二维数字图像分形维数的计算方法  

Computation Method of Fractal Dimension for 2-D Digital Image

作　　者：彭瑞东[1] 谢和平[1] 鞠杨[1] 

机构地区：[1]中国矿业大学岩石力学与分形研究所,北京100083

出　　处：《中国矿业大学学报》2004年第1期19-24,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金"创新研究群体"项目(50221402);国家973项目(2002CB412705;2002CB412707);国家自然科学基金项目(50074032)

摘　　要：许多情况下分形维数的计算是通过对二维数字图像的分析得到的.针对二维数字图像的特点,探讨了采用盒维数计算其分形维数的方法.数字图像盒维数的计算是基于对像素矩阵的分析进行的,具有数字化的特点,其计算结果的精度与图像大小有较大关系.数字图像盒维数描述了由离散像素点构成的数字图像中关心区域的分布特点,但其物理意义还应结合数字图像所赋存的物理意义加以分析.Fractal dimension plays an important role in investigating the fractal feature of an object, which is acquired from analyzing the 2-D digital image. The digital box dimension based box-counting dimension was suggested to calculate fractal dimension so as to fit the property of 2-D digital image. The essential of computing digital box dimension is to analyze the pixels matrix of image, so it is a digital process, and the precision of result is closely related to the size of image. The digital box dimension characterizes how the concerned region distributes on an image. However, its physical meaning should be discussed according to the physical sense of the relative digital image.

关 键 词：数字图像 像素矩阵 分形 分形维数 计盒维数 计算方法 

分 类 号：TP317.4[自动化与计算机技术—计算机软件与理论]