A method and system for constructing a mesh model based on the spatial parameters of a 3D Gaussian surface model.

Abstract

This invention discloses a method and system for constructing a mesh model based on the spatial parameters of a 3D Gaussian surface model, belonging to the field of 3D reconstruction technology. It includes at least the following steps: establishing an initial 3D Gaussian elliptical surface model based on the sparse point cloud of the reconstructed object; constructing a local implicit function field for each Gaussian elliptical surface model; for a single Gaussian elliptical surface model, the implicit function value of a vertex is the signed distance from the voxel vertex to the corresponding Gaussian elliptical surface; performing global weighted fusion based on the local implicit function field of the current Gaussian elliptical surface model; and extracting 0-isosurfaces using the Marching Cubes algorithm based on the vertex function values ​​of the global voxel field, thereby constructing the mesh model of the reconstructed object. This invention establishes a voxel field consistent with the distribution of the 3D Gaussian elliptical surface through the 3D spatial parameters of the 3D Gaussian elliptical surface model, enabling accurate and unobstructed surface representation and achieving high-precision 3D reconstruction of the mesh model.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional reconstruction technology, specifically relating to a method and system for constructing a mesh model based on the spatial parameters of a three-dimensional Gaussian surface model. Background Technology

[0002] Mesh reconstruction technology can generate spatial representations of points, lines, and surfaces with topological relationships, and has significant application value in spatial mapping and reconstruction tasks. 3D Gaussian sputtering technology can achieve high optimization quality and efficiency in new perspective synthesis tasks, and its optimization results can simultaneously serve 3D mesh reconstruction. However, existing technologies still face some challenges. First, the scene representation ellipsoid used in 3D Gaussian sputtering is difficult to define accurately for its normal direction and depth values, making it difficult to obtain a Gaussian ellipsoid model that geometrically fits the scene surface accurately during scene optimization and rendering. Second, although existing methods using 3D Gaussian Elliptical Surface Models (2DGS) can obtain a Gaussian elliptical surface that fits the scene relatively accurately during optimization, the process of TSDF mesh reconstruction using this model relies on 2D depth information to construct a signed function field. Multiple projection processes lead to information loss, making the mesh reconstruction quality directly dependent on the density and richness of the viewpoints, requiring a high degree of precision in viewpoint distribution. Moreover, based solely on 2D information, the TSDF method also has poor ability to handle the structural consistency of multi-view scenes with occlusion phenomena. Furthermore, the number of implicit function value fusions based on TSDF depends only on the number of images and is highly sensitive to depth noise. Depth values ​​rendered using Gaussian sputtering are affected not only by the position of the Gaussian surface itself but also by distortion due to differences in Gaussian opacity, leading to significant discrepancies between the constructed implicit function field and the real scene surface. Some existing techniques offer methods for directly optimizing the extracted mesh model vertices, but this results in long optimization times and high computational demands. Currently, most mesh extraction methods based on 3D Gaussian sputtering rely entirely on the projected information, failing to fully utilize the spatial characteristics of the Gaussian (surface) model itself as an explicit 3D scene representation.

[0003] To fully utilize the 3D information of the 3D Gaussian elliptical surface model, such as center coordinates and normals, overcome the problems widely encountered in mesh 3D reconstruction, and improve the reconstruction accuracy of 3D network models, further exploration of more reliable technologies is still needed in this field. Summary of the Invention

[0004] The purpose of this invention is to directly construct a spatial voxel implicit function field from a 3D Gaussian elliptical surface model, achieving high-precision 3D mesh model extraction and overcoming the technical shortcomings of existing technologies that construct voxel fields based on 2D information. The mesh model reconstruction method provided by this invention generates an initial 3D Gaussian elliptical surface model from sparse point clouds; then, it directly establishes a voxel field with a distribution consistent with the 3D Gaussian elliptical surface using the 3D spatial parameters of the 3D Gaussian elliptical surface model. This voxel field is used to accurately and without obstruction represent the surface, thus achieving a significant leap in thinking. This is significantly different from existing surface extraction methods based on 3D Gaussian elliptical surface models, which all utilize the TSDF method, obtaining depth values ​​through 2D rendering before establishing the voxel field representing the surface.

[0005] Therefore, the present invention provides the following technical solution:

[0006] On the one hand, the present invention provides a mesh model construction method based on the spatial parameters of a three-dimensional Gaussian surface model, which includes at least the following steps:

[0007] Step 1: Based on the sparse point cloud of the reconstructed object, establish an initial 3D Gaussian elliptical surface model. Each point cloud corresponds to a Gaussian elliptical surface model, and obtain the spatial parameters of the Gaussian elliptical surface model.

[0008] Step 2: Construct the local implicit function field for each Gaussian elliptical surface model;

[0009] For a single Gaussian elliptical surface model, a local implicit function field of the neighborhood voxel space is constructed based on the spatial parameters of the Gaussian elliptical surface model to obtain the search range of the voxel vertex and the implicit function value of the voxel vertex. The implicit function value of the voxel vertex is the signed distance from the voxel vertex to the corresponding Gaussian elliptical surface.

[0010] Step 3: Perform global weighted fusion of the local implicit function fields based on the current Gaussian elliptical surface model; wherein, the local voxel vertices are mapped to the global voxel vertices, and the implicit function values ​​of the global voxel vertices are fused to obtain the vertex function values ​​of the global voxel field;

[0011] Step 4: Based on the vertex function values ​​of the global voxel field, use the MarchingCubes algorithm based on voxel cubes to extract the 0 isosurface, and then construct the mesh model of the reconstructed object.

[0012] In some implementations, step 1 involves using the sparse point cloud corresponding to multi-view images to establish an initial 3D Gaussian elliptical surface model. After constructing the initial 3D Gaussian elliptical surface model, the method further performs the following: synthesizing new perspectives using the photometric and geometric information from the multi-view RGB images, thereby optimizing the initial model. Specifically:

[0013] Photometric error between blended rendered image and multi-view image Depth value error Depth distortion item Normal depth consistency distortion term Construct the error objective function;

[0014] Then, based on the error objective function, the spatial parameters of the initial three-dimensional Gaussian elliptical surface model are updated using the gradient descent method.

[0015] Optionally, after constructing the initial three-dimensional Gaussian elliptical surface model in step 1, the method further includes: for the Gaussian elliptical surface model located in the planar region, filling the gap between the Gaussian elliptical surface model and its neighboring Gaussian elliptical surface models in three-dimensional space.

[0016] For any two Gaussian elliptical surface models Between these points, the spatial parameters of the newly filled Gaussian elliptical surface model satisfy the following requirements:

[0017] The center position of the new Gaussian elliptic surface model Distance between two principal axes in space , The nearest point, and For two original Gaussian elliptic surface models Fill the main axis;

[0018] Normal of the new Gaussian elliptical surface model From the central position To two original Gaussian elliptic surface models The cross product of vectors is obtained;

[0019] The semi-axis of the new Gaussian elliptic surface model Central position To one of the original Gaussian elliptic surface models or The direction of the other half axis Then by and The cross product is obtained;

[0020] The scale of the semi-axis of the new Gaussian elliptical surface model: from the new Gaussian elliptical surface model to the original Gaussian elliptical surface model. The distance is determined;

[0021] Opacity and color: Both are based on the original Gaussian elliptical surface model. The mean of the corresponding parameters.

[0022] Optionally, by taking the center position and normal of each Gaussian elliptical surface and its neighboring Gaussian elliptical surfaces, it is jointly determined whether the corresponding Gaussian elliptical surface model is within a planar region, specifically as follows:

[0023] For Gaussian elliptical surface model k nearest neighbor Gaussian elliptic surface model If all conditions are met Then consider the Gaussian elliptical surface model It is located in a planar region; otherwise, it appears as a Gaussian elliptical surface model. Not located in a planar area;

[0024] in, , Gaussian elliptic surface model The center position and the direction of the normal. , These are the nearest neighbor Gaussian elliptical surface models. The center position and normal direction; , , These are all set empirical thresholds.

[0025] Optionally, in step 2, for a single Gaussian elliptical surface model, the search range of voxel vertices is represented as follows;

[0026]

[0027] in, Indicates the voxel vertex index. The distance from the center of the Gaussian elliptical surface model The most recent grid point index, The search range of voxels corresponding to the Gaussian elliptical surface model is defined by the maximum semi-axis scale of the Gaussian elliptical surface model. Compared with the pre-set reconstruction voxel size Determined by joint calculation, Indicates rounding up; Voxel space representing the neighborhood Indicated by Centered on the target, the index offsets in all three coordinate directions do not exceed the threshold. The set of neighborhood voxel indices;

[0028] For each voxel vertex within the search range, calculate the implicit function value of the voxel vertex. :

[0029]

[0030] in, These are the coordinates of the voxel vertices, which have been determined when constructing the voxel extents; Represents the vector dot product. Represents the signed distance from a voxel vertex to the surface of a Gaussian ellipse; This represents the normal direction of the Gaussian elliptical surface model.

[0031] Optionally, after constructing the local implicit function field of each Gaussian elliptical surface model in step 2 and before performing global weighted fusion in step 3, the method further includes: for each Gaussian elliptical surface model, voxel vertex clipping is performed along the plane direction and normal of the Gaussian elliptical surface model.

[0032] Voxel vertex clipping in the planar direction: First, project the voxel vertex onto the plane containing the corresponding Gaussian ellipse surface, and calculate the distance from the projection point to the center of the Gaussian ellipse surface; then clip the voxel vertices whose distance exceeds a preset threshold.

[0033] Normal direction voxel vertex clipping: Clip the corresponding voxel vertex when none of the voxels containing the voxel vertex are traversed by the corresponding Gaussian ellipse surface;

[0034] First, the distance from the voxel vertex to the corresponding Gaussian ellipse surface is calculated. If the absolute value of the distance is greater than... If so, it is assumed that none of the voxels containing the voxel vertices are traversed by the surface of the Gaussian ellipse. To reconstruct voxel size;

[0035] If the absolute value of the distance is less than If the voxel at the voxel vertex is traversed by the corresponding Gaussian ellipse surface, then it is assumed that the voxel at the voxel vertex must be traversed by the corresponding Gaussian ellipse surface.

[0036] For the remaining cases, calculate the signed distances from other voxel vertices within the voxel containing the voxel vertex to the corresponding Gaussian elliptical surface. If for each voxel, the distance value is either positive or negative, then it can be determined that the corresponding voxel has not been traversed by the Gaussian elliptical surface. That is, if any one or more voxels containing a vertex are traversed, the corresponding vertex is not deleted; if all voxels containing a vertex are simultaneously not traversed by the Gaussian elliptical surface, the corresponding vertex is deleted.

[0037] Optionally, the mathematical model for the global weighted fusion in step 3 is as follows:

[0038]

[0039]

[0040] The vertex weights are calculated as follows:

[0041]

[0042] In the formula, i represents a voxel vertex, and the weight value of each voxel vertex is calculated in relation to the function value. The opacity of the corresponding Gaussian ellipse model is also calculated. Related, e is the natural base; , Let represent the corresponding weight values ​​and implicit function values ​​stored at the vertices before the t-th fusion, respectively. , These represent the vertex weights and implicit function values ​​newly added during the t-th fusion, respectively. , Let represent the weight value and implicit function value of the vertex after the t-th fusion, respectively.

[0043] Optionally, after constructing the initial three-dimensional Gaussian elliptical surface model in step 1, the method further includes:

[0044] The current 3D Gaussian elliptical surface model is denoised based on the nearest neighbor distance and opacity threshold, specifically as follows:

[0045] Set the nearest neighbor distance threshold and transparency threshold For each Gaussian elliptical surface model, based on its distance to the nearest other Gaussian elliptical surface model... and opacity Judgment: When or If the condition is met, the corresponding Gaussian elliptical surface model is treated as noise and removed; otherwise, the corresponding Gaussian elliptical surface model is retained and no removal is performed.

[0046] Optionally, the process of extracting the 0 isosurface using the Marching Cubes algorithm based on voxel cube face matching in step 4, based on the vertex function values ​​of the global voxel field, is as follows:

[0047] For each voxel, firstly, for each face, based on the vertex function values ​​of each voxel vertex on each face. The positive and negative state distribution is determined by surface matching to determine whether the 0 contour lines exist and their shape, thereby obtaining the 0 contour lines of each surface and determining the voxel vertices used as the start and end points for interpolation.

[0048] Then, the starting and ending coordinates of the 0 contour line were obtained by linear interpolation;

[0049] After matching and interpolation are completed on each face of the voxel, the connection relationship of the 0 contour lines is determined by searching based on the distance between the start and end points for all 0 contour lines until a closed sequence of 0 contour lines is obtained.

[0050] After obtaining all the closed 0 contour lines within a voxel, the closed 0 contour line sequence is transformed into a surface represented by a voxel vertex sequence. The surface containing more than three voxel vertices is then divided into multiple triangular surfaces to obtain the contour triangle sequence corresponding to the voxel.

[0051] Secondly, the present invention also provides a system based on the above method, comprising at least:

[0052] The initial model building module is used to build an initial 3D Gaussian elliptical surface model based on the sparse point cloud of the reconstructed object. Each point cloud corresponds to a Gaussian elliptical surface model, and the spatial parameters of the Gaussian elliptical surface model are obtained.

[0053] The function field building module is used to construct the local implicit function field for each Gaussian elliptical surface model;

[0054] For a single Gaussian elliptical surface model, a local implicit function field of the neighborhood voxel space is constructed based on the spatial parameters of the Gaussian elliptical surface model to obtain the search range of the voxel vertex and the implicit function value of the voxel vertex. The implicit function value of the voxel vertex is the signed distance from the voxel vertex to the corresponding Gaussian elliptical surface.

[0055] The weighted fusion module is used to perform global weighted fusion of the local implicit function fields based on the current Gaussian elliptical surface model; in this module, local voxel vertices are mapped to global voxel vertices, and implicit function values ​​of global voxel vertices are fused to obtain the vertex function values ​​of the global voxel field.

[0056] The model building module is used to extract the 0 isosurface based on the vertex function values ​​of the global voxel field using the Marching Cubes algorithm based on voxel cube face matching, and then construct the mesh model of the reconstructed object.

[0057] In three aspects, the present invention also provides a computer device, comprising:

[0058] One or more processors;

[0059] A memory that stores one or more computer programs;

[0060] The processor invokes a computer program to implement the steps of a method for constructing a mesh model based on the spatial parameters of a three-dimensional Gaussian surface model.

[0061] Compared with the prior art, the present invention achieves the following progress and effects:

[0062] 1. This invention provides a method for 3D grid reconstruction based on the spatial parameters of a 3D Gaussian elliptical surface model, constructing a voxel implicit function field. Previous surface extraction methods based on 3D Gaussian elliptical surface models utilized the TSDF method, obtaining depth values ​​through 2D rendering and then establishing a voxel field representing the surface. This invention, however, directly uses the 3D spatial parameters of the 3D Gaussian elliptical surface model to establish a voxel field consistent with the distribution of the 3D Gaussian surface, enabling accurate and unobstructed surface representation, thus achieving a leap forward in thinking. Specifically, for a single Gaussian elliptical surface model, a local implicit function field of the neighborhood voxel space is constructed based on the spatial parameters of the Gaussian elliptical surface model, obtaining the search range of voxel vertices and the implicit function values ​​of the voxel vertices. The implicit function value of a vertex is the signed distance from the voxel vertex to the corresponding Gaussian elliptical surface.

[0063] By directly establishing a voxel field in three dimensions that is consistent with the distribution of the Gaussian elliptical surface model to represent the geometric surface, this invention essentially solves the problem that the TSDF method, which relies solely on two-dimensional information, has poor handling of structural consistency in multi-view scenes with occlusion. This invention avoids the situation where details are missing or incorrect in a certain part due to occlusion. At the same time, it can also solve the following technical defects: the depth value rendered using Gaussian sputtering is not only affected by the position of the Gaussian itself, but also distorted by the difference in Gaussian opacity, which makes it easy for the constructed implicit function field to have obvious differences from the real scene surface.

[0064] 2. Further optimization of the present invention includes an optimization strategy for plane filling and control of the influence range of each Gaussian surface on voxels. Specifically, for each Gaussian elliptical surface model, voxel vertices are clipped along the plane direction and normal of the Gaussian elliptical surface model, thereby avoiding the reconstruction of excessively redundant structures based on the three-dimensional features of the Gaussian surface.

[0065] In the past, existing technologies were based on densification after rendering to two dimensions, and there was no related technology to directly fill the Gaussian ellipse surface from the three-dimensional spatial features. The plane filling optimization strategy proposed in this invention is designed based on the three-dimensional distribution features of each three-dimensional Gaussian ellipse surface, and this step can significantly reduce the voids in the extracted mesh surface. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method for constructing voxel implicit function fields and reconstructing mesh models based on a three-dimensional Gaussian elliptical surface model according to the present invention;

[0067] Figure 2 This is a schematic diagram of the Gaussian elliptical surface filling strategy of the present invention;

[0068] Figure 3This is a schematic diagram of the grid model constructed based on vertical photogrammetric images according to the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The technical features involved in the various embodiments of the invention described below can be combined with each other as long as they do not conflict with each other.

[0070] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0071] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0072] This invention provides a mesh model construction method based on the spatial parameters of a 3D Gaussian elliptical surface model. It directly establishes a voxel field with a distribution consistent with the 3D Gaussian surface using the 3D spatial parameters of the model, enabling accurate and unobstructed surface representation. This significantly improves the spatial accuracy and surface orientation consistency of the reconstructed mesh model, achieving high-precision 3D reconstruction. It solves the problem in the industry of directly constructing a spatial implicit function field and reconstructing a mesh model using a 3D Gaussian elliptical surface model. The technical approach is as follows:

[0073] Step 1: Based on the sparse point cloud of the reconstructed object, establish an initial 3D Gaussian elliptical surface model. Each point cloud corresponds to a Gaussian elliptical surface model, and obtain the spatial parameters of the Gaussian elliptical surface model.

[0074] Step 2: Construct the local implicit function field for each Gaussian elliptical surface model;

[0075] Step 3: Perform global weighted fusion of the local implicit function fields based on the current Gaussian elliptical surface model; wherein, the local voxel vertices are mapped to the global voxel vertices, and the implicit function values ​​of the global voxel vertices are fused to obtain the vertex function values ​​of the global voxel field;

[0076] Step 4: Based on the vertex function values ​​of the global voxel field, use the MarchingCubes algorithm based on voxel cube face matching to extract the 0 isosurface, and then construct the mesh model of the reconstructed object.

[0077] It should be understood that the above-mentioned technical ideas are the core of the present invention. On this basis, the present invention has also carried out many optimizations, such as proposing an optimization strategy for plane filling, proposing a technical means to control the influence range of each Gaussian surface on the voxel, and proposing a three-dimensional Gaussian elliptical surface model obtained by multiple noise reduction and introducing a new perspective of Gaussian sputtering for synthesis optimization.

[0078] Therefore, the preferred embodiment of the technical solution of the present invention is as follows:

[0079] S1. Generate an initial 3D Gaussian elliptical surface model based on the sparse point cloud of the reconstructed object, and optimize the 3D Gaussian elliptical surface model using multi-view Gaussian sputtering technology; S2. Denoise the 3D Gaussian elliptical surface model based on the nearest neighbor distance and opacity threshold; S3. Directly fill the 3D Gaussian elliptical surface model in 3D space; S4. Establish a local implicit function field near the 3D Gaussian elliptical surface model; S5. Clip the vertices of the function field along the plane direction and normal direction of the Gaussian elliptical surface model; S6. Globally weighted fusion of the implicit function field; S7. Clip the vertices of the function field based on the fusion weight; S8. Extract the 0-isosurface from the implicit function field using the Marching Cubes algorithm, where the 0-isosurface represents the surface location of the Gaussian ellipse; S9. Obtain the mesh model after denoising the 0-isosurface.

[0080] It should be understood that in other feasible embodiments, some steps of the above-described preferred embodiment may not be performed or some steps may be replaced. The preferred embodiment will be described in detail below.

[0081] like Figure 1 As shown in the figure, an embodiment of the present invention provides a mesh model construction method based on the spatial parameters of a three-dimensional Gaussian elliptical surface model, which includes the following steps:

[0082] Step S1: Data Acquisition and Initial Model Construction. This embodiment requires at least acquiring multi-view images and point cloud data and geometric information of the target scene / object.

[0083] It should be understood that the technical solution of the present invention is applicable to the scenario requirements of three-dimensional mesh model reconstruction, especially to the scenario requirements of three-dimensional mesh model reconstruction through multi-view images, such as UAV aerial photography and mapping, real-time reconstruction of SLAM system and digitization of cultural heritage, etc., to construct three-dimensional mesh models of the objects to be reconstructed in the above scenarios.

[0084] In this embodiment, the data acquisition process is as follows: acquiring multi-view RGB images of the target scene / object using RGB sensors such as cameras; acquiring sparse point clouds corresponding to the images using the SfM (Structure from Motion) sparse reconstruction method; and acquiring depth map priors (geometric information) corresponding to the RGB images using a pre-trained neural network model based on monocular depth estimation. Both the SfM sparse reconstruction method and the pre-trained neural network model based on monocular depth estimation can be implemented using existing technologies, and this invention does not specifically limit or explain them.

[0085] The initial model construction involves first constructing an initial 3D Gaussian elliptical surface model, and then optimizing the initial 3D Gaussian elliptical surface model using photometric and geometric information from multi-view RGB images based on multi-view Gaussian sputtering technology. Details are as follows:

[0086] First, an initial 3D Gaussian elliptical surface model is generated from sparse point cloud. The sparse point cloud provides prior information for the 3D Gaussian elliptical surface model, initializing its center coordinates, color, semi-axis scale, and normal vector, as follows:

[0087] Each point cloud corresponds to a Gaussian elliptical surface model. Based on the sparse point cloud, the parameters of the 3D Gaussian elliptical surface model include: the center coordinates, normal direction, semi-axis direction, semi-axis scale, spherical harmonic function, and opacity parameter. In this embodiment, the specific settings of these parameters are as follows:

[0088]

[0089] in, The center position of the Gaussian elliptical surface. The coordinates of each point in the sparse point cloud.

[0090]

[0091] in, Let be the normal direction of the Gaussian elliptical surface. The normal vector direction of each point is estimated from the sparse point cloud.

[0092]

[0093]

[0094] in, Let the direction be one of the semi-axis directions of the Gaussian elliptical surface. The direction of the other half-axis.

[0095]

[0096] in, , These are the corresponding half-shafts , The scale, The distance from the sparse point cloud corresponding to the Gaussian elliptical surface to its nearest neighbor point cloud is considered as the distance from a Gaussian elliptical model to the nearest other Gaussian elliptical model.

[0097]

[0098] in, Let be the spherical harmonic function of the Gaussian elliptical surface, i.e., the color representation. The color corresponds to the point cloud color; sh represents the mapping from the point cloud color to the spherical harmonic function value; additionally, the opacity parameter of the Gaussian ellipse surface. The initial value is directly and uniformly set to 0.1.

[0099] The process of optimizing the initial 3D Gaussian elliptical surface model using the photometric and geometric information of multi-view RGB images based on multi-view Gaussian sputtering technology is as follows: The parameters of the 3D Gaussian elliptical surface model are supervised using the following error loss term:

[0100] First, calculate the photometric error between the rendered image corresponding to the Gaussian elliptical surface model and the multi-view images. Depth value error Depth distortion item (Control the Gaussian elliptical surface to cluster on the scene surface), normal depth consistency distortion term (This allows the Gaussian normal distribution to better fit the shape of the depth distribution).

[0101] Then, based on the above errors, the errors are propagated to the parameters of the 3D Gaussian elliptical surface model projected into the image through gradient descent, thereby correcting and initially optimizing the parameters of the 3D Gaussian elliptical surface model. Essentially, this optimization is achieved by utilizing the consistency of photometric and geometric rendering.

[0102] In this embodiment, the rendered image is produced using GPU parallel differentiable rasterization rendering technology. The Gaussian elliptical surface model is projected onto a two-dimensional planar region, then sorted based on depth, and finally composited pixel-by-pixel based on opacity. This is achievable with existing Gaussian sputtering technology, and therefore will not be described in detail. It should be understood that constructing a minimum objective function using multiple error terms, solving for the objective function, and dynamically updating the parameters of the three-dimensional Gaussian elliptical surface model are processes that can be implemented by those skilled in the art. Furthermore, the aforementioned error loss terms are all existing loss models; therefore, the calculation and optimization process of the error loss terms will not be described in detail.

[0103] It should also be understood that performing model parameter optimization is the preferred method in this embodiment. However, in other feasible embodiments, this step may not be performed to meet the accuracy requirements of this application, and the data type obtained in step S1 may be adjusted accordingly.

[0104] Step S2: Model denoising. The optimized 3D Gaussian elliptical surface model is denoised based on the nearest neighbor distance and opacity threshold.

[0105] For each Gaussian elliptical surface model, consider its distance to the nearest other Gaussian elliptical surface model. and opacity Set the nearest neighbor distance threshold respectively and transparency threshold (like and ),when or If the Gaussian elliptical surface model is considered noise, it is removed; otherwise, the Gaussian elliptical surface model is retained without removal. It should be understood that the threshold values ​​mentioned above in this embodiment... and For illustrative purposes only, in other feasible embodiments, the threshold can be adaptively adjusted according to accuracy requirements and application needs.

[0106] Step S3: Model filling. For Gaussian elliptical surface models located within a planar region, fill the gaps between the Gaussian elliptical surface model and its neighboring Gaussian elliptical surface models in three-dimensional space. The implementation process of step S3 in this embodiment is as follows:

[0107] Step S31: Determine whether each Gaussian elliptical surface model is within a planar region. If yes, proceed to step S32; otherwise, do not perform model filling.

[0108] Among them, for the Gaussian elliptical surface model k nearest neighbor Gaussian elliptic surface model If all conditions are met Then consider the Gaussian elliptical surface model If the surface is in a planar region, execute S32; otherwise, use a Gaussian elliptical surface model. Not located in a planar area , Gaussian elliptic surface model Center position and normal direction ; , The nearest Gaussian elliptic surface model The center position and normal direction; , , All are set empirical thresholds, which are 0.8, 0.07, and 0.93 respectively in this embodiment; k is an empirical value, which is 15 in this embodiment; in other feasible embodiments, the value of k and the above empirical thresholds can be adaptively adjusted.

[0109] Step S32, for the Gaussian elliptical surface model Model of k nearest Gaussian elliptic surfaces The spaces between them are filled, and the parameters of the new Gaussian elliptical surface model after filling are as follows:

[0110] For any two Gaussian elliptical surface models Fill in the gaps between the points to determine the center position of the new Gaussian elliptical surface model. The distance between the two principal axes in space , The nearest point, and For two Gaussian elliptical surface models The principal axis of filling. Specifically, for two Gaussian elliptical surface models... Each of the main axes of filling and From their respective half-axis directions Select from the options to fill the spindle. For example:

[0111]

[0112] Determine using the same method :

[0113]

[0114] In the formula, , For two Gaussian elliptical surface models The central location, , Gaussian elliptical surface model half-axis direction ; , Gaussian elliptical surface model half-axis direction .

[0115] In this embodiment, a further preferred embodiment is that the two Gaussian ellipse models only function when the sum of the scales of the two principal axes is too small. Only when the sum of the scales is a new Gaussian elliptical surface needs to be filled; otherwise, no filling is performed. Specifically: when the sum of the scales is... Distance less than 1.1 times the Gaussian distance If it is too small, it is considered too small. Fill the principal axis for the two Gaussian correspondences , The scale.

[0116] The center position of the newly filled Gaussian elliptical surface The distance between the two principal axes in space , The nearest point is expressed as:

[0117]

[0118]

[0119]

[0120] Where s, t, B, E, and D are all user-defined parameters, and satisfy the following: , , .

[0121] Normal of the new Gaussian elliptical surface model From the central position To the two original Gaussian elliptical surface models The vector cross product is obtained.

[0122] The semi-axis of the new Gaussian elliptic surface model central position To one of the original Gaussian elliptical surface models or The direction of the other half axis Then by and The cross product is obtained.

[0123] The scales of the semi-axis of the new Gaussian elliptical surface model are respectively from the scales of the new Gaussian elliptical surface model to the scales of the original Gaussian elliptical surface model. The distance is determined; the opacity and color are the same as the original Gaussian elliptical surface model. The mean of the corresponding parameters.

[0124] Step S4: Construct the local implicit function field for each Gaussian elliptical surface model. For each voxel in the neighborhood voxel space of a single Gaussian elliptical surface model, construct a local implicit function field for the voxel vertices to obtain the search range of the voxel vertices and the implicit function values ​​of the voxel vertices.

[0125] First, determine the vertex search range:

[0126]

[0127] in, Indicates the voxel vertex index. The distance from the center of the Gaussian ellipse surface The most recent grid point index, The search range for the voxels corresponding to the Gaussian elliptical surface model is determined by the maximum semi-axis scale of the Gaussian elliptical surface and the pre-set reconstructed voxel size. Determined by joint calculation, Indicates rounding up; This represents the neighborhood voxel space. The global voxel space is known, and the global voxel field is a predefined space. In practice, the voxel field extent is obtained from the global bounding box of all Gaussian surface models, and the voxel field vertices (i.e., vertex spacing) are derived from the predefined voxel size parameter. The vertices are obtained and assigned in the voxel field at specified intervals. Each Gaussian elliptical surface model has a neighborhood voxel space, representing its multiple neighboring voxels, which are used to find the voxel vertices around the Gaussian elliptical surface model to obtain the local implicit function field.

[0128] For each voxel vertex within the vertex search range, compute the implicit function value:

[0129]

[0130] in, These are the coordinates of the voxel vertices, which were determined when constructing the voxel extents. Let G be the coordinates of the center position of the Gaussian elliptical surface. Represents the vector dot product. Represents the signed distance from the voxel vertex to the surface of the Gaussian ellipse.

[0131] This step involves determining the voxel vertices within the search range for each Gaussian elliptical surface model, calculating the implicit function values ​​of the voxel vertices, and using these values ​​to filter the voxel vertices.

[0132] Step S5: Clip the voxel vertices along the direction of the Gaussian ellipse surface plane and along the normal direction of the Gaussian ellipse surface.

[0133] Voxel pruning in the planar direction involves projecting the voxel vertices onto the plane containing the Gaussian ellipse surface, calculating the Mahalanobis distance from the projection point to the center of the Gaussian ellipse surface, and then pruning vertices with excessive Mahalanobis distances, without considering their implicit function values.

[0134] The Mahalanobis distance formula is as follows:

[0135]

[0136] In the formula, The distance is Mahalanobis distance. In other embodiments, it is also feasible to use other distance characteristic formulas, which fall within the protection scope of this invention. Furthermore, the distance threshold is set as an empirical value, and this invention does not impose specific limitations on its value.

[0137] Normal direction voxel pruning: Plexes whose voxels are not traversed by the Gaussian ellipse surface are pruned, without considering their implicit function values.

[0138] It should be understood that each voxel has 8 voxel vertices. The voxel is considered to be the voxel in which these eight voxel vertices are located. Each voxel vertex can be in multiple voxels at the same time (a voxel is a cube in space, and voxel space is composed of a large number of voxel cubes. Therefore, a cube and its neighboring cubes will share faces, edges, and vertices. Thus, each voxel vertex can belong to multiple voxels at the same time).

[0139] Calculate the distance from the voxel vertex to the surface of the Gaussian ellipse. If the absolute value of the distance is greater than... Based on geometric relationships, it can be known that the voxel containing the vertex of this voxel is not traversed by the Gaussian ellipse surface. It should be understood that if a vertex has multiple voxels, then each voxel is considered not to be traversed by the Gaussian ellipse surface, and the corresponding voxel vertex is discarded.

[0140] If the absolute value of the distance is less than If a voxel vertex is located in one or more voxels, then it is assumed that the voxel vertex must be traversed by the Gaussian ellipse surface. It should be understood that if a voxel vertex has multiple voxels, then each voxel containing the vertex must be traversed, and the corresponding voxel vertex does not need to be clipped.

[0141] For the remaining cases, calculate the signed distances from other vertices within the voxel to the Gaussian surface. If for each voxel, the distance values ​​are all either positive or negative, then it can be determined that the voxel has not been traversed by the Gaussian elliptical surface. If any one or more voxels containing the vertex are traversed, the corresponding voxel vertex is not deleted. If all voxels containing the vertex are not traversed by the Gaussian elliptical surface at the same time, the corresponding voxel vertex is deleted, and its implicit function value is not considered.

[0142] Step S6: Global weighted fusion of implicit function fields, that is, for voxel vertices, global weighted fusion is performed based on the implicit function fields of the vertex voxel spaces of all Gaussian elliptical surface models.

[0143] Step S4 obtains the local implicit function field of each Gaussian elliptical surface model. That is, the global vertices of the global acceleration field are indexed using the Gaussian model to obtain a search space. The voxel vertices in this search space are regarded as local vertices, and the implicit function values ​​of the local vertices are determined. The fusion in this step starts from the global voxel field and maps the local vertices back to the global vertices. That is, for the same voxel vertex, the features of the corresponding local implicit function field are fused on the basis of the original value (the function value and weight value of each local vertex are added to the corresponding vertex of the global voxel field, so that each vertex in the global voxel field has accumulated function value and weight value, thus achieving the purpose of fusion).

[0144] Based on the coordinates, local vertices are mapped to global vertices, and function values ​​are fused for the global vertices. The fusion formula is as follows:

[0145]

[0146]

[0147] The vertex weights are calculated as follows:

[0148]

[0149] This represents the opacity of the Gaussian ellipse model corresponding to the weight value of each vertex and the implicit function value calculation formula. Related to, e is the natural base, and refers to the vertex of each voxel in the neighborhood of the same Gaussian model. They are all the same. 'i' represents the voxel vertex. , Let represent the corresponding weight value and implicit function value stored at vertex i of the voxel before the t-th fusion, respectively. , These represent the newly added vertex weights and implicit function values ​​during this fusion, respectively. , Let represent the weight value and implicit function value of voxel vertex i after this fusion, respectively. During the fusion process, each use of all local vertices of a Gaussian surface model is considered as one iteration, and the iteration stops when all Gaussian models have been superimposed.

[0150] Step S7: Prune the fused voxel vertices based on a weight threshold; for each fused top voxel, prune it based on its cumulative weight value. A threshold is set to prune voxel vertices with excessively small cumulative weight values, and these voxels are not considered during isosurface extraction. Similarly, voxel vertices that have not participated in function value fusion are also excluded from isosurface extraction. For vertices in the global voxel field, since each neighboring voxel is fused into a specific global vertex based on its spatial location, some vertices will be considered as not having participated in function value fusion because their location is not among neighboring voxels and therefore lacks function values ​​and weight values.

[0151] It should be understood that this step is an optional step in the technical solution of the present invention.

[0152] Step S8: Use the Marching Cubes method based on surface matching to determine the contour lines and then construct the contour surfaces for the voxels in the function field.

[0153] It should be understood that the existing Marching Cubes method, when determining the reconstructed shape of isomorphic surfaces in voxels, uses a matching table to match the positive and negative distribution patterns of function values ​​at each voxel vertex. This method is also applicable to the technical solution of this invention. However, this embodiment further improves the Marching Cubes method by using a matching table based on the positive and negative distribution patterns of function values ​​at each voxel vertex, and designs a Marching Cubes method based on surface matching. The implementation process is as follows:

[0154] For each voxel, first, for each of its faces, based on the vertex function value... The positive and negative state distribution is used to determine the existence and shape of zero contour lines through matching. The resulting zero contour lines for each face are used to determine the interpolation vertices used as start and end points. Specifically, for each face with four vertices and each vertex having two states (positive and negative), 16 possible combinations of positive and negative states are obtained, forming 16 templates. These templates are then used to match the actual positive and negative distribution of each face, determining the positions of the interpolation vertices and zero contour lines (i.e., determining which edges of the face the interpolation vertices should be on and how the zero contour lines connect between vertices). This is specifically based on the existing Marching Cubes method for cube matching, using predefined templates for the vertices and zero contour line shapes corresponding to different positive and negative states.

[0155] Then, the start and end coordinates of the contour lines are obtained through linear interpolation. After matching and interpolation are completed on each face of the voxel, the connection relationship of the contour lines is determined by searching the distance between the start and end points for the 0 contour lines of all faces until a closed sequence of 0 contour lines is obtained. After obtaining all the closed sequence of 0 contour lines in the voxel, it is transformed into a face represented by a vertex sequence, i.e., a 0 contour surface. Faces containing more than three vertices are divided into multiple triangular faces to obtain the contour surface triangle sequence corresponding to the voxel.

[0156] Step S9: Merge the vertices of the obtained 0 isosurfaces, identify clusters and remove noise patches to obtain the final mesh model.

[0157] Existing techniques, after extracting the isosurfaces of each voxel, do not remove redundant vertices that are repeated in adjacent voxels. To address this, the present invention further optimizes the vertex merging process with lightweight improvements. For the isosurface sequence corresponding to all voxels, vertices with the same coordinates are merged to reduce redundant representations. Furthermore, triangular facet clusters are identified based on the topological connectivity of the triangular faces. A threshold is set, and clusters containing too few triangular faces are considered noise and removed. Finally, a mesh model composed of vertices (coordinates) and triangular faces (vertex indices) is obtained.

[0158] It should be understood that this step is an optional step of the present invention, and its purpose is to further achieve model noise reduction; in other feasible embodiments, the obtained isosurface can also be used to construct a mesh model of the reconstructed object, referring to the prior art.

[0159] Based on the above technical means, the technical solution of the present invention can be directly used for 3D reconstruction of mesh models based on UAV aerial photography. Figure 3 This paper demonstrates an example of building model reconstruction based on digital photogrammetry imagery. Vertical photogrammetric images of a region were acquired through UAV aerial photography, and then processed using the aforementioned method to obtain the final mesh building model. This includes the original building mesh model, detailed displays of the mesh model with vertex colors, and the location of the detailed areas within the vertical photogrammetric imagery.

[0160] In some embodiments, the present invention also provides a system based on the above method, which includes an initial model building module, a function field building module, a weighted fusion module, and a model building module that are connected sequentially or interconnected.

[0161] The initial model building module is used to build an initial three-dimensional Gaussian elliptical surface model based on the sparse point cloud of the reconstructed object. Each point cloud corresponds to a Gaussian elliptical surface model, and the spatial parameters of the Gaussian elliptical surface model are obtained.

[0162] The function field building module is used to construct the local implicit function field for each Gaussian elliptical surface model.

[0163] The weighted fusion module is used to perform global weighted fusion of the local implicit function field based on the current Gaussian elliptical surface model. Specifically, local voxel vertices are mapped to global voxel vertices, and implicit function values ​​are fused for global voxel vertices to obtain the vertex function values ​​of the global voxel field.

[0164] The model building module is used to extract the 0 isosurface based on the vertex function values ​​of the global voxel field using the Marching Cubes algorithm based on voxel cube face matching, and then construct the mesh model of the reconstructed object.

[0165] In other embodiments, the system may also include: an initial model building module, a model denoising module, a model filling module, a function field building module, a vertex clipping module, a weighted fusion module, a vertex secondary clipping module, an isosurface extraction module, and a denoising module that are sequentially connected or interconnected.

[0166] The initial model building module generates an initial 3D Gaussian elliptical surface model based on the sparse point cloud of the reconstructed object, with each point cloud corresponding to one Gaussian elliptical surface model. The model denoising module identifies and removes Gaussian elliptical surface models with excessively large nearest neighbor distances and excessively low opacity as noise. The model filling module fills the gaps between Gaussian elliptical surface models in planar regions and their neighboring Gaussian elliptical surface models with new Gaussian elliptical surface models. The function field building module constructs an implicit function field in the neighborhood voxel space for each Gaussian elliptical surface model to obtain the search range of vertices and the implicit function values ​​of vertices. The vertex clipping module clips vertices along the planar direction and normal of each Gaussian elliptical surface model, specifically clipping implicit function values ​​of vertices far from the center of the corresponding Gaussian elliptical surface model and implicit function values ​​of vertices whose voxels are not traversed by the corresponding Gaussian elliptical surface. The weighted fusion module performs global weighted fusion of the implicit function values ​​of vertices in the neighborhood voxel space of each Gaussian elliptical surface model; the vertex secondary pruning module performs threshold-based pruning of the cumulative weights of the fused vertices, excluding voxels containing vertices with excessively low cumulative weights from isosurface extraction; the isosurface extraction module uses the Marching Cubes algorithm based on voxel cube face matching to extract 0 isosurfaces from the voxels in the implicit function field; the denoising module performs vertex merging and face clustering on the 0 isosurfaces, and then obtains the mesh model of the reconstructed object after denoising by setting a threshold for the number of faces in each cluster. The isosurface extraction module and the denoising module can be considered as decompositions of the aforementioned model construction modules.

[0167] It should also be understood that the specific implementation process of each module is described in the above method. This invention will not repeat it here. The above division of functional modules is only for illustrative purposes. In some embodiments, some functional modules can be combined and some functional modules can be separated. Each functional module can be implemented in software, hardware, or a combination of software and hardware. The software and hardware devices include, but are not limited to, general-purpose computer equipment, programmable gate arrays, digital signal processors, microprocessors and their corresponding programming or burning software.

[0168] In some embodiments, the present invention also provides a computer device, including: one or more processors and a memory storing one or more computer programs; wherein the processor invokes the computer programs to implement: the steps of a method for constructing a mesh model based on spatial parameters of a three-dimensional Gaussian elliptical surface model. See the description of the foregoing method embodiments for details.

[0169] In some embodiments, the electronic components of a computer device include:

[0170] The processor can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention.

[0171] The memory can be implemented in the form of read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory, and the processor calls the algorithm program of the methods described above in the embodiments of this invention.

[0172] Input / output interfaces are used to implement information input and output.

[0173] The communication interface is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0174] A bus is used to transfer information between various components of a device, such as processors, memory, input / output interfaces, and communication interfaces.

[0175] The processor, memory, input / output interfaces, and communication interfaces communicate with each other within the device via a bus.

[0176] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application refers to flowchart illustrations and / or instructions executed by a processor of a method, apparatus (system), and computer program product according to embodiments of this application to create means for implementing the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more blocks of a block diagram.

[0177] It should be emphasized that the examples described in this invention are illustrative rather than limiting. Therefore, this invention is not limited to the examples described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of this invention, without departing from the spirit and scope of this invention, whether modifications or substitutions, are also within the protection scope of this invention.

Claims

1. A method for constructing a mesh model based on the spatial parameters of a three-dimensional Gaussian surface model, characterized in that: At least the following steps are included: Step 1: Based on the sparse point cloud of the reconstructed object, establish an initial 3D Gaussian elliptical surface model. Each point cloud corresponds to a Gaussian elliptical surface model, and obtain the spatial parameters of the Gaussian elliptical surface model. Step 2: Construct the local implicit function field for each Gaussian elliptical surface model; For a single Gaussian elliptical surface model, a local implicit function field of the neighborhood voxel space is constructed based on the spatial parameters of the Gaussian elliptical surface model to obtain the search range of the voxel vertex and the implicit function value of the voxel vertex. The implicit function value of the voxel vertex is the signed distance from the voxel vertex to the corresponding Gaussian elliptical surface. Step 3: Perform global weighted fusion of the local implicit function fields based on the current Gaussian elliptical surface model; wherein, the local voxel vertices are mapped to the global voxel vertices, and the implicit function values ​​of the global voxel vertices are fused to obtain the vertex function values ​​of the global voxel field; Step 4: Based on the vertex function values ​​of the global voxel field, use the Marching Cubes algorithm based on voxel cubes to extract the 0 isosurface, and then construct the mesh model of the reconstructed object.

2. The method according to claim 1, characterized in that: After constructing the initial three-dimensional Gaussian elliptical surface model in step 1, the method further includes: for the Gaussian elliptical surface model located in the planar region, filling the gap between the Gaussian elliptical surface model and its neighboring Gaussian elliptical surface models in three-dimensional space; For any two Gaussian elliptical surface models Between these points, the spatial parameters of the newly filled Gaussian elliptical surface model satisfy the following requirements: The center position of the new Gaussian elliptic surface model Distance between two principal axes in space , The nearest point, and For two original Gaussian elliptic surface models Fill the main axis; Normal of the new Gaussian elliptical surface model From the central position To two original Gaussian elliptic surface models The cross product of vectors is obtained; The semi-axis of the new Gaussian elliptic surface model Central position To one of the original Gaussian elliptic surface models or The direction of the other half axis Then by and The cross product is obtained; The scale of the semi-axis of the new Gaussian elliptical surface model: from the new Gaussian elliptical surface model to the original Gaussian elliptical surface model. The distance is determined; Opacity and color: Both are based on the original Gaussian elliptical surface model. The mean of the corresponding parameters.

3. The method according to claim 2, characterized in that: By jointly determining whether the corresponding Gaussian elliptical surface model lies within a planar region, based on the center position and normal of each Gaussian elliptical surface and its neighboring Gaussian elliptical surfaces, the following steps are taken: For Gaussian elliptical surface model k nearest neighbor Gaussian elliptic surface model If all conditions are met Then the Gaussian elliptical surface model It is located in a planar region; otherwise, it appears as a Gaussian elliptical surface model. Not located in a planar area; in, , Gaussian elliptic surface model The center position and the direction of the normal. , These are the nearest neighbor Gaussian elliptic surface models. The center position and normal direction; , , These are all set empirical thresholds.

4. The method according to claim 1, characterized in that: In step 2, for a single Gaussian elliptical surface model, the search range of voxel vertices is represented as follows; ； in, Indicates the voxel vertex index. The distance from the center of the Gaussian elliptical surface model The most recent grid point index, The search range of voxels corresponding to the Gaussian elliptical surface model is defined by the maximum semi-axis scale of the Gaussian elliptical surface model. Compared with the pre-set reconstruction voxel size Determined by joint calculation, Indicates rounding up; Voxel space representing the neighborhood Indicated by Centered on the target, the index offsets in all three coordinate directions do not exceed the threshold. The set of neighborhood voxel indices; For each voxel vertex within the search range, calculate the implicit function value of the voxel vertex. : ； in, These are the coordinates of the voxel vertices, which have been determined when constructing the voxel extents; Represents the vector dot product. Represents the signed distance from a voxel vertex to the surface of a Gaussian ellipse; This represents the normal direction of the Gaussian elliptical surface model.

5. The method according to claim 1, characterized in that: After constructing the local implicit function field for each Gaussian elliptical surface model in step 2, and before performing global weighted fusion in step 3, the method further includes: for each Gaussian elliptical surface model, voxel vertex clipping is performed along the planar direction and normal of the Gaussian elliptical surface model. Voxel vertex clipping in the planar direction: First, project the voxel vertex onto the plane containing the corresponding Gaussian ellipse surface, and calculate the distance from the projection point to the center of the Gaussian ellipse surface; then clip the voxel vertices whose distance exceeds a preset threshold. Voxel vertex clipping in the normal direction: Clip the corresponding voxel vertex when none of the voxels containing the voxel vertex are traversed by the corresponding Gaussian ellipse surface; First, the distance from the voxel vertex to the corresponding Gaussian ellipse surface is calculated. If the absolute value of the distance is greater than... If so, it is assumed that none of the voxels containing the voxel vertices are traversed by the surface of the Gaussian ellipse. To reconstruct voxel size; If the absolute value of the distance is less than If the voxel at the voxel vertex is traversed by the corresponding Gaussian ellipse surface, then it is assumed that the voxel at the voxel vertex must be traversed by the corresponding Gaussian ellipse surface. For the remaining cases, calculate the signed distances from other voxel vertices within the voxel to the corresponding Gaussian elliptical surface. If the distance values ​​for each voxel are both positive or negative, it can be determined that the corresponding voxel has not been traversed by the Gaussian elliptical surface.

6. The method according to claim 1, characterized in that: The mathematical model for global weighted fusion in step 3 is as follows: 、 ； The vertex weights are calculated as follows: ； In the formula, i represents a voxel vertex, and the weight value of each voxel vertex is calculated in relation to the function value. The opacity of the corresponding Gaussian ellipse model is also calculated. Related, e is the natural base; , Let represent the corresponding weight values ​​and implicit function values ​​stored at the vertices before the t-th fusion, respectively. , These represent the vertex weights and implicit function values ​​newly added during the t-th fusion, respectively. , Let represent the weight value and implicit function value of the vertex after the t-th fusion, respectively.

7. The method according to claim 1, characterized in that: After constructing the initial three-dimensional Gaussian elliptical surface model in step 1, the method further includes: The current 3D Gaussian elliptical surface model is denoised based on the nearest neighbor distance and opacity threshold, specifically as follows: Set the nearest neighbor distance threshold and transparency threshold For each Gaussian elliptical surface model, based on its distance to the nearest other Gaussian elliptical surface model... and opacity Judgment: When or If the condition is met, the corresponding Gaussian elliptical surface model is treated as noise and removed; otherwise, the corresponding Gaussian elliptical surface model is retained and no removal is performed.

8. The method according to claim 1, characterized in that: In step 4, the process of extracting the 0-isosurface using the Marching Cubes algorithm based on voxel cube face matching, based on the vertex function values ​​of the global voxel field, is as follows: For each voxel, firstly, for each face, based on the vertex function values ​​of each voxel vertex on each face. The positive and negative state distribution is determined by surface matching to determine whether the 0 contour lines exist and their shape, thereby obtaining the 0 contour lines of each surface and determining the voxel vertices used as the start and end points for interpolation. Then, the starting and ending coordinates of the 0 contour line were obtained by linear interpolation; After matching and interpolation are completed on each face of the voxel, the connection relationship of the 0 contour lines is determined by searching based on the distance between the start and end points for all 0 contour lines until a closed sequence of 0 contour lines is obtained. After obtaining all the closed 0 contour lines within a voxel, the closed 0 contour line sequence is transformed into a surface represented by a voxel vertex sequence. The surface containing more than three voxel vertices is then divided into multiple triangular surfaces to obtain the contour triangle sequence corresponding to the voxel.

9. A system based on the method of any one of claims 1-8, characterized in that: At least including: The initial model building module is used to build an initial 3D Gaussian elliptical surface model based on the sparse point cloud of the reconstructed object. Each point cloud corresponds to a Gaussian elliptical surface model, and the spatial parameters of the Gaussian elliptical surface model are obtained. The function field building module is used to construct the local implicit function field for each Gaussian elliptical surface model; For a single Gaussian elliptical surface model, a local implicit function field of the neighborhood voxel space is constructed based on the spatial parameters of the Gaussian elliptical surface model to obtain the search range of the voxel vertex and the implicit function value of the voxel vertex. The implicit function value of the voxel vertex is the signed distance from the voxel vertex to the corresponding Gaussian elliptical surface. The weighted fusion module is used to perform global weighted fusion of the local implicit function fields based on the current Gaussian elliptical surface model; in this module, local voxel vertices are mapped to global voxel vertices, and implicit function values ​​of global voxel vertices are fused to obtain the vertex function values ​​of the global voxel field. The model building module is used to extract the 0 isosurface based on the vertex function values ​​of the global voxel field using the Marching Cubes algorithm based on voxel cube face matching, and then construct the mesh model of the reconstructed object.

10. A computer device, characterized in that: include: One or more processors; A memory that stores one or more computer programs; The processor invokes a computer program to achieve the following: The steps of the method according to any one of claims 1-8.

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