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,且简单可靠;(3)从某种意义上讲,由于迭代的次数可以是无穷的,所以能非常精确地确定图形的标度空间,并可获得精确的分维值。因此矢量计盒算法是一种方便、实用而且精确的维数计算方法。
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.
出处
《中国图象图形学报》
CSCD
北大核心
2008年第3期525-530,共6页
Journal of Image and Graphics
关键词
分形
计盒算法
栅格
矢量
KOCH曲线
骨肿瘤边界
fractal, box-counting algorithm, grid, vector, Koch curve, osteoma boundary, channel systems
