Abstract: To efficiently simplify point cloud by multi-resolution, firstly, uniform grids were used to represent the spatial topology relationship of point cloud and calculate the k-nearest neighbors for each data point. Then normal vectors of data points were estimated by constructing covariance matrix, and normal vectors were directed to the outside of the point cloud. Finally, the formulation for measuring the importance of data point was achieved according the effect of this point on eigenvalues spectrum of the Laplace-Beltrami operator, and it was associated with the k-nearest neighbors of this point and normal vectors, and then multi-resolution simplification of point cloud was realized by changing the value of control factor. The experimental result shows that this algorithm has high simplification rate, fast speed, strong stability, and maitains the small detailed information of point cloud.

Key words: point cloud, k-nearest neighbor, normal vector, measuring formulation, multi-resolution simplification

摘要： 为了有效地多分辨率简化点云模型,首先,采用均匀栅格法建立点云模型的拓扑关系,计算每个数据点的k邻域;然后,通过建立点云模型中数据点的协方差矩阵求得这些点的法向量,并且进行法向重定向,使所有法向量的方向都指向点云模型的外部;最后,通过衡量数据点对Laplace-Beltrami算子特征值频谱的影响,得到与数据点k邻域及其法向量相关的量化该点重要性的度量公式,随后调节控制因子的取值,实现点云模型的多分辨率简化。实验结果表明,该算法具有简化率高、保留点云模型的微小细节特征信息、简化速度快、稳定性强的特点。

关键词: 点云, k邻域, 法向量, 度量公式, 多分辨率简化