Clustering of spatial point patterns

Spatial point patterns arise as the natural sampling information in many problems. An ophthalmologic problem gave rise to the problem of detecting clusters of point patterns. A set of human corneal endothelium images is given. Each image is described by using a point pattern, the cell centroids. The main problem is to find groups of images corresponding with groups of spatial point patterns. This is interesting from a descriptive point of view and for clinical purposes. A new image can be compared with prototypes of each group and finally evaluated by the physician. Usual descriptors of spatial point patterns such as the empty-space function, the nearest distribution function or Ripley's K-function, are used to define dissimilarity measures. Moreover, the relationship between some estimation problems in spatial point processes and survival analysis is used to define dissimilarity measures between point patterns. All the proposed dissimilarities and the cluster procedures are evaluated in a simulation study. Finally, a detailed analysis of the images of corneal endothelia is provided.