Line simplification with sidedness relationship consistency using the constrained total least squares method

IF 2.1 3区 地球科学 Q2 GEOGRAPHY
Yanmin Jin, Lejingyi Zhou, Zhengxiang Song, Lingling Wei, Xinyi Zheng, Xiaohua Tong, Xiongfeng Yan
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引用次数: 0

Abstract

The simplification of lines plays a crucial role in map generalization and multiscale representation; however, addressing inconsistent sidedness relationships between the simplified lines and their neighboring features poses a persistent challenge. In order to preserve correct and consistent sidedness relationships following simplification, this study introduces a novel line simplification method. This method incorporates topological constraints pertaining to left–right sidedness relationships, formulated as an optimization procedure based on the proposed partial total least squares method with constraints. The primary objective is to minimize the positional difference between the line features before and after simplification, with the sidedness relationship represented as an inequality constraint. Moreover, an optimization algorithm is derived to address the simplification problem effectively while adhering to the specified constraints. The proposed method is then applied to simplify the lines within three distinct datasets. Experimental results validate the efficacy of the proposed method in maintaining sidedness consistency across all tested datasets. In comparison to the Douglas–Peucker (DP) method, the proposed method exhibits minimal vertical displacement variance in the line feature points post-simplification. Additionally, it achieves a smaller overall positional difference between the simplified and original lines compared to the DP method. These findings underscore the superior performance of the proposed method in maintaining sidedness relationships and minimizing positional differences during the line simplification process.
利用受约束总最小二乘法简化具有边度关系一致性的直线
线条的简化在地图泛化和多尺度表示中起着至关重要的作用;然而,如何处理简化后的线条与其邻近地物之间不一致的边度关系是一项长期的挑战。为了在简化后保留正确一致的边度关系,本研究引入了一种新颖的线条简化方法。该方法结合了与左右边度关系相关的拓扑约束条件,并根据所提出的带约束条件的部分全最小二乘法制定了优化程序。主要目标是最小化简化前后线条特征之间的位置差,而左右边度关系则表示为不等式约束。此外,还推导出了一种优化算法,可在遵守指定约束条件的同时有效解决简化问题。然后,将所提出的方法应用于简化三个不同数据集中的线条。实验结果验证了所提方法在所有测试数据集中保持边度一致性的有效性。与道格拉斯-皮克(Douglas-Peucker,DP)方法相比,所提出的方法在简化后的线条特征点中表现出最小的垂直位移方差。此外,与 DP 方法相比,简化后的线条与原始线条之间的整体位置差异更小。这些研究结果表明,在线条简化过程中,拟议方法在保持边度关系和最小化位置差异方面表现出色。
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来源期刊
Transactions in GIS
Transactions in GIS GEOGRAPHY-
CiteScore
4.60
自引率
8.30%
发文量
116
期刊介绍: Transactions in GIS is an international journal which provides a forum for high quality, original research articles, review articles, short notes and book reviews that focus on: - practical and theoretical issues influencing the development of GIS - the collection, analysis, modelling, interpretation and display of spatial data within GIS - the connections between GIS and related technologies - new GIS applications which help to solve problems affecting the natural or built environments, or business
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