保特征的点云骨架提取算法

三维模型的骨架提取是计算机图形学中一个重要的研究方向。对于有噪声的点云模型，曲线骨 架提取的难点在于保持正确的拓扑结构以及良好的中心性；对于无噪声的点云模型，曲线骨架提取的难点在于 对模型细节特征的保留。目前主流的点云骨架提取方法往往无法同时解决这 2 个难点。算法在最优传输理论的 基础之上结合聚类的思想，将点云骨架提取的问题转化为一个最优化问题。首先使用最优传输得到原始点云与 采样点云之间的传输计划。然后使用聚类的思想将原始点云进行分割，采样点即成为了簇的中心。接着通过簇 与簇之间的调整与合并减少聚类个数，优化聚类结果。最后通过迭代的方式得到粗糙的骨架并使用插点操作进 行优化。大量实验结果表明，该算法在有噪声与无噪声的三维点云模型上均能提取出质量良好的曲线骨架并保 留模型的特征。

Feature-preserving skeleton extraction algorithm for point clouds

The skeleton extraction of 3D models is one of the most important research topics in computer graphics. For point clouds with noise, the difficulty of curve skeleton extraction lies in maintaining the correct topology and good centrality. For point clouds without noise, the difficulty of curve skeleton extraction lies in the preservation of the detail features of the model. The current mainstream point clouds skeleton extraction methods usually cannot solve these two difficulties at the same time. The proposed algorithm combined the idea of clustering on the basis of the optimal transport theory, and transformed the problem of point clouds skeleton extraction into an optimization problem. Firstly, the optimal transport plan between the original point cloud and the sampled point cloud was computed. The original point cloud was segmented by clustering and the sampling points served as the center of the clusters. Then the number of clusters was reduced and the clustering results were optimized by adjusting and merging between clusters. Finally, after being obtained by the iterative method, the rough skeleton was optimized by interpolation operation. A large number of experimental results show that the proposed algorithm can extract good-quality curve skeletons and retain the features of the model on both noisy and noise-free 3D point clouds.