An Optimization-Based Approach for Continuous Map Generalization

• Main Author: Peng, Dongliang
• Format: Doctoral Thesis
• Language: English
• Published: 2019
• Subjects: ddc:004
• Online Access: https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/17442; http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-174427; https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-174427; https://doi.org/10.25972/WUP-978-3-95826-105-1; https://opus.bibliothek.uni-wuerzburg.de/files/17442/978-3-95826-105-1_Peng_Dongliang_OPUS_17442.pdf

Maps are the main tool to represent geographical information. Geographical information is usually scale-dependent, so users need to have access to maps at different scales. In our digital age, the access is realized by zooming. As discrete changes during the zooming tend to distract users, smooth changes are preferred. This is why some digital maps are trying to make the zooming as continuous as they can. The process of producing maps at different scales with smooth changes is called continuous map generalization. In order to produce maps of high quality, cartographers often take into account additional requirements. These requirements are transferred to models in map generalization. Optimization for map generalization is important not only because it finds optimal solutions in the sense of the models, but also because it helps us to evaluate the quality of the models. Optimization, however, becomes more delicate when we deal with continuous map generalization. In this area, there are requirements not only for a specific map but also for relations between maps at difference scales. This thesis is about continuous map generalization based on optimization. First, we show the background of our research topics. Second, we find optimal sequences for aggregating land-cover areas. We compare the A$^{\!\star}$\xspace algorithm and integer linear programming in completing this task. Third, we continuously generalize county boundaries to provincial boundaries based on compatible triangulations. We morph between the two sets of boundaries, using dynamic programming to compute the correspondence. Fourth, we continuously generalize buildings to built-up areas by aggregating and growing. In this work, we group buildings with the help of a minimum spanning tree. Fifth, we define vertex trajectories that allow us to morph between polylines. We require that both the angles and the edge lengths change linearly over time. As it is impossible to fulfill all of these requirements simultaneously, we mediate between them using least-squares adjustment. Sixth, we discuss the performance of some commonly used data structures for a specific spatial problem. Seventh, we conclude this thesis and present open problems. === Maps are the main tool to represent geographical information. Users often zoom in and out to access maps at different scales. Continuous map generalization tries to make the changes between different scales smooth, which is essential to provide users with comfortable zooming experience. In order to achieve continuous map generalization with high quality, we optimize some important aspects of maps. In this book, we have used optimization in the generalization of land-cover areas, administrative boundaries, buildings, and coastlines. According to our experiments, continuous map generalization indeed benefits from optimization. === Landkarten sind das wichtigste Werkzeug zur Repräsentation geografischer Information. Unter der Generalisierung von Landkarten versteht man die Aufbereitung von geografischen Informationen aus detaillierten Daten zur Generierung von kleinmaßstäbigen Karten. Nutzer von Online-Karten zoomen oft in eine Karte hinein oder aus einer Karte heraus, um mehr Details bzw. mehr Überblick zu bekommen. Die kontinuierliche Generalisierung von Landkarten versucht die Änderungen zwischen verschiedenen Maßstäben stetig zu machen. Dies ist wichtig, um Nutzern eine angenehme Zoom-Erfahrung zu bieten. Um eine qualitativ hochwertige kontinuierliche Generalisierung zu erreichen, kann man wichtige Aspekte bei der Generierung von Online-Karten optimieren. In diesem Buch haben wir Optimierung bei der Generalisierung von Landnutzungskarten, von administrativen Grenzen, Gebäuden und Küstenlinien eingesetzt. Unsere Experimente zeigen, dass die kontinuierliche Generalisierung von Landkarten in der Tat von Optimierung profitiert.