The α-shape algorithm is not suitable for surface reconstruction of scattered and non-uniformly sampled points. In order to solve the problem, an improved surface reconstruction algorithm with adaptive α-shape based on Local Feature Size (LFS) of point cloud data was proposed. Firstly, Medial Axis (MA) of the surface was approximated by the negative poles computed by k-nearest neighbors of sampled points. Secondly, the LFS of sampled points was calculated by the approximated MA, and the original point clouds were unequally simplified based on LFS. Finally, the surface was adaptively reconstructed based on the radius of circumscribed ball of triangles and the corresponding α value. In the comparison experiments with α-shape algorithm, the proposed algorithm could effectively and reasonably reduce the number of point clouds, and the simplification rate of point clouds achieved about 70%. Simultaneously, the reconstruction result were obtained with less redundant triangles and few holes. The experimental results show that the proposed algorithm can adaptively reconstruct the surface of non-uniformly sampled point clouds.

To satisfy ε-sample condition for Delaunay-based triangulation surface reconstruction algorithm, a Delaunay-based non-uniform sampling algorithm for noisy point clouds was proposed. Firstly, the surface Medial Axis (MA) was approximated by the negative poles computed by k-nearest neighbors Voronoi vertices. Secondly, the Local Feature Size (LFS) of surface was estimated with the approximated medial axis. Finally, combined with the Bound Cocone algorithm, the unwanted interior points were removed. Experiments show that the new algorithm can simplify noisy point clouds accurately and robustly while keeping the boundary features well. The simplified point clouds are suitable for Delaunay-based triangulation surface reconstruction algorithm.