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测量分维的矢量计盒算法研究

韩杰1, 陆桂华1(河海大学水文水资源和水利工程科学国家重点实验室,南京 210098)

摘 要
分形理论目前在众多学科领域中取得了广泛的应用,研究这些对象主要通过确定它们的分维,其中计盒算法是一种最常用的方法。传统的计盒算法是基于栅格(位图)文件的方法,由于其存在图像放大后失真、过程繁琐和迭代次数有限等缺陷,因此为了准确简单方便地进行分维计算,开发了一种以矢量文件为载体的矢量计盒算法,并详细阐述了这种算法的数据结构、处理流程和主要函数,同时以Koch曲线、骨肿瘤边界及水系证明了矢量计盒算法的准确性和优越性。实践表明,该算法有3个优点:(1)图像不会随着放大缩小而失真;(2)可完全进行计算机操作,且简
关键词
Research on the Vector Box counting Algorithm in Fractal Dimension Measurement

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Abstract
The fractal theory developed by the French scientist Mandelbort in 1970s is beneficial in many areas. It greatly expands and deepens our knowledge on irregular geometric bodies. Fractal theory quantifies these phenomena mainly by ascertaining their fractal dimensions. Box counting algorithm is the one most practical and also most frequently adopted method. The traditional box counting algorithm is based on the grid document and has some serious shortcomings, such as the distortion of the image being enlarged, the trivialness of the process and the finite of the iterative degree, etc. The vector box counting algorithm developed in this paper takes vector document as the carrier and has three advantages. First, the image will not be distorted after being enlarged. Second, the process is completely handled by computer, simple and reliable. Third, to some degree, the iterative degree can be infinite. Therefore, it can ascertain precisely the scaling space of the graph and acquire accurate fractional dimension value. This paper expounds the data structures, the process of disposing and the main functions in detail. Whats more, it proves the precision and advantages of the vector box counting algorithm by making use of Koch curve, osteoma boundary and river system. The result shows that the vector box counting algorithm is a convenient, useful and precise way of dimensional calculating method.
Keywords

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