Abstract: For solve the problem that the current algorithms for estimating normals of point cloud are difficult to achieve a trade-off between accuracy and robustness of estimation results, a method for normal estimation based on local isomorphic surface is proposed. In this method, a set of neighborhood points of the target sample point is taken as the local sample to reconstruct the surface, and the local mesh surface interpolated in the sampling point set and isomorphic with the sampling surface topology is obtained. The results of Gauss mapping in the local area are clustered to obtain the isotropic neighborhood of the target sample point. Based on the regularity of the patches and the geodesic distance from the patches to the target sample point, the weighted mean of the normal of the patches in the isotropic neighborhood of the target sample point is determined, and the result obtained is taken as the normal estimation result of the target sample point. The experimental results show that the normal estimation deviation of more than 98% points can be guaranteed to be less than under the condition of point cloud data SNR of 40 dB. The proposed algorithm can robustly deal with the problem of normal estimation of scattered point clouds with noise and non-uniform sampling. It can also accurately estimate the normal of surface samples in sharp feature areas and has high computational efficiency.

Key words: neighborhood of sample point, topological isomorphism, normal estimation, local reconstruction, Gaussian mapping