A Method of Curve Reconstruction Based on Point Cloud Clustering and PCA
Abstract
:1. Introduction
1.1. Context
1.2. Analysis of Existing Methods and Research Objectives
- PCPCA is proposed to find the projection line and main direction of each cluster, and -principle is adopted to remove the outliers.
- For complex point clouds with self-intersection, using the main direction of each cluster, we can divide all main control points into two groups and sort the points in groups.
- The method proposed in this paper has wider application fields than state-of-the-art methods, including planar point cloud curve reconstruction, time series data fitting, image refinement and image edge smoothing.
- In the curve reconstruction of high-density point cloud, our method takes 20% of the time of classical methods (such as MLS).
2. K-Means Clustering
2.1. Classical K-Means Clustering
2.2. Improved K-Means Clustering (K-Means++)
3. Point Cloud Principal Component Analysis (PCPCA)
3.1. The Main Line and the Main Control Point of Points Cloud
- (1)
- The abscissa and ordinate of each point in the point cloud are used to form two -dimensional columnvectors and ;
- (2)
- A -order square matrix is obtained by using the formula , and eigenvalues and eigenvectors of are found;
- (3)
- The eigenvector corresponding to the maximum eigenvalue is recorded as , and the projection vector set is obtained from the formula .
3.2. Processing of Point Cloud Outliers
4. The Subdivision of the Main Control Points
5. Numerical Examples
5.1. Curve Fitting of the Planar Point Clouds
5.2. Curve Reconstruction of the Complex Point Clouds
5.3. Curve Reconstruction of the Time Series
5.4. Image Refinement
5.5. Image Edge Smoothing
6. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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The Number of Clusters | 10 | 12 | 14 | 16 | 18 | 20 |
---|---|---|---|---|---|---|
K-means | 0.1318 | 0.1145 | 0.1019 | 0.0929 | 0.0907 | 0.0864 |
K-means++ | 0.1315 | 0.1136 | 0.1017 | 0.0927 | 0.0906 | 0.0853 |
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Peng, K.; Tan, J.; Zhang, G. A Method of Curve Reconstruction Based on Point Cloud Clustering and PCA. Symmetry 2022, 14, 726. https://doi.org/10.3390/sym14040726
Peng K, Tan J, Zhang G. A Method of Curve Reconstruction Based on Point Cloud Clustering and PCA. Symmetry. 2022; 14(4):726. https://doi.org/10.3390/sym14040726
Chicago/Turabian StylePeng, Kaijun, Jieqing Tan, and Guochang Zhang. 2022. "A Method of Curve Reconstruction Based on Point Cloud Clustering and PCA" Symmetry 14, no. 4: 726. https://doi.org/10.3390/sym14040726
APA StylePeng, K., Tan, J., & Zhang, G. (2022). A Method of Curve Reconstruction Based on Point Cloud Clustering and PCA. Symmetry, 14(4), 726. https://doi.org/10.3390/sym14040726