Normal estimation of point cloud based on sub-neighborhood clustering

The normal vector is a basic attribute of point clouds and it has important applications in point clouds matching, surface reconstruction, feature line extraction and many other domains. Traditional normal vector estimation methods have poor robustness and are vulnerable to complex features, noise and outliers. Recently, convolutional neural network (CNN) has made great progress in normal vector estimation. However, the algorithm needs high hardware configuration and the efficiency becomes low on devices without Graphic Processing Unit (GPU). To address the problem, we propose a normal vector estimation algorithm combining the principal component analysis (PCA) and CNN. Firstly, with Surface Variation (SV) applied, the point clouds is divided into two subsets: the feature region and the flat region. Then, the PCA algorithm is adopted in the flat region while the CNN method is adopted in the region close to complex features. Meanwhile, the structure of an existing CNN is optimized to reduce the running time and improve the estimation accuracy. Experiments show that our method achieves good results in dealing with complex features and noise. Also, compared with CNN with the original network structure, the algorithm effectively reduces the computation time and improves the accuracy of normal vector estimation.

An adaptive normal estimation method for scanned point clouds with sharp features

The normal vector estimation of the large-scale scattered point cloud (LSSPC) plays an important role in point-based shape editing. However, the normal vector estimation for LSSPC cannot meet the great challenge of the sharp increase of the point cloud that is mainly attributed to its low computational efficiency. In this paper, a novel, fast method-based on bi-linear interpolation is reported on the normal vector estimation for LSSPC. We divide the point sets into many small cubes to speed up the local point search and construct interpolation nodes on the isosurface expressed by the point cloud. On the premise of calculating the normal vectors of these interpolated nodes, a normal vector bi-linear interpolation of the points in the cube is realized. The proposed approach has the merits of accurate, simple, and high efficiency, because the algorithm only needs to search neighbor and calculates normal vectors for interpolation nodes that are usually far less than the point cloud. The experimental results of several real and simulated point sets show that our method is over three times faster than the Elliptic Gabriel Graph-based method, and the average deviation is less than 0.01 mm.

A novel algorithm is proposed for extracting sharp features automatically from scanned 3D data of man-made CAD-like objects. The input of our method consists of a mesh or an unstructured point cloud that is captured on the object surface. First, the vector between a given point and the centroid of its neighborhood at a given scale is projected on the normal vector and called the ‘projected distance’ at this point. This projected distance is calculated for every data point. In a second stage, Otsu's method is applied to the histogram of the projected distances in order to select the optimal threshold value, which is used to detect potential sharp features at a single scale. These two stages are applied iteratively with the other incremental scales. Finally, points recorded as potential features at every scale are marked as valid sharp features. The method has many advantages over existing methods such as intrinsic simplicity, automatic selection of threshold value, accurate and robust detection of sharp features on various objects. To demonstrate the robustness of the method, it is applied on both synthetic and real 3D data of point clouds and meshes with different noise levels.

The accurate segmentation of roof point cloud will directly affect the quality of building model reconstruction. Because of the complexity of building roof structure, the uneven distribution of point cloud density obtained by lidar, and the interference of external environment, it is very difficult to accurately segment the point cloud on the roof. In order to improve the quality of point cloud segmentation, this paper proposes a joint optimization method of region growth and RANSAC for Airborne LIDAR point cloud segmentation. Firstly, the point cloud is voxeled, and the normal vector and curvature of the point cloud are calculated based on principal component analysis (PCA). After setting the correlation threshold, the region growing algorithm is used to extract the initial reliable patch. Then, RANSAC algorithm is used to regularize the irregular or deviation areas in the extracted patch, optimize and set new roof surface parameters. Finally, for the unclassified points, the Euclidean distance to each plane is calculated. According to the minimum distance principle and the set distance threshold, they are classified to the corresponding roof surface, and the segmentation results are refined. Tests on several representative building point clouds show that this method significantly improves the accuracy, recall and overall accuracy of roof point cloud segmentation, and provides high-quality basic data for building 3D model reconstruction

For the depth data of a single time of flight (TOF) sensor, the existing detection can determine the safe distance and issue a safety alarm, but it cannot be combined with the robot attitude. Based on this, a TOF sensor based Principal component analysis (PCA) normal vector estimation method is proposed in this paper, which transforms the depth data into a three-dimensional point cloud, and uses the PCA method to calculate the normal vector of the point cloud. It lays a foundation for real-time attitude adjustment of future robots.

A 3D object can be recovered from scanned point data, which requires accurate estimating normal directions of the object surface from the cloud data. Many point cloud processing algorithms rely on the accurate normal as input to generate an accurate 3D surface model. The neighborhood of a data point in its smooth region can be well approximated by a plane. However, the neighborhood of a feature point employed for the normal estimation is isotropic which would enclose points belonging to different surface patches across the sharp feature. In this paper, isotropic neighborhoods are segmented to search anisotropic neighborhoods for the accurate normal estimation. Normals and candidate feature points are first estimated by the principal component analysis (PCA) method. Neighborhoods of the feature point are then mapped into a Gaussian image. A k-means clustering algorithm is then used for the Gaussian image to identify an anisotropic sub-neighborhood for the data point. The normal of the candidate feature point is finally estimated by the anisotropic neighborhood with the PCA method. The proposed method can accurately estimate normal directions while preserving sharp features of the object surface. Applications have demonstrated the effectiveness of the proposed method.

A novel sharp features extraction method is proposed in this paper. First, we calculate the displacement between the point and its local weighted average position and we label the point with salient this value as the candidate sharp feature points and we estimate the normal direction of those candidate sharp feature points by means of local PCA methods. Then we refine the normal estimated by inferring the orientation of the points near the candidate sharp feature region and bilateral filtering in the normal field of point clouds. At last we project the displacement between point and its local weighted average position along the direction of normal .We use value of this projection as the criteria of whether a point can be labeled as sharp feature. The extracted discrete sharp feature points are represented in the form of piecewised B-Spline lines. Experiment on both real scanner point clouds and synthesized point clouds show that our method of sharp features extraction are simple to be implemented and efficient for both space and time overhead as well as it robust to the noise ,outlier and un even sample witch are inherent in the point clouds.

Sharp features of 3D point clouds play an important role in many geometric computations and modeling application. In this paper, a novel modified Partition of Unity (PoU) Based Sharp feature extraction algorithm is proposed, which is directly operated on discrete point clouds. For every point in target point cloud, spherical neighborhood with radius δ is acquired with the help of KD-Tree and weighted average position of points within the δ -neighborhood is computed using modified PoU method. Distance which is the projection of the displace between original point and its Weighted average position along normal direction is defined as the criteria for a point belong to sharp feature or crease line. Experiments on both synthetic data and practical scanner point clouds indicate that our algorithm are both efficient and effective to the task of sharp feature extraction from point clouds. Our method is easy to be implemented and more sensitive to sharp features as well as its low computational complexity.

In the acquisition process of 3D cultural relics, it is common to encounter noise. To facilitate the generation of high-quality 3D models, we propose an approach based on graph signal processing that combines color and geometric features to denoise the point cloud. We divide the 3D point cloud into patches based on self-similarity theory and create an appropriate underlying graph with a Markov property. The features of the vertices in the graph are represented using 3D coordinates, normal vectors, and color. We formulate the point cloud denoising problem as a maximum a posteriori (MAP) estimation problem and use a graph Laplacian regularization (GLR) prior to identifying the most probable noise-free point cloud. In the denoising process, we moderately simplify the 3D point to reduce the running time of the denoising algorithm. The experimental results demonstrate that our proposed approach outperforms five competing methods in both subjective and objective assessments. It requires fewer iterations and exhibits strong robustness, effectively removing noise from the surface of cultural relic point clouds while preserving fine-scale 3D features such as texture and ornamentation. This results in more realistic 3D representations of cultural relics.

To address the challenges of automatic detection caused by the variation of surface normal vectors in automotive steering knuckles, an automatic detection method based on ultrasonic phased array technology is herein proposed. First, a point cloud model of the workpiece was constructed using ultrasonic distance measurement, and Gaussian-weighted principal component analysis was used to estimate the normal vectors of the point cloud. By utilizing the normal vectors, water layer thickness during detection, and the incident angle of the sound beam, the probe pose information corresponding to the detection point was precisely calculated, ensuring the stability of the sound beam incident angle during the detection process. At the same time, in the trajectory planning process, piecewise cubic Hermite interpolation was used to optimize the detection trajectory, ensuring continuity during probe movement. Finally, an automatic detection system was set up to test a steering knuckle specimen with surface circumferential cracks. The results show that the point cloud data of the steering knuckle specimen, obtained using phased array ultrasound, had a relative measurement error controlled within 1.4%, and the error between the calculated probe angle and the theoretical angle did not exceed 0.5°. The probe trajectory derived from these data effectively improved the B-scan image quality during the automatic detection of the steering knuckle and increased the defect signal amplitude by 5.6 dB, demonstrating the effectiveness of this method in the automatic detection of automotive steering knuckles.

This study is interested in the normal calculation of artillery cradle. When the beam axis of ultrasonic phased array probe cannot detect the workpiece surface vertically, the detection result is usually inaccurate. Thus, in order to determine the normal of the surface to be detected, a method based on visual point cloud to calculate the normal of artillery cradle is proposed in this paper. The proposed method solves two key problems. One is to sparse the point cloud while preserving the tiny information on the surface. A mesh division method along the uv direction is proposed. The disordered point cloud data in 3D space are connected into regular polygon meshes. While establishing the local relationship of point cloud data, it also maintains the overall integrity of point cloud data. The other is to calculate the normal vector of the point cloud. The local plane fitting method based on the least square method calculates the normal at a point of the point cloud. At this time, the calculated normal are nondirective. When there is no abrupt curvature change near the calculated point cloud, the direction of the normal is determined based on the same slope at two adjacent points. The calculated point cloud normal vector is compared with the actual normal vector of the mathematical model. The maximum deviation between the theoretical value and the actual value of the normal vector is 0.465°, and the average deviation is 0.302°. The experimental results show that the proposed method can be used to detect the actual normal of artillery cradle.

Complete swept volume generation, Part I: Swept volume of a piecewise C 1-continuous cutter at five-axis milling via Gauss map

The traditional mapping and surveying approach as a long-established practice in identifying rock mass discontinuities comes with various limitations. Remote sensing and surveying techniques mitigate those limitations and can quickly capture accurate 3D point cloud data. An automatic workflow is presented to extract the discontinuity planes from highly irregular rock mass surfaces captured in point cloud data. The point cloud is down sampled with a voxelization technique and a k-nearest neighbor search used through a hybrid approach, considering the distance and the number of neighbor points. The normal vectors are estimated and then used in a mean-shift clustering algorithm. The obtained orientation results for the discontinuity planes are compared with similar results in the literature. The effect of down sampling size is considered to investigate the sensitivity of the results to the density of the point cloud. A well-studied point cloud dataset representing an irregular rock mass is used in this work.

Robust normal estimation for point clouds with sharp features