8A_2_A containment-first search algorithm for higher-order analysis of urban topology
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- 2. Overview Introduction Preparation of the polygon data base Implementation aspects: Construction of graph of adjacencies Graph analysis: depth-first search vs. breadth-first search; containment-first search Polygon-ring containments Construction of graph of touchings Further work & applications
- 3. Introduction (i) Interpretation and analysis of spatial phenomena is a highly time consuming and laborious task. Automation of these tasks is especially needed in areas such as GISc. Little work has been devoted to the interpretation of initially unstructured geospatial datasets.
- 4. Introduction (ii) Topological relationships Topology is a central defining feature of a GIS. First order vs. higher order connections A graph-based approach Graph theory widely used to represent connections and relationships between spatial entities. Extremely valuable in storing and describing the spatial structure of geographical entities and their spatial arrangement.
- 5. Preparation of the polygon data base ⢠Identifying meaningful structures ⢠Understanding the spatial arrangement between them Unstructured data set Retrieving information More meaningful homogeneous regions ( e.g. land-use parcels)
- 6. Test environment: LiDAR data
- 7. First order information TIN based on the Delaunay triangulation, the maximal planar description of the given point set (Kirkpatrick and Radke, 1985)
- 8. TIN facets binary classification ( using 45 ° slope threshold )
- 9. Graph of adjacencies construction
- 10. Depth-first search vs. Breadth-first search 15 graph vertices 6 2 3 12 11 9 7 4 5 8 10 13 15 14 1 6 2 3 12 11 9 7 4 10 15 14 1 8 13 5 Depth - first search Breadth - first search 1 6 2 3 12 11 9 7 4 5 8 10 13 15 14 traversed edges LEGEND 1, 1,âŚ, 6 2 3 12 11 9 7 4 5 10 13 15 14 1 8
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- 13. Problem: containment relationship between rings of âsteepâ polygons and âflatâ polygons 200 Graph vertices Graph edges Polygon arcs Polygon nodes â Flatâ polygons â Steepâ polygons LEGEND 250 256 257 260 200
- 14. Graph of âtouchingsâ between âsteepâ polygons
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- 16. Summary and further work Unstructured data (LiDAR points) TIN Features Understanding process Polygonal regions (x,y,z) coordinates Structures clustering into homogeneous regions Binary classification based on Î slopes Identification of meaningful structures Cluster shapes delineation, derivation of its characteristics for the identification of higher order structures
- 17. Future applications The results expected might be useful to support: Land-use mapping Image understanding Clustering analysis & generalisation processes