Poisson Voronoï tiling for finding clusters in spatial point patterns

Abstract

In forest stand mapping a delineation of spatial compact clusters of trees with similar attributes can improve inventory accuracy and growth and yield predictions. To this end a Poisson Voronoï tiling (PVT) for identifying and delineating clusters (features) in spatial point patterns is proposed. PVT operates on the assumption that the point density in clusters is higher than that outside the clusters. A spatial domain of an observed point pattern is tessellated repeatedly into k (random) Poisson Voronoï cells. An average EM-based likelihood of feature based on observed cell point densities is computed for each point and location of interest. Points and locations of interest are then classified by maximizing a classification likelihood. PVT avoids the need to specify the number of clusters. In a direct comparison with a non-parametric maximum profile likelihood procedure, and a smoothed version of the same, PVT performed well on two artificial point patterns with known feature domain and points, and on two spatial point patterns of first returns from a forest lidar survey on Vancouver Island, British Columbia, Canada.

Keywords:

• Bayes information criterion
• EM classification
• lidar
• maximum profile log-likelihood