accuracy of the overall surface fitting by weighted average, so that the reconstructed surface can fit the original point cloud data more accurately, and effectively improve the reconstruction accuracy of the point cloud data.

Description

Technical Field

[0001] The present 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 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, and plays an important role in multiple applications such as autonomous driving, virtual reality, 3D printing, cultural heritage protection, industrial inspection, and medical imaging. Point cloud data is usually obtained by lidar (LiDAR), structured light scanning, stereo vision systems, or depth cameras. Its essence is discrete sampled three-dimensional coordinate points used to describe the geometric structure of an object. However, due to factors such as measurement errors, environmental noise, point cloud sparsity, and occlusion, how to accurately reconstruct the three-dimensional surface 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 three-dimensional reconstruction methods mainly rely on geometric modeling and optimization techniques to generate a continuous and smooth surface by constructing an explicit mathematical model to fit the point cloud data. In addition, global fitting methods aim to fit the surface of the point cloud data through an accurate mathematical model. These methods can handle 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 lead to an unsmooth or self-intersecting generated mesh. Second, point cloud data in reality often has uneven distribution, especially in areas with complex geometric shapes or rich details. Traditional meshing methods are difficult to accurately capture local features. Summary of the Invention

[0004] 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:

[0006] A robust three-dimensional reconstruction method based on weighted local surface approximation, comprising the following steps:

[0007] Subdivide the original triangular mesh in the three-dimensional space of the point cloud into multiple small triangles; wherein, the vertices of the multiple small triangles include point cloud data points and generated vertices;

[0008] Based on the weighted average method of triangle area, calculate the normal vector of the generated vertex; construct a fitting surface based on the neighborhood points of the generated vertex, and calculate the intersection point between the movement trajectory of the generated vertex along the normal vector and the fitting surface;

[0009] Calculate the distances between the neighborhood points of the generated vertex and the intersection point, and determine the influence weights of the neighborhood points of the generated vertex on the generated vertex according to the distances; based on the abnormal influence weight elimination strategy of the mean square error, screen and remove the abnormal neighborhood points;

[0010] Based on the positions of the neighborhood points and their influence weights, calculate the final coordinates of the generated vertex by the weighted average method, and thus generate a refined point cloud reconstruction model.

[0011] Further, subdividing the original triangular mesh in the three-dimensional space of the point cloud into multiple small triangles includes: evenly dividing each side of the original triangle, and generating new segmentation points on each side; forming new boundary relationships between the boundaries of the original triangle and the new segmentation points, and then constructing a regular grid structure inside the original triangle and dividing it into multiple small triangles.

[0012] Further, based on the weighted average method of the triangle area, calculate the normal vector of the generated vertex, specifically including:

[0013] Obtain the normal vectors of the three vertices of the original triangle;

[0014] Determine the three small triangles formed by the generated vertex, and obtain the areas of the three sub-triangles;

[0015] Based on the normal vectors of the three vertices of the original triangle and the areas of the three sub-triangles, calculate the normal vector of the generated vertex by weighted calculation: and perform normalization processing on the normal vector of the generated vertex to obtain the normalized normal vector of the generated vertex.

[0016] Further, constructing a fitting surface based on the neighborhood points of the generated vertex, and calculating the intersection point between the movement trajectory of the generated vertex along the normal vector and the fitting surface, specifically including:

[0017] Construct a set of neighborhood points of the generated vertex; for each neighborhood point in the set of neighborhood points, construct a fitting surface equation and parameterize the movement trajectory of the generated vertex along the normal vector;

[0018] Substitute the movement trajectory of the generated vertex into the surface equation, calculate the intersection point position between the movement trajectory of the generated vertex along the normal vector and the fitting surface, and determine the position of the generated vertex on the fitting surface.

[0019] Further, the calculating the distances between the neighborhood points of the generated vertex and the intersection point, and determining the influence weights of the neighborhood points of the generated vertex on the generated vertex according to the distances specifically includes:

[0020] Calculate the influence radius of the neighborhood points of the generated vertex, and the influence radius is the distance from the neighborhood points of the generated vertex to its farthest first-order neighborhood point;

[0021] When the intersection point is within the influence radius of the neighborhood points of the generated vertex, the influence weight of the neighborhood points of the generated vertex is the difference between the influence radius and the distance between the two points; when the intersection point is outside the influence range of the neighborhood points of the generated vertex, the influence weight is zero.

[0022] Further, the abnormal influence weight elimination strategy based on the mean square error screens and removes abnormal neighborhood points, specifically including:

[0023] 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;

[0024] Preset threshold , if the difference between the influence weight of the neighborhood points of the generated vertex and the average value of the influence weights 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.

[0025] Further, based on the position of the neighborhood points and their influence weights, the final coordinates of the generated vertex are calculated by the weighted average method, specifically including:

[0026] The final position of the generated vertex :

[0027] ;

[0028] ;

[0029] ;

[0030] Among them, represents the coordinates of the neighborhood points; represents the number of neighborhood points; represents the influence weight of each neighborhood point.

[0031] Compared with the prior art, the present invention has the following technical effects:

[0032] (1) The present invention proposes a robust three-dimensional reconstruction method based on weighted local surface approximation, which can effectively reduce the error accumulation in the global fitting method, improve the reconstruction accuracy of the local surface, and make it more suitable for the point cloud data of complex surface structures.

[0033] (2) The present invention further optimizes the surface structure through the refined reconstructed fitting surface, so that the reconstruction result more accurately approximates the true three-dimensional shape, and alleviates the problem of local structure missing caused by sparse data sampling or point cloud holes to a certain extent.

[0034] (3) The present invention proposes an unreasonable weight elimination mechanism based on mean square error screening. When calculating the point cloud weight, it adaptively eliminates abnormal points, reduces the interference of noise points on the surface fitting result, thereby improving the stability of reconstruction and ensuring the reliability of surface reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0036] Figure 1 It is a flow chart of the present invention;

[0037] Figure 2 It shows the rendering result of the original point cloud and the rendering result diagram after reconstruction by the method of the present invention;

[0038] Figure 3 It is the rendering result diagram before reconstruction;

[0039] Figure 4 It is the rendering result diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following will, in combination with the drawings and preferred embodiments, detail the specific implementation manners, structures, features and their effects of the technical solutions proposed according to the present invention. The specific features, structures or characteristics in one or more embodiments can be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs.

[0041] This embodiment starts from the complex geometric features of point cloud data and proposes a robust three-dimensional reconstruction method based on weighted local surface approximation. This method enhances the reconstruction accuracy through the weighted local surface approximation method combined with local fitting optimization strategies, weighted neighborhood point influence calculation, and abnormal point elimination mechanisms. Combining with the weighted calculation of normal vectors ensures that the reconstructed surface of the point cloud data is smoother and conforms to the actual geometric shape. On this basis, the normal vector weighting method is introduced, and the normal vectors are weighted according to the area of each small triangle, so that the normal vectors can smoothly transition in the subdivided grid, avoiding the problem of inconsistent normal vectors caused by local errors, thereby improving the accuracy and robustness of the reconstructed model.

[0042] In addition, to better handle the local complexity and geometric details in point cloud data, this embodiment proposes a calculation method for the intersection points of the fitted surface and the generated vertices. This method further precisely locates the generated vertices by solving the intersection points of the generated vertices and the point cloud data point fitted surface. This method can effectively avoid the problem of the generated vertices deviating from the true geometric surface and improve the accuracy of point cloud reconstruction. To handle the noise and irregularities in point cloud data, an outlier removal mechanism is also designed to identify and remove outliers using the mean square error algorithm, thereby ensuring that each point in the reconstruction process makes a positive contribution to the precise positioning of the generated vertices.

[0043] By combining techniques such as triangle subdivision, normal vector weighting, and intersection calculation of the fitted surface, a high-precision and robust point cloud reconstruction method is proposed. This method can not only handle point clouds with complex shapes and large-scale data but also cope with point cloud datasets with high noise, significantly improving the accuracy and stability of the point cloud reconstruction model. After a large number of experimental verifications, this embodiment improves the accuracy of point cloud data while greatly enhancing the robustness of the algorithm and providing an effective solution for the refined reconstruction of point cloud data.

[0044] In one embodiment of the present invention, referring to Figure 1 , a robust three-dimensional reconstruction method for weighted local surface approximation is provided, including the following steps:

[0045] Step 100: Subdivide the original triangular mesh in the three-dimensional space of the point cloud into multiple small triangles; among them, the vertices of the multiple small triangles include point cloud data points and generated vertices;

[0046] Step 200: Calculate the normal vector of the generated vertices based on the weighted average method of triangle areas;

[0047] Step 300: Construct a fitted surface based on the neighborhood points of the generated vertices and calculate the intersection points between the movement trajectory of the generated vertices along the normal vector and the fitted surface;

[0048] Step 400: Calculate the distances between the neighborhood points of the generated vertices and the intersection points, and determine the influence weights of the neighborhood points of the generated vertices on the generated vertices according to the distances;

[0049] Step 500: Screen and remove abnormal neighborhood points based on the outlier influence weight removal strategy of the mean square error;

[0050] Step 600: Calculate the final coordinates of the generated vertices by the weighted average method based on the positions of the neighborhood points and their influence weights, and generate a refined point cloud reconstruction model.

[0051] The above steps will be detailed as follows:

[0052] Step 100: Connect the 3D point cloud data into a triangular mesh, namely the original triangular mesh, and subdivide the original triangular mesh into multiple small triangles. Among them, the vertices of the multiple 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.

[0053] Connect the discrete point set into a triangular mesh, namely the original triangular mesh, through a triangulation algorithm, and subdivide the original triangular mesh. First, evenly divide each edge of the original triangle. Specifically, divide each edge of the original triangle into five equal parts according to a ratio, thereby generating four new division points on each edge; next, by connecting the vertices, further divide the interior of the original triangle into 25 small triangles. Specifically, new boundary relationships are formed between the boundary of the original triangle and the newly added division points, and then a regular mesh structure is constructed inside the original triangle. Through this operation, each division point on the three edges of the original triangle will form new connection relationships with other division points and the original vertices of the triangle, and form a vertex set containing 21 vertices. These vertices are jointly composed of the three original point cloud data points of the original triangle, the sub-nodes generated by the uniform division of the boundary, and the new vertices generated after the division points are connected through topological relationships. Among them, 21 vertices include 3 original point cloud data points and 18 generated vertices.

[0054] The subdivided mesh has a higher resolution and a finer structure, and can better capture the local geometric details in the point cloud data. The subdivision operation increases the density of the mesh, enabling the surface shape to be more accurately restored in subsequent interpolation and reconstruction processes. By increasing the number of small triangles, a more regular mesh can be obtained, avoiding the geometric irregularities that the original triangular mesh may bring. This process enables subsequent steps such as normal vector calculation, interpolation, and outlier removal to be carried out on a finer and more uniform mesh basis, thus ensuring the accuracy and robustness of the reconstruction result. Subdivision not only optimizes the local calculation accuracy but also provides a more suitable mesh structure for the processing of complex geometric shapes, avoiding error accumulation caused by a rough mesh.

[0055] Step 200: Calculate the normal vector of the generated vertices based on the weighted average method of triangle area. The normal vector of each small triangle is given different weights according to its area, and finally a smooth normal vector of the generated vertices is obtained. This method ensures the stability of the normal vector and avoids the influence of local errors on the reconstruction result.

[0056] The calculation of generating vertex normal vectors adopts a weighted average method based on triangle area. First, determine the three small triangles formed by the generating vertex, and calculate the normal vector of the generating vertex according to the area and normal vector direction of each small triangle. The normal vectors of each small triangle are given different weights according to their areas, and the final normal vector of the generating vertex is obtained through the weighted average method. The advantage of doing 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. Since there may be noise and irregularities in the point cloud data, directly using the normal vector of a single triangle may lead to uneven calculation results. Therefore, by weighting and averaging the normal vectors of multiple triangles, the normal vectors are effectively smoothed and the consistency of the geometric surface is ensured. The normal vectors calculated by this method can better reflect the geometric structure changes around the generating vertex, thus providing more stable and consistent direction information for subsequent interpolation calculations. Generally speaking, this calculation method of weighted normal vectors improves the accuracy of the normal vectors while ensuring the smooth transition of the surface and geometric consistency.

[0057] Specifically, let the three vertices of the original triangle be , , , and the normal vectors of the three vertices be , , ; and the generating vertex is located at a certain position within the plane of the triangle . The original triangle is divided into three sub-triangles: , , , corresponding to the areas , , .

[0058] By calculating the vertex normal vector through weighting, the normal vector of the generating vertex is as shown in formula (1):

[0059] (1);

[0060] where , , are the normal vector components of the generating vertex in the , , directions respectively.

[0061] Furthermore, normalization processing is carried out to ensure the unity of the direction and scale of the calculated normal vectors:

[0062] (2);

[0063] In the above formula, represents the generated vertex after normalization of the normal vector.

[0064] Step 300: Construct a fitting surface based on the neighborhood points of the generated vertex, and calculate the intersection point between the movement 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 surface of the point cloud data, thereby improving the accuracy and geometric consistency of point cloud reconstruction.

[0065] The present invention constructs a quadratic polynomial fitting surface for the neighborhood points and parameterizes the movement trajectory of the generated vertex along the normal vector. By substituting the movement trajectory of the generated vertex along the normal vector into the equation of the fitting surface, the intersection point of the generated vertex along the normal vector direction and the fitting surface is calculated. The quadratic polynomial fitting can effectively capture the local geometric features of the point cloud data and provide accurate position correction for the generated vertex. In this way, the generated vertex can be accurately mapped onto the fitting surface, avoiding error accumulation caused by surface irregularities. The fitting surface can not only improve the positioning accuracy of the generated vertex, but also better adapt to the complex shapes and local variations in the point cloud data, improving the accuracy and geometric consistency of the reconstructed model. In addition, the parametric equation provides a flexible description of the movement, enabling the method to be optimized according to different data distributions, improving the adaptability and computational efficiency of the algorithm.

[0066] In this step, for the original triangle vertices , , in the point cloud data and their first-order neighborhood point sets, calculate the intersection points between the movement trajectory of the generated vertex along the normal vector and the fitting surfaces where these points are located.

[0067] First, construct the neighborhood point set. For the generated vertex , its neighborhood point set is:

[0068] , where is the point , , of the first-order neighborhood points.

[0069] For each first-order neighborhood point in , construct a fitting surface in the form of a quadratic polynomial for them. The polynomial equation is as shown in formula (3):

[0070] (3);

[0071] It is necessary to solve the generated vertex The intersection point between the movement trajectory along the normal vector and the fitting surface.

[0072] Assumed generated vertex The coordinates are , and the generated vertex is represented in parametric form The movement along the normal vector direction. Specifically, the generated vertex The movement trajectory along the normal vector can be expressed by formula (4):

[0073] (4);

[0074] Substitute the above parametric equation into the polynomial equation formula (3) of the fitting surface, and an equation about the parameter can be obtained:

[0075] (5);

[0076] Solve this equation to obtain the parameter . Since the positive direction along the normal vector is concerned, the positive solution of is selected as the result, so the specific coordinates JD of the intersection point can be calculated , thereby determining the generated vertex The intersection point between the movement trajectory along the normal vector and the fitting surface, and the position of the generated vertex on the fitting surface is determined by the intersection point.

[0077] Step 400: Calculate the distance between the neighborhood points of the generated vertex and the intersection point obtained in step 300, and determine the influence weight of the neighborhood points of the generated vertex on the generated vertex according to the distance. By reasonably allocating the 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.

[0078] First, calculate the Euclidean distance between the neighborhood points of the generated vertex and the intersection points obtained in step 300, and then determine its influence range on the generated vertex. Based on these distances, a weight is assigned to each point cloud data point. The point cloud data points closer to the generated vertex have larger weights, while the points far from the generated vertex have less influence on the generated vertex. By this method, the point cloud data points that affect the position of the generated vertex can be effectively controlled, and the interference of points far from the generated vertex on the calculation results is 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. When calculating the coordinates of the generated vertex by weighted average, important neighborhood points will have a greater impact on the result, while the far-away points are weakened. Through this weight assignment, the calculation of the generated vertex can more accurately reflect the local spatial distribution of the point cloud data. Especially in the case of uneven point cloud density or complex geometric shapes, a fine reconstruction surface can be generated more stably. Generally speaking, the reasonable assignment of the influence weight improves the accuracy of interpolation, accelerates the calculation process, avoids the interference of irrelevant points, and ensures the high quality and accuracy of the generated vertex.

[0079] In this step, it is necessary to clarify the influence range of the neighborhood points of the generated vertex and the weight distribution of the related point cloud data points.

[0080] For point (where , that is, the set of neighborhood points of the generated vertex ), first define the influence radius of this point to measure its role range in the local geometric structure. Among them, the influence radius can be understood as the influence range of point . Determine that the distance from point to its farthest first-order neighborhood point is the maximum influence radius of point . The formula is shown as follows:

[0081] (6);

[0082] Among them, represents the Euclidean distance between point and its first-order neighborhood point .

[0083] Define the influence weight to quantify the influence of point on the intersection point JD. This influence weight is related to the distance between these two points of the neighborhood point intersection and the influence range. The specific formula is shown as follows:

[0084] (7);

[0085] When the intersection point JD is within the influence range of point , point The influence weight is the difference between the influence radius and the distance of the intersection point of the neighborhood points; if the intersection point JD is outside the influence range of point , then this point has no influence on the intersection point JD, and the weight is zero.

[0086] Step 500: Based on the abnormal influence weight elimination strategy of mean square error, screen and remove abnormal neighborhood points. This step effectively eliminates the negative impact of noise points and irregular points on the generation of vertex interpolation, ensuring the stability and accuracy of the reconstruction result.

[0087] Abnormal point elimination is to identify and eliminate the point cloud data points that have an adverse effect on the generation of vertex interpolation results through mean square error. In this process, first calculate the mean and mean square error of all neighborhood points, and then judge whether it is an abnormal point according to the ratio of the influence weight of each neighborhood point to the mean square error. Abnormal points are usually caused by noise or measurement errors, and they may have a greater negative impact on the coordinate calculation of the generated vertices. Eliminating these abnormal points can effectively improve the smoothness and accuracy of the interpolation result, ensuring that the reconstruction 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 the points that deviate from the true geometric surface and affect the interpolation result can be identified. The practice of eliminating abnormal points can not only reduce the error in the calculation, but also improve the stability of the entire reconstruction process. Especially when there is noise or outliers in the point cloud data, this process can significantly improve the quality of the final model. Through this abnormal point elimination mechanism, the reconstruction result is more accurate and has higher geometric consistency, making the point cloud reconstruction process more robust.

[0088] Calculate the influence weight of each neighborhood point After that, use the mean square error to measure the degree of difference in influence weights. The calculation formula is as follows:

[0089] (8);

[0090] where is the number of first-order neighborhood points of the generated vertex ; is the average value of the weights of all neighborhood points, used as a reference value to measure the rationality of the weights. The calculated by the above formula provides a standard for the rationality of the weights for subsequent influence weight elimination.

[0091] Set a threshold , used to measure the degree of deviation of the weight from the average value. If the influence weight of a certain neighborhood point and the average value of the influence weights differ by more than If the mean square error is several times higher, it is considered that the weight is unreasonable and the point may be a noise point. Then, the influence weight of this point on the neighboring points is removed. The specific judgment criteria are as follows:

[0092] (9);

[0093] If a certain weight meets the above conditions, then this weight is considered abnormal and will be removed during 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 neighboring points and their influence weights to refit the local surface of the point, which can more accurately reflect the geometric relationship between the generated vertex and its neighboring points, thereby improving the accuracy of the overall reconstruction.

[0094] Step 600: Calculate the final coordinates of the generated vertex based on the positions of the neighboring points and their influence weights through the weighted average method. This method effectively integrates the spatial information of the point cloud data, improves the accuracy of the generated vertex, and provides accurate vertex coordinates for the subsequent triangle mesh construction.

[0095] In the previous steps, the abnormal points have been removed and the effective points and corresponding influence weights affecting the generated vertex have been determined. In this step, the final coordinates of the generated vertex are calculated through the weighted average method. The calculation of each coordinate component takes into account the spatial positions of the effective points and their influence weight information. Through weighted average, the position of the generated vertex can synthesize 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 neighboring points in the interpolation calculation, thereby improving the position accuracy and stability of the generated vertex. The finally obtained coordinates of the generated vertex can more accurately reflect the true surface of the point cloud data and provide a more accurate vertex position for the subsequent mesh construction. Through this weighted average calculation, the reconstruction quality of the entire point cloud data has been significantly improved, and the generated triangle mesh is smoother, more detailed, and more in line with the actual geometric shape. This process enables the reconstruction of the point cloud data to show significant advantages in terms of accuracy, robustness, and detail retention, especially in complex geometric scenarios, where a high-precision reconstruction model can be generated.

[0096] The generated vertex 's final position calculation depends on the positions and influence weights of the three vertices of the triangle it belongs to and its first-order neighboring points. The calculated point positions will be on the fitting surface of this triangular patch. The generated vertex 's final position can be calculated by formula (10):

[0097] ;

[0098] ;

[0099] (10);

[0100] Among them, represents the coordinates of the first-order neighborhood point, represents the point the number of first-order neighborhood points.

[0101] The final position of the vertex is calculated and generated by the weighted average method, and a more accurate geometric description can be obtained within the local area. When calculating and generating the position of the vertex , not only its original coordinates are considered, but also the geometric information of the neighborhood points is combined. This method enables the shape of the local surface to better maintain the geometric characteristics of the original point cloud and avoids the problem of error magnification caused by single-point calculation. Since the position of each point is optimized by weighted average, the entire surface can maintain a high degree of smoothness, and this method makes the fitted surface more conform to the point cloud data. Since the weighted average method comprehensively considers the neighborhood points during calculation and filters out some possible outliers through the influence weights, it can reduce the influence of noise on the final surface calculation to a certain extent, improve the stability of the reconstruction, and make the reconstruction result closer to the true surface shape.

[0102] For the generated vertices, the coordinates will be solved according to the weighted average, and they will be connected according to the subdivided triangular topological structure to construct a new mesh structure.

[0103] Table 1 Comparison of experimental results

[0104]

[0105] Table 1 shows the comparison results of the method of the present invention and other methods with F-Score and CD-L1 as evaluation indicators. Other methods include: SPSR (Surface Piecewise Smooth Reconstruction), POCO (Point Cloud Optimization), N-P (Neural Points), SAL (ShapeAlignment Layer), SALD (Shape Alignment and Deformation), IGR (Implicit Geometric Regularization), DiGS (DifferentiableGeometry Synthesis), SSP (Sparse Surface Prior). F-Score is the harmonic mean of Precision and Recall, which is used to comprehensively evaluate the accuracy and integrity of the reconstruction results. CD-L1 calculates the distance between two points using the L1-norm, which is used to measure the average nearest neighbor distance between the reconstructed model and the real model.

[0106] Referring to Figure 2 , ten models with different complexities were selected for the experiment and rendered respectively. The first row and the third row show the rendering results of the original point cloud, and the second row and the fourth row correspond to the rendering results after reconstruction by the method of the present invention. Figure 3 Rendering before reconstruction, Figure 4 Rendering after reconstruction.

[0107] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A robust three-dimensional reconstruction method based on weighted local surface approximation, characterized in that Including the following steps: Subdivide the original triangular mesh in the three-dimensional point cloud space into multiple small triangles; among them, the vertices of the multiple small triangles include point cloud data points and generated vertices; Based on the weighted average method of triangle area, calculate the normal vector of the generated vertex; construct a fitting surface based on the neighborhood points of the generated vertex, and calculate the intersection point between the movement trajectory of the generated vertex along the normal vector and the fitting surface; Calculate the distance between the neighborhood points of the generated vertex and the intersection point, and determine the influence weight of the neighborhood points of the generated vertex on the generated vertex according to the distance, including: calculating the influence radius of the neighborhood points of the generated vertex, and the influence radius is the distance from the neighborhood points of the generated vertex to its farthest first-order neighborhood point; when the intersection point is within the influence radius of the neighborhood points of the generated vertex, the influence weight of the neighborhood points of the generated vertex is the difference between the influence radius and the distance between the two points; when the intersection point is outside the influence range of the neighborhood points of the generated vertex, the influence weight is zero; Based on the abnormal influence weight elimination strategy of mean square error, screen and remove abnormal neighborhood points; Based on the position of the neighborhood points and their influence weights, calculate the final coordinates of the generated vertex by the weighted average method, and thus generate a refined point cloud reconstruction model.

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

3. A robust three-dimensional reconstruction method based on weighted local surface approximation according to claim 1, characterized in that Based on the weighted average method of triangle area, calculate the normal vector of the generated vertex, specifically including: Obtain the normal vectors of the three vertices of the original triangle; Determine the three small triangles formed by the generated vertex, 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, calculate the normal vector of the generated vertex by weighted calculation: and normalize the normal vector of the generated vertex to obtain the normalized normal vector of the generated vertex.

4. A robust three-dimensional reconstruction method based on weighted local surface approximation according to claim 1, characterized in that The construction of a fitting surface based on the neighborhood points of the generated vertex and the calculation of the intersection point between the movement trajectory of the generated vertex along the normal vector and the fitting surface specifically include: Construct a set of neighborhood points of the generated vertex; for each neighborhood point in the set of neighborhood points, construct a fitting surface equation, and parameterize the movement trajectory of the generated vertex along the normal vector; Substitute the movement trajectory of the generated vertex into the surface equation, calculate the intersection point position between the movement trajectory of the generated vertex along the normal vector and the fitting surface, and determine the position of the generated vertex on the fitting surface.

5. A robust three-dimensional reconstruction method based on weighted local surface approximation according to claim 1, characterized in that, The abnormal influence weight elimination strategy based on mean square error, screening and removing abnormal neighborhood points specifically includes: Calculate the average value of the neighborhood point influence weights, and calculate the mean square error based on the average value of the neighborhood point influence weights and the neighborhood point influence weights; Preset threshold , if the difference between the influence weight of the neighborhood points of the generated vertex and the average value of the influence weights 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.

6. A robust three-dimensional reconstruction method based on weighted local surface approximation according to claim 1, characterized in that Based on the position of the neighborhood points and their influence weights, calculate the final coordinates of the generated vertex by the weighted average method, specifically including: Generate the final position of the vertex : ； ； ； Among them, represents the coordinates of the neighborhood points; represents the number of neighborhood points; represents the influence weight of each neighborhood point.

Images