R2空间上分布数据的多重分形维数谱计算和分形特征提取

近年来多重分形的概念在物理、化学等领域得到了发展和应用 ,在这些领域中 ,这种方法显示出了对于研究物理和化学量的空间分布是很有用的 .多重分形谱的计算是其中重要而又较难处理的问题 .从多重分形的理论出发 ,讨论了在数据处理的实际工作中有广泛应用的二维空间中多重分形谱的计算及分形特征提取的算法 ,介绍了算法的数学原理 ,描述了完整的算法流程 ,并给出了此算法的一个计算实例

Computation of Multifractal Dimentional Spectrum and Distilling of Fractal Feature of the Data Distributing on R2 Space

The concept of multifractal has been developed and applied recently in physics and chemistry where this method was shown to be useful for the study of the spatial distribution of physical and chemical quantities. The calculation of multifractal spectrum is a important and difficult question. In this paper, start from the theory of multifractal, the algorithm that has a wide application in the work of data processing to calculate multifractal spectrum and to distill the multifractal feature is discussed, the mathematical theory of the algorithm is introduced, the complete algorithmic diagram is described, and a calculation instance use this algorithm is given.