Point cloud fusion method and system based on Riemannian geometry constraints

Abstract

The present invention discloses a point cloud fusion method and system based on Riemannian geometry constraints, which reads input point clouds, calculates voxel resolution, meshes voxelization, hashes neighboring voxels for searching, searches for objects to be fused by using Wasserstein distance, and calculates the optimal transmission scheme by network simplex, and finally utilizes Riemannian geometry constraint optimization to maximize the use of local geometric characteristics of point clouds to significantly improve the point cloud fusion output accuracy; through the point cloud fusion method and system, high-precision three-dimensional models can be obtained, which solves the problem of insufficient three-dimensional reconstruction accuracy under the condition of limited precision and limited resolution sensor data input, and has important application value in multiple application fields such as cultural relics digitization, advanced medical treatment, automatic driving, virtual reality, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional reconstruction, and in particular to a point cloud fusion method and system based on Riemannian geometry constraints. Background Art

[0002] 3D reconstruction has become the main supporting technology for many application fields such as cultural relics digitization, advanced medical care, autonomous driving, virtual reality, etc. The development of the above fields is restricted by the accuracy of 3D reconstruction models, and high-precision 3D models often rely on high-precision, high-resolution sensors; at the same time, the high cost of high-precision, high-resolution sensors limits the application and popularization of 3D reconstruction in various fields; how to reconstruct high-precision 3D models under the condition of limited sensor accuracy and resolution is a difficult problem and challenge that needs to be solved urgently.

[0003] Point cloud fusion is a key step to improve the accuracy of 3D models. Computational fusion of multiple sampled point clouds can effectively reduce sensor noise and computational error interference. Currently, traditional 3D reconstruction methods use weighted averaging of reprojected nearest neighbor points in the point cloud fusion step, or average the nearest points after iterative closest point (ICP) calculation between the source point cloud and the point cloud to be fused.

[0004] Due to the limitations of current technology, the following bottlenecks still exist in the fusion process:

[0005] 1. The reprojection nearest neighbor weighted average method relies on 3D to 2D reprojection. The projection accuracy is limited by the sensor's internal calibration parameters and cannot be applied to some lidar sensors that directly output point clouds.

[0006] 2. The iterative closest point algorithm is an iterative algorithm for global registration. The calculation result ignores the local geometric characteristics, resulting in the loss of local geometric details after fusion;

[0007] 3. The current algorithm only considers point-to-point proximity and ignores important local geometric information such as curvature. Summary of the invention

[0008] In view of the above problems, the present invention provides a point cloud fusion method and system based on Riemannian geometry constraints. The technical solution of the present invention is:

[0009] 1. Read the source point cloud and the point cloud to be fused;

[0010] 2. Calculate the average point radius of the source point cloud and the point cloud to be fused respectively, and take the maximum average point radius of the two as the voxel resolution;

[0011] 3. Use the voxel resolution obtained in 2. to voxel-grid the source point cloud and the point cloud to be fused, calculate the variance and mean of each voxel, and use a hash table to store the voxel grid;

[0012] 4. Each voxel grid in the point cloud to be fused uses a hash function to quickly search for the corresponding neighboring voxel grid in the source point cloud. If the search returns empty, all points in the voxel grid are retained in the output target point cloud. If the search returns not empty, proceed to the next step.

[0013] 5. The point cloud voxel grid to be fused 4. Find several neighboring voxel grids returned and calculate the Wasserstein distance respectively, and take all the points in the nearest voxel grid as the objects to be fused;

[0014] 6. Calculate the optimal transmission scheme between the points in the voxel grid of the point cloud to be fused and the objects to be fused in 5. by using the network simplex method;

[0015] 7. Under the constraints of Riemannian geometry minimum Gaussian curvature and minimum mean curvature, iterative optimization calculation fusion results are output to the target point cloud;

[0016] 8. Repeat 4-7 for each voxel grid in the fused point cloud, and finally output the target point cloud. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a point cloud fusion method and system flow chart based on Riemannian geometry constraints of the present invention. DETAILED DESCRIPTION

[0018] The technical content of the present invention is further described below in conjunction with specific implementation:

[0019] 1. Read the source point cloud And the point cloud to be fused where s i , t j are the source point cloud S and the spatial coordinates of the points in the point cloud T to be fused;

[0020] 2. Calculate the average point radius r of the source point cloud S and the point cloud to be fused T respectively s , r t , for each point of radius r i , the radius r of all points in the world is obtained by averaging the distances from the 50 nearest neighbors of the point to the point i Take the average to get the average point radius of the point cloud

[0021]

[0022] Where n and m are the number of point clouds of the source point cloud S and the point cloud T to be fused, respectively. The maximum average point radius of the two is used as the voxel resolution r = max{r s , r t};

[0023] 3. Use the voxel resolution r obtained in 2. to voxel-grid the source point cloud S and the point cloud to be fused T respectively, and calculate the variance ∑ and mean m of each voxel, and use a hash table to store the voxel grid;

[0024] 4. Each voxel grid in the point cloud to be fused uses a hash function to quickly search for the corresponding neighboring voxel grid in the source point cloud. If the search returns empty, all points in the voxel grid are retained in the output target point cloud. If the search returns not empty, proceed to the next step.

[0025] 5. The point cloud voxel grid to be fused calculates the Wasserstein distance for each of the adjacent voxel grids returned in 4. The Wasserstein distance between Gaussian distributions is defined as follows:

[0026]

[0027] Where m is the mean, ∑ is the covariance matrix, and tr is the trace of the matrix; all points in the voxel grid with the closest Wasserstein distance are taken as the objects to be fused;

[0028] 6. Calculate the optimal transmission scheme between the points in the voxel grid of the point cloud to be fused and the objects to be fused in 5. by using the network simplex method;

[0029]

[0030] where w i is the coordinate of the fused point, α is 7. The fusion parameter to be optimized, s i , t j are the source point cloud S and the point space coordinates in the point cloud T to be fused, respectively. is the optimal transmission scheme solved by the network simplex method;

[0031] 7. Gaussian curvature is defined as k 0 ·k 1 , the mean curvature is defined as (k 0 +k 1 ) / 2,k 0 , k 1 is the principal curvature of the surface represented by the voxel grid; under the constraints of the minimum Gaussian curvature and the minimum mean curvature of Riemannian geometry, it is iteratively optimized according to formula (4), and the fusion result is calculated according to formula (3) and output to the target point cloud;

[0032]

[0033] 8. Repeat 4-7 for each voxel grid in the fused point cloud, and finally output the target point cloud.

Claims

1. A point cloud fusion method based on Riemannian geometry constraints, comprising the following steps: 1) Read the source point cloud and the point cloud to be fused; 2) Calculate the average point radius of the source point cloud and the point cloud to be fused respectively, and take the maximum average point radius of the two as the voxel resolution; 3) The source point cloud and the point cloud to be fused are respectively voxel-meshed at the voxel resolution obtained in 2), and the variance and mean of each voxel are calculated, and the voxel grid is stored in a hash table; 4) Each voxel grid in the point cloud to be fused uses a hash function to quickly search for the corresponding neighboring voxel grid in the source point cloud. If the search returns empty, all points in the voxel grid are retained in the output target point cloud. If the search returns not empty, proceed to the next step; 5) The voxel grid of the point cloud to be fused is matched with the neighboring voxel grids returned in 4) and the Wasserstein distance is calculated respectively, and all the points in the voxel grid with the closest distance are taken as the objects to be fused; 6) Calculating the optimal transmission scheme between the points in the voxel grid of the point cloud to be fused and the objects to be fused in 5) by using the network simplex method; 7) Under the constraints of Riemannian geometry minimum Gaussian curvature and minimum mean curvature, iterative optimization calculation fusion results are output to the target point cloud; 8) Repeat 4)-7) for each voxel grid in the fused point cloud, and finally output the target point cloud.

2. The point cloud fusion method based on Riemannian geometry constraints according to claim 1, It is characterized in that In the step 2), the voxel resolution may be adaptively selected by calculating the average point radius of the source point cloud and the point cloud to be fused.

3. The point cloud fusion method based on Riemannian geometry constraints according to claim 1, It is characterized in that In the step 3), the voxel grid may be stored in a hash table, and the voxel grid includes the voxel mean, variance, and point information.

4. The point cloud fusion method based on Riemannian geometry constraints according to claim 1, It is characterized in that In step 4), each voxel grid in the point cloud to be fused can quickly search for an adjacent voxel grid in the corresponding source point cloud through a hash function.

5. The point cloud fusion method based on Riemannian geometry constraints according to claim 1, It is characterized in that In step 5), the nearest voxel grid can be selected by calculating the Wasserstein distance to obtain the object to be fused.

6. The point cloud fusion method based on Riemannian geometry constraints according to claim 1, It is characterized in that In step 6), the optimal transmission scheme between the objects to be fused may be calculated by the network simplex method.

7. The point cloud fusion method based on Riemannian geometry constraints according to claim 1, It is characterized in that In the step 7), the fusion result is calculated by iterative optimization under the constraints of minimum Gaussian curvature and minimum mean curvature.

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