Identifying parent locations in the Neyman-Scott process using Delaunay triangulation

In a clustered point pattern, consisting of parent and offspring points, in order to study the attributes of parent points as well as the behavior of offspring points which are scattered around the parents, one needs to know the locations of parent points generating offsprings. In this paper we use the Delaunay triangulation and present a general method to detect parent locations. The performance of the method is evaluated by applying the method to various simulations of a well-known case of the Neyman-Scott cluster process, the Thomas process. Furthermore, the method is used to find parent locations in tropical rain forest data sets.