卫星图像的村落民居Lebesgue测度η值研究

摘要

Based on the topology for residence in Huizhou, the topological change of different age village is fitted numerical curve. Huizhou has some villages over 1, 000 years. The images can get by Google satellite, and form the yearly(dynasty) topology after identification. The analysis is based on the Lebesgue measure theory. Topology identification graceful graph algorithms are introduced to quantify graceful graph topology diagram in the village. Theηof the graceful values of village is defined by the measure concept graceful graph structure. Whenηis about 8, 000, the village of ancient is rich in humani-ties;when it is less than 6, 000, villages in the humanities remains minimal;villages of about 700 years,ηvalue is close to 9, 600. The research result conforms to the actual status. Through the curve ofηvalue changed by age, a preliminary analysis of the evolution of the ancient village is made. Results comply with reality.%以古民居的分布与发展演变为变量参数所形成的古村落拓扑图，通过对Lebesgue测度计算形成几何拟合数值曲线，在引入优美图优美标号的基础上，形成对村落优美度η的勒贝格测度值，在古村落发育（时间增长）过程中，η值是单调变化的。以徽州地区存在1000年古村落google卫星图像为基础，结合历史文献获得不同年代民居拓扑图，依据上述方法对村落拓扑中优美图进行统计量化，定义出村落优美度值η。结论认为η介于8000左右时，村落民居年代人文分布丰富；而低于6000时村落民居数量发展上升，但人文资料零乱；在700年左右的村落中，η值稳定在9600附近，呈现出古村落的明显拓扑特征。通过村落优美度按年代变化的η值曲线，对村落的（年代）演变做了分析。