High-quality implicit surface reconstruction method based on adaptive search radius

Abstract

The invention provides a high-quality implicit surface reconstruction method based on an adaptive search radius, and the method comprises the following steps: S1, collecting the point cloud data of a to-be-reconstructed surface of a target, and carrying out the preprocessing of the collected point cloud data; s2, dynamically adjusting the point cloud data search radius according to the point cloud distribution density, and sampling the preprocessed point cloud data; s3, inputting the sampling points into the trained MLP network, and predicting SDF values of the sampling points; and S4, based on the predicted SDF value, adopting a surface fitting algorithm to extract a zero contour surface. According to the method, the neighborhood search radius is adaptively adjusted according to the local density of the point cloud data, it is ensured that enough neighborhood point information is obtained in the point cloud sparse region, the integrity and continuity of reconstruction are remarkably improved, and holes and fractures are avoided; the method focuses on a more relevant local structure in a dense point cloud area, effectively reduces redundant calculation and noise interference, and effectively solves the inherent contradiction of traditional fixed radius search in different density areas.

Description

Technical Field

[0001] This invention relates to the field of surface reconstruction technology, and in particular to a high-quality implicit surface reconstruction method based on adaptive search radius. Background Technology

[0002] Surface reconstruction technology is one of the important application methods in modern digital industry, widely used in measurement, reconstruction, fault diagnosis, electronics, energy and chemical industries. To meet the practical needs of industry such as 3D digital measurement, 3D reconstruction, and 3D visualization, surface reconstruction technology has always been an important research direction.

[0003] Surface reconstruction is mainly divided into two approaches: explicit and implicit. Explicit representation mainly uses geometric elements such as triangular meshes or voxel blocks to represent the surface, while implicit representation uses oriented normals to fit implicit functions, then extracts the zero-order surface, and generates the required 3D mesh model. The latter can better restore surface details than the former and can generate a more complete surface when the input quality is poor.

[0004] However, the point cloud search radius of current implicit surface reconstruction technology is generally fixed. In the presence of noise, non-uniform distribution or missing surface points, the reconstructed surface is prone to problems such as poor accuracy, holes, and missing details. Summary of the Invention

[0005] This invention proposes a high-quality implicit surface reconstruction method based on adaptive search radius, which solves the problems of poor accuracy, holes, and missing details in the reconstructed surface due to the fixed point cloud search radius in the existing implicit surface reconstruction technology under conditions such as noise, non-uniform distribution or missing surface points.

[0006] The technical solution of this invention is implemented as follows: This invention provides a high-quality implicit surface reconstruction method based on adaptive search radius, comprising the following steps: S1, Collect point cloud data of the target surface to be reconstructed, and preprocess the collected point cloud data; S2, dynamically adjust the search radius of the point cloud data according to the point cloud distribution density, and sample the preprocessed point cloud data; S3, input the sampling points into the trained MLP network to predict the SDF value of the sampling points; S4. Based on the predicted SDF values, a surface fitting algorithm is used to extract the zero isosurface.

[0007] Specifically, in step S1, the preprocessing of the collected point cloud data includes: The region of interest is cropped from the original 3D point cloud data to remove background point clouds that are irrelevant to the target surface; A statistical outlier removal algorithm is used to filter noise in point cloud data. The filtered point cloud is then normalized to a unit sphere.

[0008] Furthermore, the method for noise filtering of point cloud data is as follows: Calculate the first i Point cloud and k The average distance of each neighboring point d i : ; in, p j Indicates the first i Point cloud p i The j 1 neighboring point; like ,but p i These are the outliers that need to be removed. in, μ , σ Each of the entire point cloud d i The mean and standard deviation.

[0009] Furthermore, the method for performing unit sphere normalization on the filtered point cloud is as follows: Translate all point clouds to their geometric center and scale all point clouds to a radius of a unit sphere, such that: ; in, N The total number of point clouds, c The geometric center of the point cloud, r The maximum distance from all point clouds to the geometric center. Represents the normalized i-th i A point cloud, p i The first before normalization i Point cloud.

[0010] Specifically, step S2 includes the following steps: For each query point q The KNN algorithm is used to search for the distance to the query point in the preprocessed point cloud. q Recent k 1 neighboring point, calculate k Neighboring points and query points q The average Euclidean distance between : ; in, p j Indicates query point q The j 1 neighboring point; Then query point q Point cloud search radius at the location r q for: ; in, α This is the search radius scaling factor; The larger the value, the higher the query point. q The smaller the local point cloud density at a given location, the better the query point. q Point cloud search radius at the location r q The larger.

[0011] Furthermore, to increase the number of sampling points in regions with high curvature variations and to avoid the search radius being too small due to the dense point cloud in these regions, a density modulation factor is introduced. w ( q ): ; in, μ , σ Each of the entire point cloud The mean and standard deviation; γ As a regulating factor; Then the query point is adjusted q Point cloud search radius at the location for: .

[0012] Specifically, in step S3, the MLP network includes an input layer, multiple fully connected layers connected in sequence, and an output layer. The input layer is used to input the three-dimensional coordinates of the sampling points, and the output layer is used to output the SDF value. The activation function of the MLP network is the Softplus activation function, and the input layer is connected to a certain fully connected layer in the middle by skip connection.

[0013] Furthermore, the loss function of the MLP network is: ; in, L SDF For SDF regression loss, L grad The loss is the gradient regularization loss. These are the hyperparameters of the MLP network; N The total number of point clouds in the training data. The first prediction for the MLP networki SDF values ​​of a point cloud, x i For the first i The three-dimensional coordinates of a point cloud; For the first i The actual SDF value of a point cloud; The first prediction for the MLP network i The gradient value of the SDF value of the point cloud; n i For the first i The normal vector of a point cloud.

[0014] Specifically, in step S4, the Maching Cube algorithm is used to extract the zero isosurface, as shown in the following formula: ; in, f ( q ) represents the sampling points predicted by the MLP network. q SDF value, S The zero isosurface is the surface reconstructed from the input 3D point cloud data.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention dynamically senses the local density characteristics of point cloud data and adaptively adjusts the neighborhood search radius, effectively solving the inherent contradictions faced by traditional fixed-radius search in different density regions. In sparse point cloud regions, it can automatically expand the search range to ensure that a sufficient number of neighborhood point information is obtained, significantly improving the integrity and continuity of the reconstruction and avoiding the generation of holes and breaks; while in dense point cloud regions, it can narrow the search range and focus on more relevant local structures, effectively reducing redundant calculations and noise interference, and improving the efficiency and stability of the algorithm. This adaptability fundamentally improves the robustness of implicit surface reconstruction methods to non-uniform distribution and density changes of input point clouds; (2) This invention introduces a modulation factor related to local curvature changes to specifically weight and adjust the search radius. It can proactively and moderately expand the search radius in high curvature regions, thereby capturing richer geometric context information and effectively enhancing the algorithm's ability to perceive and express complex local geometric structures. This significantly improves the fidelity and structural integrity of the reconstruction results in terms of detailed features, edge sharpness, and complex surface transition regions, overcoming the blurring or distortion problems that may occur in high-frequency geometric features due to simple density adaptation, and ultimately greatly improving the geometric accuracy and visual quality of the overall reconstruction model. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating a high-quality implicit surface reconstruction method based on adaptive search radius according to the present invention. Figure 2 This is a schematic diagram illustrating the principle of the adaptive radius search mechanism in an embodiment of the present invention; Figure 3 This is a schematic diagram of the MLP mesh architecture in an embodiment of the present invention; Figure 4 This is a comparison chart of CD distance evaluation metrics for different algorithms under different 3D models in embodiments of the present invention; Figure 5 This is a comparison chart of HD distance evaluation metrics for different algorithms under different 3D models in embodiments of the present invention; Figure 6 This is a comparison chart of the visualization effects of the three algorithms after reconstruction on three types of models in the embodiments of the present invention. Detailed Implementation

[0018] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] Reference Figure 1 This invention provides a high-quality implicit surface reconstruction method based on adaptive search radius, comprising the following steps: S1, Collect point cloud data of the target surface to be reconstructed, and preprocess the collected point cloud data; S2, dynamically adjust the search radius of the point cloud data according to the point cloud distribution density, and sample the preprocessed point cloud data; S3, input the sampling points into the trained MLP network to predict the SDF value of the sampling points; S4. Based on the predicted SDF values, a surface fitting algorithm is used to extract the zero isosurface.

[0020] Specifically, in step S1, the preprocessing of the collected point cloud data includes: The region of interest is clipped from the raw 3D point cloud data acquired by the camera or other sensors to segment the surface region to be reconstructed, remove background point cloud that is not related to the target surface, reduce data redundancy, and improve the efficiency of subsequent processing. A statistical outlier removal algorithm is used to filter noise in point cloud data, removing outliers caused by measurement errors, thereby improving the overall quality and stability of the data. The filtered point cloud is normalized to a unit sphere, which means that the entire point cloud is translated to the origin and scaled to the range of a unit sphere to ensure the uniformity of the input data in terms of scale.

[0021] Furthermore, the method for noise filtering of point cloud data is as follows: Calculate the first i Point cloud and k The average distance of each neighboring point d i : ; in, p j Indicates the first i Point cloud p i The j 1 neighboring point; like ,but p i These are the outliers that need to be removed. in, μ , σ Each of the entire point cloud d i The mean and standard deviation.

[0022] Furthermore, the method for performing unit sphere normalization on the filtered point cloud is as follows: Translate all point clouds to their geometric center and scale all point clouds to a radius of a unit sphere, such that: ; in, N The total number of point clouds, c This is the geometric center of the point cloud, used to center the point cloud; r The maximum distance from all point clouds to the geometric center is used for scale normalization, and the maximum distance is... r As a scaling factor, it ensures that the normalized point cloud does not exceed the radius of a unit sphere. Represents the normalized i-th i A point cloud, p i The first before normalization i Point cloud.

[0023] After normalization, point cloud data of arbitrary scale and spatial distribution is mapped to a unit sphere with radius 1 centered at the origin. This has advantages such as uniform scale and translation invariance, while significantly improving the consistency and scale standardization of point cloud data, which is beneficial to the stability and generalization ability of neural network training.

[0024] Specifically, in step S2, during the data sampling stage, a local density-aware mechanism of KNN is introduced. This dynamically adjusts the search radius to adapt to point cloud sampling in regions with different density distributions. During density estimation, a KNN (K-Nearest Neighbors) search method is used to estimate the local density of the point cloud. KNN measures the distribution density of neighboring points around the query point to determine the density of the point cloud distribution in that region, which is then used to dynamically adjust the sampling radius of that region. This includes the following steps: For each query point q The KNN algorithm is used to search for the distance to the query point in the preprocessed point cloud. q Recent k 1 neighboring point, calculate k Neighboring points and query points q The average Euclidean distance between : ; in, p j Indicates query point q The j 1 neighboring point; Then query point q Point cloud search radius at the location r q for: ; in, α This is the search radius scaling factor, used to control the overall radius scale and avoid the search radius being too large or too small; The larger the value, the higher the query point. q The smaller the local point cloud density at a given location, the better the query point. q Point cloud search radius at the location r q The larger.

[0025] As can be seen from the above formula, in areas where the point cloud is relatively dense, a smaller sampling radius should be used to ensure the integrity of the reconstruction details in the dense area; while in areas where the point cloud is relatively sparse, a larger sampling radius should be used to avoid insufficient sampling points affecting the estimation quality. Through this CNN-based local density perception mechanism, adaptive modeling of different regional structures can be achieved, thereby improving the accuracy and robustness of the final implicit surface reconstruction.

[0026] After completing the local density estimation based on KNN, although the sampling radius can be adaptively adjusted for point cloud regions with different densities, considering only the density information of the point cloud still has certain limitations. In some regions with drastic curvature changes (such as edges, sharp corners, or feature surfaces), even if the point cloud is relatively dense, the complexity of the local shape may still lead to a decrease in the quality of implicit surface reconstruction. Therefore, it is necessary to introduce a curvature compensation mechanism to further refine the sampling strategy.

[0027] Furthermore, in order to increase the number of sampling points in high curvature variation regions and avoid the implicit surface reconstruction quality deterioration due to the small search radius caused by the dense point cloud in high curvature variation regions, the curvature compensation mechanism is implemented by introducing a density modulation factor. This aims to adjust the local average distance so that even if the point cloud itself is relatively dense in high curvature regions, a relatively larger sampling radius can still be allocated, thereby improving the ability to express neighborhood information. Introducing density modulation factor w ( q ): ; in, μ , σ Each of the entire point cloud The mean and standard deviation; γ As a regulating factor; This factor enhances the weight of high-curvature regions through an exponential function, making the final calculated search radius more reasonable. It participates as a weight term in subsequent adaptive radius calculations, controlling the radius's size variation during sampling and avoiding the limitations of considering point cloud density information alone. This helps improve the overall structural fidelity and robustness of the implicit reconstruction.

[0028] Then the query point is adjusted q Point cloud search radius at the location for: .

[0029] The principle of the adaptive radius search mechanism in this embodiment is as follows: Figure 2 As shown, the curve represents the surface of the target object at a certain local location. For ease of representation, any sampling point in the figure is used. pOnly three neighboring points x1, x2, and x3 are shown. Sampling is estimated based on the density of the point cloud. For example, for the denser point cloud region on the right, a smaller sampling radius R2 is selected to focus on local geometric features; while for the sparser region on the left, a larger sampling radius R1 is selected to ensure the coverage and sampling stability of the neighboring points. At the same time, query points that fail to have neighboring points sampled are directly removed to ensure the stability and integrity of subsequent training.

[0030] Specifically, such as Figure 3 As shown, in step S3, the MLP network includes an input layer, multiple fully connected layers connected in sequence (in this embodiment, there are a total of 8 fully connected layers, each with 512 neurons), and an output layer. The input layer is used to input the three-dimensional coordinates of the sampling points, and the output layer is used to output the SDF value. The activation function of the MLP network is the Softplus activation function. The input layer and one of the middle fully connected layers (the 4th one in this embodiment) are connected by a skip connection to improve expressive power and convergence speed.

[0031] Furthermore, the loss function of the MLP network is: ; in, L SDF For SDF regression loss, L grad The loss is the gradient regularization loss. These are the hyperparameters of the MLP network; N The total number of point clouds in the training data. The first prediction for the MLP network i SDF values ​​of a point cloud, x i For the first i The three-dimensional coordinates of a point cloud; For the first i The actual SDF value of a point cloud; The first prediction for the MLP network i The gradient value of the SDF value of the point cloud; n i For the first i The normal vector of a point cloud.

[0032] Specifically, in step S4, the Maching Cube algorithm is used to extract the zero isosurface, as shown in the following formula: ; in, f ( q ) represents the symbolic distance function learned by the MLP network, which indicates the sampling points predicted by the MLP network. q SDF value,S The zero-saturation surface is the surface reconstructed from the input 3D point cloud data. A positive SDF value for a query point indicates it's on the outer edge of the surface; a negative SDF value indicates it's on the inner edge. The set of points from all point cloud objects with an SDF value of 0 represents the surface of the point cloud object to be reconstructed. Applying the MachingCube algorithm to this set of surface points calculated by the MLP network generates the desired reconstructed surface.

[0033] To verify the effectiveness of this invention, this embodiment evaluates the CD distance and HD distance of reconstruction results from selected models in the Stanford database, and compares and analyzes the experimental results of different 3D reconstruction algorithms. The comparison algorithms used in this embodiment are the existing surface adaptive learning algorithm and the neural implicit moving least squares algorithm. The CD distance measures the average point-to-point distance between the reconstructed surface and the real surface, and can reflect the overall fitting accuracy well; while the HD distance measures the maximum distance in the worst case, used to evaluate the extreme deviation of the reconstructed surface at local details. The two indicators complement each other and can comprehensively reflect the performance of the reconstruction algorithm in terms of accuracy and robustness.

[0034] like Figure 4 As shown, Figure 4 The comparison results of different algorithms for evaluating CD distance metrics under different 3D models are shown. Figure 4 As can be seen, the 3D surface reconstruction algorithm of this embodiment achieved excellent error indices in the CD distance test for all types of 3D models. The CD indices of all three types of models decreased, indicating that the generated results are geometrically closer to the real mesh, achieving more effective mesh completion. Among them, the CD distance of the rabbit model decreased by 27.3%, the CD distance of the armadillo model decreased by 16.6%, and the CD distance of the Happy Buddha model decreased by 2.6%. The reason for this is that the overall structure of the Happy Buddha model is relatively rounded and the curvature changes gently, so the effect of the adaptive radius is not as significant as in other high curvature objects. The other two models showed better improvement in this index after the improvement.

[0035] like Figure 5 As shown, Figure 5 The comparison results of different algorithms for evaluating HD distance metrics under different 3D models are shown. Figure 5 As can be seen, the 3D surface reconstruction algorithm in this embodiment reduces the HD index for two of the three models: the rabbit model (53.1%) and the armadillo model (55.3%), both achieving good results. However, the improvement is not significant for the Happy Buddha model due to its higher overall geometric complexity, numerous self-occluding regions, and missing point clouds.

[0036] To more intuitively demonstrate the performance advantages of the algorithm of this invention, this embodiment visualizes the reconstruction results of three types of models and analyzes and compares the visualization results. The visualization effects of the three algorithms on the three types of models are compared as follows: Figure 6 As shown, Figure 6 In the diagram, the point cloud represents the original point cloud of the three types of models, and the real mesh represents the real surface mesh corresponding to the original point cloud. This is used to compare and evaluate the surface reconstruction performance of the 3D surface reconstruction algorithms. Figure 6 As can be seen, the 3D surface reconstruction algorithm of this invention accurately preserves the slender structure and edge contour of the ears in the rabbit model without any breakage or blurring, and the texture of the body fur is also improved compared with existing algorithms. In the armadillo model, the texture of the chest decoration is relatively clearer, and the ears are also enhanced. As for the complex Happy Buddha model, the facial features, abdominal contours, and high-frequency details such as beads are effectively restored, demonstrating the powerful ability of the method of this invention to handle complex topology and dense details.

[0037] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A high-quality implicit surface reconstruction method based on adaptive search radius, characterized in that, Includes the following steps: S1, Collect point cloud data of the target surface to be reconstructed, and preprocess the collected point cloud data; S2, dynamically adjust the search radius of the point cloud data according to the point cloud distribution density, and sample the preprocessed point cloud data; S3, input the sampling points into the trained MLP network to predict the SDF value of the sampling points; S4. Based on the predicted SDF values, a surface fitting algorithm is used to extract the zero isosurface.

2. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 1, characterized in that, In step S1, the preprocessing of the collected point cloud data includes: The region of interest is cropped from the original 3D point cloud data to remove background point clouds that are irrelevant to the target surface; A statistical outlier removal algorithm is used to filter noise in point cloud data. The filtered point cloud is then normalized to a unit sphere.

3. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 2, characterized in that, The method for noise filtering of point cloud data is as follows: Calculate the first i Point cloud and k The average distance of each neighboring point d i : ； in, p j Indicates the first i Point cloud p i The j 1 neighboring point; like ,but p i These are the outliers that need to be removed. in, μ , σ Each of the entire point cloud d i The mean and standard deviation.

4. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 2, characterized in that, The method for performing unit sphere normalization on the filtered point cloud is as follows: Translate all point clouds to their geometric center and scale all point clouds to a radius of a unit sphere, such that: ； in, N The total number of point clouds, c The geometric center of the point cloud, r The maximum distance from all point clouds to the geometric center. Represents the normalized i-th i A point cloud, p i The first before normalization i Point cloud.

5. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 1, characterized in that, Step S2 includes the following steps: For each query point q The KNN algorithm is used to search for the distance to the query point in the preprocessed point cloud. q Recent k 1 neighboring point, calculate k Neighboring points and query points q The average Euclidean distance between : ； in, p j Indicates query point q The j 1 neighboring point; Then query point q Point cloud search radius at the location r q for: ； in, α This is the search radius scaling factor; The larger the value, the higher the query point. q The smaller the local point cloud density at a given location, the better the query point. q Point cloud search radius at the location r q The larger.

6. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 5, characterized in that, To increase the number of sampling points in regions with high curvature variations and to avoid an excessively small search radius due to dense point cloud density in these regions, a density modulation factor is introduced. w ( q ): ； in, μ , σ Each of the entire point cloud The mean and standard deviation; γ As a regulating factor; Then the query point is adjusted q Point cloud search radius at the location for: 。 7. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 1, characterized in that, In step S3, the MLP network includes an input layer, multiple fully connected layers connected in sequence, and an output layer. The input layer is used to input the three-dimensional coordinates of the sampling points, and the output layer is used to output the SDF value. The activation function of the MLP network is the Softplus activation function, and the input layer is connected to a certain fully connected layer in the middle by skip connection.

8. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 7, characterized in that, The loss function of the MLP network is: ； in, L SDF For SDF regression loss, L grad For gradient regularization loss; These are the hyperparameters of the MLP network; N The total number of point clouds in the training data. The first prediction for the MLP network i SDF values ​​of a point cloud, x i For the first i The three-dimensional coordinates of a point cloud; For the first i The actual SDF value of a point cloud; The first prediction for the MLP network i The gradient value of the SDF value of the point cloud; n i For the first i The normal vector of a point cloud.

9. The high-quality implicit surface reconstruction method based on adaptive search radius as described in claim 1, characterized in that, In step S4, the Maching Cube algorithm is used to extract the zero isosurface, as shown in the following formula: ； in, f ( q ) represents the sampling points predicted by the MLP network. q SDF value, S The zero isosurface is the surface reconstructed from the input 3D point cloud data.

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