散乱点云数据曲率估计方法

针对带有强噪声离散点云数据曲率计算问题，提出一种基于稳健统计的曲率估计方法。首先，用一个二次曲面拟合三维空间采样点处的局部形状；其次，随机地选择该采样点邻域内的子集，多次执行这样的拟合过程，通过变窗宽的最大核密度估计，就得到了最优拟合曲面；最后，将采样点投影到该曲面上，计算投影点曲率信息，就得到采样点曲率。实验结果表明，所提方法对噪声和离群点是稳健的，特别是随着噪声方差的增大，要明显好于传统的抛物拟合方法。

Curvature estimation for scattered point cloud data

For resolving the problem of curvature calculation for scattered point cloud data with strong noise, a robust statistics approach to curvature estimation was presented. Firstly the local shape at a sample point in 3D space was fitted by a quadratic surface. In addition,the fitting was performed at multiple times with randomly sampled subsets of points, and the best fitting result evaluated by variable-bandwidth maximum kernel density estimator was obtained. At last, the sample point was projected onto the best fitted surface and the curvatures of the projected point was estimated. The experimental results demonstrate that the proposed method is robust to noise and outliers. Especially with increasing noise variance, the proposed method is significantly better than the traditional parabolic fitting method.