Cross S S
Department of Pathology, University of Sheffield Medical School, U.K.
Micron. 1994;25(1):101-13. doi: 10.1016/0968-4328(94)90057-4.
Fractal geometry is a relatively new tool for the quantitative microscopist that is a more valid way of measuring dimensions of complex irregular objects than the integer-dimensional geometries (such as Euclidean geometry). This review discusses the theory of fractal geometry using the classic examples of the Von Koch curve, the Cantor set and the Sierpinski gasket. The problems of describing the dimensions of these objects are discussed and the concept of fractal dimensionality is introduced. Methods for measuring fractal dimensions are discussed, including their implementation on microcomputer-based image analysis systems . The advantages and problems of fractal geometric analysis are discussed and current applications in the field of microscopy are reviewed.
分形几何是定量显微镜学家的一种相对较新的工具，与整数维几何（如欧几里得几何）相比，它是测量复杂不规则物体尺寸的一种更有效的方法。本综述使用冯·科赫曲线、康托尔集和谢尔宾斯基垫片等经典例子来讨论分形几何理论。讨论了描述这些物体尺寸的问题，并引入了分形维数的概念。讨论了测量分形维数的方法，包括在基于微机的图像分析系统上的实现。讨论了分形几何分析的优点和问题，并综述了其在显微镜领域的当前应用。
