Efficient map reconstruction and augmentation via topological methods

Abstract

In recent years, with the rapid growth in the amount of publicly available Volunteered Geographic Information (VGI) data, automatic map generation from GPS trajectories has attracted great attention. Maps generated from these data can for example complement commercial maps in less developed areas. Two main challenges in the automatic generation of maps from volunteered GPS data are the handling of noise and of non-homogeneous sampling of road segments (for example, roads in downtown area can receive significantly more GPS traces than roads in residential areas). In this paper, we present a novel framework for map reconstruction based on a topological idea: the Morse theory. In particular, the use of Morse theory and topological simplification allows us to handle the issues of both noise and non-homogeneous sampling in an elegant unified framework. Our algorithm is significantly simpler than previous approaches, both conceptually and implementation speaking. Little pre- and post-processing is required, and yet the algorithm can reconstruct robust road-networks from challenging data sets (such as GPS traces for Berlin or Beijing cities) that are comparable or better than the output of previous state-of-the-art approaches. The new algorithm is also orders of magnitude faster than previous approaches on large data sets (for example, the entire processing of the Berlin city data with about 27189 trajectories takes less than one minute). Furthermore, our framework can be easily extended to handle the map integration problem, where one wishes to integrate multiple maps into a single one. Here, roads in different maps can have different confidence levels, and higher confident roads will have larger influence in the final integrated road. We also present an effective algorithm for a slightly different map augmentation problem, where one wishes to augment a map, say G2, using partial but more trust-worthy map G1, in the sense that in the final map, information in G1 needs to be completely preserved.