摘要
对康托集的研究一直是分形领域的经典而又热点的课题。本文尝试用一种新的模式——“格图像”来研究康托集的分形特性,给出了康托集的格图像构造与分形维数计算方法,计算表明:康托集的自相似分维是格图像分维的特例,格图像分维是自相似分维的扩展。文章首次在分形领域引入泛逻辑的概念,给出了基于格图像的康托集的泛逻辑“与,或,非”运算模型,它不仅考虑了集合的代数测度大小,而且考虑了在参考格中的几何位置关系,这给分形图像的研究提供了一种新的思路,同时也拓展了泛逻辑学的应用领域。
The study of cantor-set is classical but heated subject in fractal field. This paper tries to study the fractal characteristic of cantor-set by a new model called 'grid image', gives the method of construction of grid image and calculation of fractal dimension. The results show that the self-similar dimension is the specialty of grid image dimension, and the grid image dimension is the extended case of self-similar dimension. The paper imports the conception of universal logic firstly, gives the operation models of 'NOT', 'AND', and 'OR' based on grid image. They take into account not only the values of algebraic measure but also the relationship of geometric location. This work provides a new thought-way for studying fractal image, and enlarges the applied fields of universal logic.
出处
《计算机科学》
CSCD
北大核心
2004年第4期92-95,共4页
Computer Science
基金
国家自然科学基金(编号:60273087)
关键词
图像处理
计算机
格图像
康托集分维
泛逻辑运算
图像分维
Cantor-set, Fractal object, Fractal dimension, Self-similar, Grid image, Universal logic
