Robust and Fast Normal Mollification via Consistent Neighborhood Reconstruction for Unorganized Point Clouds.

This paper introduces a robust normal estimation method for point cloud data that can handle both smooth and sharp features. Our method is based on the inclusion of neighborhood recognition into the normal mollification process in the neighborhood of the current point: First, the point cloud surfaces are assigned normals via a normal estimator of robust location (NERL), which guarantees the reliability of the smooth region normals, and then a robust feature point recognition method is proposed to identify points around sharp features accurately. Furthermore, Gaussian maps and clustering are adopted for feature points to seek a rough isotropic neighborhood for the first-stage normal mollification. In order to further deal with non-uniform sampling or various complex scenes efficiently, the second-stage normal mollification based on residual is proposed. The proposed method was experimentally validated on synthetic and real-world datasets and compared to state-of-the-art methods.

On approximation and energy estimates for delta 6-convex functions.

The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.