The characterization of the arrangement of feature centroids in planes and volumes

The quantitative characterization of the arrangement of microstructural features is important for understanding the properties or function of materials or tissues. In this paper, the well-known analysis of nearest neighbour distances is modified in order to separate clusters from a background of randomly disposed features and to characterize significant parameters of such sets. In addition, simple procedures are indicated to detect and to characterize regular arrangements, and computer simulated examples are used to demonstrate the efficiency of the suggested algorithms. Each step of the procedures can be used for three-dimensional arrangements as well.