Analysis and application of polygon side distribution of Voronoi diagram in tree patterns

Voronoi diagram segmentation algorithm has been widely used in several fields,and successfully applied in the analysis of the number of competitive trees presently. In this study we applied polygon side distribution of Voronoi diagram in the analysis of tree patterns, and used the German geostatistical software Stochastic Geometry and R programming language to analyze the polygon side distributions of Voronoi diagrams with different tree patterns. We found that: 1) the number of polygon sides obeys Gaussian distribution in all types of tree patterns, with the maximum number of frequency of sides of 5 or 6; 2) the mean number of sides of Voronoi diagram is always around 6 for different tree patterns; 3) for different tree patterns there are significant differences in mean values of standard deviations of the number of Voronoi polygon sides, following the order as clustered distribution＞ random distribution＞ uniform distribution. We further simulated 500 randomly distributed forest stands and found that the standard deviations (SD) of number of sides of Voronoi polygon follow Gaussian distribution. On this basis, we give the distribution range of standard deviation of the number of Voronoi polygon sides for randomly distributed forest stands based on a confidence interval of 95% probability (1.96 times of SD): μ±1.96σ=1.333±0.035×1.96, that is, the range of value for SD of Voronoi polygon of randomly distributed forest stands is 1.264, 1.402; if SD1.264, it is a uniform distribution pattern; if SD1.402, it turns out to be a cluster-form distribution. Subsequently, we applied the Voronoi polygon-based forest pattern judgment method (Vs) into five pieces of actual forest stands with different types, and compared the results with those obtained by the commonly-used uniform angle index method (W)based on four closest adjacent trees. The comparison indicated that the distribution patterns obtained by the two methods are completely the same. Our results suggest that Vs can be used as a new method to judge indirectly the distribution pattern of trees.