This section covers how to obtain a sub-sampled set of points for extraction of local neighborhoods of the point clouds. The idea behind using local neighborhoods is that some information is best not calculated for every point in a point cloud, but rather at a subset of points, called central points. Usually the information will require computations with a small region around each central point. Once computed for the small region, there is no need to compute it at points in the small region that differ from the chosen central point.

Below are a few ways to obtain these local neighborhoods. They are not all the same. Some allow for the neighborhood regions to overlap, some may not. all involve specifying how big the neighborhood should be. Usually that is done through a radius specification $\bar \rho$.