Voronoi多边形的边数分布规律及其在林木格局分析中的应用

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

Voronoi空间分割算法在各个领域已得到广泛应用,目前Voronoi图已经成功应用于林木竞争分析中竞争木数量的选择上。本研究旨在将Voronoi多边形边数分布规律应用于样地的林木格局分析中。借助德国Stochastic Geometry统计软件和R语言程序绘制并分析不同分布格局林分的Voronoi多边形边数分布规律,研究发现:1)不同分布格局的林分,其Voronoi多边形边数分布都呈近似正态分布,频数最大值基本聚集于5或6株;2)无论何种格局分布,Voronoi多边形边数均值皆为6株左右;3)不同分布格局的林分,其Voronoi多边形边数分布标准差的均值具有较为明显的差异,表现为:团状>随机>均匀。进一步模拟500个随机分布林分发现,Voronoi多边形边数的标准差分布遵循正态分布。基于此,本文利用95%概率,即1.96倍标准差为置信区间的方法,确定了随机分布林分Voronoi多边形边数标准差的分布范围为:μ±1.96σ=1.333±0.035×1.96,即随机分布林分的Voronoi多边形边数标准差(SD)的置信区间为[1.264,1.402];当SD<1.264时,该林分格局为均匀分布,当SD>1.402时为团状分布。将这种基于Voronoi多边形的林木格局判定方法(Vs)应用于5块不同类型的现实林分,并与目前常用的基于4株最近相邻木的角尺度(W—)方法进行了对比,得到的格局分布类型Vs与W—二者完全相同。可见,Vs可作为一个间接判定林木分布格局的新途径。

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 x 1.96, that is, the range of value for SD of Voronoi polygon of randomly distributed forest stands is [1.264, 1.402]; if SD 〈1.264, it is a uniform distribution pattern; if SD 〉 1.402, 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.