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

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.