Douglas-Peucker算法全自动化的多尺度空间相似关系方法

地图综合本质上是空间相似变换,研究Douglas-Peucker算法及其参数的设置,实质是研究算法的最佳距离阈值与尺度变化间的定量关系,但目前二者关系未知,导致参数设置及化简结果的选择主观性强。为此,提出以多尺度线要素空间相似关系为契合点,利用阈值参数寻优原理确定二者间定量关系,以实现基于DP算法线要素的全自动化简。结果表明：① 二次函数是描述最佳距离阈值与尺度变化间定量关系的最优函数;② 针对来源于相同地理特征区,如长江下游平原,的线要素可行,利用同一最佳距离阈值可实现基于DP算法线要素的全自动化简,且化简结果与已有成果数据吻合度较高;而来源于不同地理特征区域,如长江下游平原和江淮平原,的线要素,用同一最佳距离阈值化简是不合理。因此,应选择不同的最佳距离阈值,以实现不同地理特征区域线要素的DP算法全自动化简。

Automation of the Douglas-Peucker Algorithm based on Spatial Similarity Relations

Map generalization is in essence a spatial similarity transformation of maps. Studying the Douglas-Peucker algorithm and its parameter setting is in essence studying the relationship between the optimal distance threshold of the algorithm and map scale change. However, the quantitative relationship between them is still unknown, which leads to strong subjectivity in parameter setting and selection of simplification results. Therefore, in order to realize the automated simplification of polyline based on DP algorithm, this paper proposes to take the spatial similarity evaluation model of multi-scale polylines as the coincidence point, and determine the quantitative relationship between them using the principle of threshold parameter optimization. The results indicate that quadratic function is the optimal function to describe the quantitative relationship between the optimal distance threshold and map scale change. It is feasible to use the same optimal distance to automatically simplify the polylines from the same geographical feature area based on the Douglas-Peucker algorithm, such as the polylines from the Lower Yangtze River plain. The simplification results match well with the existing target scale data. However, it is unreasonable to use the same optimal distance threshold to simplify the polylines from different geographical feature areas, such as polylines from the Lower Yangtze River plain and the Jianghuai plain. Therefore, different optimal distance thresholds should be selected to realize full automated simplification of DP algorithm for polylines from different geographical feature areas.