附有约束总体最小二乘地图线要素化简优化处理理论与方法

Line simplification is the most significant operator in auto map generalization. There have been lots of line simplification methods and algorithms. However, little attention is paid to the data error and data quality in line simplification. The method to guarantee the data quality of line simplification is the urgent need of high-precision geographic information service. This research focuses on the data quality optimizing processing theory and methods in line simplification, which contains the following contents: (1) Analyzing the data quality problems caused by line simplification operator, and establishing the data quality evaluation system. (2) Data quality constraint modeling of single line feature. The quality constraints include geometric and non-geometric ones; (3) Data quality constraint modeling of multi-line-features. These constraints depict the spatial relations between the neighboring line and point, line and line, line and polygon, the polygon and polygon which are constituted by closed line. (4) Developing the total least squares methods for the multi-constraints data quality optimizing system of line simplification. The purpose of this research is to improve the data quality in line simplification, and provide technical and method guarantee for the high precision map and multi-scale representation.

地图线要素自动化简是地图综合中最重要的综合算子，目前已有很多线要素化简的算法与实现研究，但是对线要素化简造成的数据误差和质量（精度）优化处理研究较少。如何保证线要素化简的数据质量是高精度地理信息服务的迫切需求。本项目研究地图线要素化简质量优化处理理论与方法，包括：（1）系统分析线化简算法造成的数据质量问题，建立线要素化简的质量评价指标体系；（2）单个线要素数据质量约束建模，涵盖几何信息与非几何信息的约束模型；（3）线要素与相邻多个要素之间的质量约束建模，包括线与点、线与线、线与面、线要素构成的面与面等多要素质量约束模型；（4）线要素化简质量控制系统的总体最小二乘优化处理方法研究。目的是提高线要素化简的数据质量，为高质量地图数据与多尺度表达提供技术方法保障。

本项目提出了附有质量约束的地图线要素化简理论与方法，有效保证了地图线要素化简前后质量指标的一致性。（1）针对地图线要素数据分别构建了几何移位、端点、面积、拓扑、直角特性等质量约束模型，表达为线性/非线性、等式/不等式代数表达式。（2）针对多种质量约束构成的线要素化简质量优化系统，提出了部分总体最小二乘多目标约束质量优化处理理论与方法。包括部分总体最小二乘方法、附有线性等式/不等式约束的总体最小二乘方法、附有非线性等式/不等式约束的总体最小二乘方法，并推导了相应的精度评估指标。（3）开展了附有质量约束的地图线要素化简的应用与验证，提出了一种附有拓扑不等式约束的道路线化简方法，以及附有面积、角度等几何特性约束的建筑物多边形化简方法。有效保证了地图线要素化简前后拓扑一致性，以及面积、角度等几何特性的一致。