论文标题
球形表面上的二项点过程的最近的邻居和接触距离分布
Nearest Neighbor and Contact Distance Distribution for Binomial Point Process on Spherical Surfaces
论文作者
论文摘要
这封信表征了接触距离的统计数据和在球形表面上空间分布的二项点过程（BPP）的最接近邻居（NN）距离。我们考虑了$ n $同心球的设置，每个球体$ s_k $都有一个半径$ r_k $和$ n_k $点，这些点均匀分布在其表面上。对于该设置，我们获得了到两种类型o观察点最近距离的累积分布函数（CDF）：（i）观察点不是该点过程的一部分，并且位于带有半径$ r_e <r_e <r_k \ forall k $的同心球上，与触点分布相对应的距离距离距离距离距离距离距离距离，该过程属于点距离距离距离。
This letter characterizes the statistics of the contact distance and the nearest neighbor (NN) distance for binomial point processes (BPP) spatially-distributed on spherical surfaces. We consider a setup of $n$ concentric spheres, with each sphere $S_k$ has a radius $r_k$ and $N_k$ points that are uniformly distributed on its surface. For that setup, we obtain the cumulative distribution function (CDF) of the distance to the nearest point from two types o observation points: (i) the observation point is not a part of the point process and located on a concentric sphere with a radius $r_e<r_k\forall k$, which corresponds to the contact distance distribution, and (ii) the observation point belongs to the point process, which corresponds to the nearest-neighbor (NN) distance distribution.
