Analysis and application of polygon side distribution of Voronoi diagram in tree patterns
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摘要: 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SD1.264时,该林分格局为均匀分布,当SD1.402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。
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关键词:
- Voronoi多边形 /
- 边数分布规律 /
- 边数标准差分布规律 /
- 林木分布格局
Abstract: 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. -
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[1] 吴立新,史文中.地理信息系统原理与算法[M].北京:科学出版社,2003. [1] WU L X,SHI W Z.Principle and algorithm of geographical information systems [M]. Beijing:Science Press,2003.
[2] CAI H D, LIN S M, WEI A S.Cartography technique and methods of continuous forest inventory[J].Journal of Nanjing Forestry University:Natural Sciences Edition,2006, 30(5):132-134.
[2] GERSTEIN M, RICHARDS F M. Protein geometry: volumes, areas, and distances[J].International Tables for Crystallography, 2001,22:531-539.
[3] FENG Z K,GUO Q W,ZHU P.Application of the Voronoi diagram-Thiessen polygon method in tree surveying with angle gauges[J].Forest Resources Management,2006(3):44-47.
[3] GERSTEIN M, TSAI J, LEVITT M. The volume of atoms on the protein surface: calculated from simulation, using Voronoi polyhedra[J]. Journal of molecular biology,1995,249(5):955-966.
[4] TSAI J,VOSS N,GERSTEIN M.Determining the minimum number of types necessary to represent the sizes of protein atoms[J].Bioinformatics,2001,17(10):949-956.
[4] HE R Z,HUANG J R,QUAN F.Research and application of GIS and ANN in individual growth model[J].Journal of Henan Agricultural University,2009,43(3):260-263.
[5] TANG M P,CHEN Y G,SHI Y J,et al.Intraspecific and interspecific competition analysis of community dominant plant populations based on Voronoi diagram[J].Acta Ecologica Sinica,2007,27(11):4707-4716.
[5] TSAI J,GERSTEIN M,LEVITT M. Simulating the minimum core for hydrophobic collapse in globular proteins[J].Protein Science,1997,6(12):2606-2616.
[6] TANG M P,ZHOU G M,CHEN Y G,et al.Mingling of evergreen broad-leaved forests in Tianmu Mountain based on Voronoi diagram[J].Scientia Silvae Sinicae,2009,45(6):1-5.
[6] BROWN G S.Point density in stems per acre[J].New Zealand Forestry Service Research Notes, 1965, 38:1-11.
[7] 蔡会德,林寿明,魏安世.森林资源连续清查图件生成的技术与方法[J].南京林业大学学报:自然科学版,2006,30(5):132-134. [7] ZHAO C Y,LI J P,LI J J.Quantitative analysis of forest stand spatial structure based on Voronoi diagram Delaunay triangulated network[J].Scientia Silvae Sinicae,2010,46(6):78-84.
[8] LIU S,WU S C,WANG H,et al.The stand spatial model and pattern based on Voronoi diagram[J].Acta Ecologica Sinica,2014,34(6):1436-1443.
[8] 冯仲科,郭清文,朱萍.Voronoi 图-泰森多边形法在角规测树中的应用[J].林业资源管理,2006(3):44-47. [9] XUE Y.Statistical modeling and R software[M].Beijing:Tsinghua University Press,2007:128-130.
[9] 何瑞珍,黄家荣,全锋.基于泰森多边形与人工神经网络的单木模型研究[J].河南农业大学学报,2009,43(3): 260-263. [10] HUI G Y.The neighborhood pattern:a new structure parameter for describing distribution of forest tree position[J].Scientia Silvae Sinicae,1999,35(1):37-42.
[10] 汤孟平,陈永刚,施拥军,等.基于 Voronoi 图的群落优势树种种内种间竞争[J].生态学报,2007,27(11):4707-4716. [11] LI J.Study on structural characteristics and growth model of typical stand types in southern collective forest region[D]. Changsha:Central South University of Forestry and Technology, 2012.
[11] 汤孟平,周国模,陈永刚,等.基于Voronoi图的天目山常绿阔叶林混交度[J].林业科学,2009,45(6):1-5. [12] 赵春燕,李际平,李建军.基于Voronoi图和Delaunay三角网的林分空间结构量化分析[J].林业科学,2010,46(6):78-84. [12] HAO Y L,ZHANG H R,TANG S Z.Study on cutting tree determining method based on forest stand spatial structure optimization[J].Journal of Northwest Forestry University,2012,27(5):163-168.
[13] WU A B.Analyzing and optimizing forest stand spatial structure based on high-resolution remote sensing image[D]. Beijing:Beijing Forestry University,2012.
[13] 刘帅,吴舒辞,王红,等.基于 Voronoi 图的林分空间模型及分布格局研究[J].生态学报,2014,34(6):1436-1443. [14] AN H J.Study on the spatial structure of the broad-leaved Korean pine forest[D].Beijing:Beijing Forestry University,2003.
[14] CHIU S N,STOYAN D,KENDALL W S,et al.Stochastic geometry and its applications[M].New York:John Wiley Sons,2013.
[15] LIU Y J.Study of forest stand spatial structure and competition based on three-dimensional simulation technique[D].Beijing Forestry University,2011.
[15] 薛毅.统计建模与R软件[M].北京:清华大学出版社,2007:128-130. [16] 惠刚盈,GADOW K V,ALBERT M.角尺度:一个描述林木个体分布格局的结构参数[J].林业科学,1999,35(1):37-42. [17] 李俊.南方集体林区典型林分类型结构特征及生长模型研究[D].长沙:中南林业科技大学,2012. [18] 郝月兰,张会儒,唐守正.基于空间结构优化的采伐木确定方法研究[J].西北林学院学报,2012,27(5):163-168. [19] 武爱彬.基于高分辨率遥感图像获取与优化林分空间结构研究[D].北京:北京林业大学,2012. [20] 安慧君.阔叶红松林空间结构研究 [D].北京:北京林业大学,2003. [21] 刘彦君.应用三维模拟进行林分空间结构及竞争的研究[D].北京:北京林业大学,2011. -
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