1. Topological Consistent Generalization of OpenStreetMap By Padraig Corcoran, Peter Mooney, Adam Winstanley NUI Maynooth, Ireland 1

2. Problem Specification 2 LBS Device

3. Generalisation by Simplification Remove vertices in a guided and simplified manner 3

4. A simplification should be invariant with respect to certain properties. In the context of LBS, shape, size and topological invariants are particularly important. Few techniques satisfy multiple invariants. 4

5. Topological Invariance 5 Simplification not Topological Invariant Original OSM Map

6. The Research Question Given a map and corresponding simplification, can we determine if the simplification is topological consistent without constraints? 6

7. Any method for determining topological invariant may be summarized in terms of the followingconstraints : constraints on the types of topology for which the technique can determine consistency without returning a false-positive; constraints on the types of topology for which the technique can determine consistency without returning a false-negative; constraints on the types of simplification to which the technique can be applied. 7

8. Topological features can be classified as planar or non-planar. 8 Planar Topology Non-Planar Topology

9. Planar topology analysis An analysis of three methods for determining planar topology invariance were examined in terms of their corresponds constrains: De Berg et al. (1998) strategy; Saalfeld (1999) strategy; da Silva and Wu (2006) stragegy. 9

10. Symbol * indicates that determining topological invariance not subject to any constraint. Symbol x indicates that determining topological invariance is subject to constraints. 10

11. Non-Planar topology analysis We analysized the techniques Kulik et al. (2005) and Weihua(2008). Constraints on the forms of simplifications to which they can be applied. 11 Simplification Original Features

12. Shape and size invariants To satisfy shape invariants the contour evolution technique of Latecki and Lakmper (1999) was used. Satisfy size invariants presented a challenge. 12

13. We determine if removing a vertex will significantly reduce the representation of the polygons shape and in turn not maintain size invariance. 13

14. Results 14 38 Vertices 182 Vertices

15. 15 375 Vertices 34 Vertices

16. Conclusions / Future Work For LBS reducing map data size is very important. This reduction must be subject to certain invariants. Results on OSM data show this can be achieved. Future work Simplify all linear features. Progressive transmission of maps for LBS. 16