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8A_2_A containment-first search algorithm for higher-order analysis of urban topology
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8A_2_A containment-first search algorithm for higher-order analysis of urban topology

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Session 8A, Paper 2

Session 8A, Paper 2


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  • 1.  
  • 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,…, 6 2 3 12 11 9 7 4 5 10 13 15 14 1 8
  • 11. 3
  • 12.  
  • 13. Problem: containment relationship between rings of “steep” polygons and “flat” polygons 200 Graph vertices Graph edges Polygon arcs Polygon nodes “ Flat” polygons “ Steep” polygons LEGEND 250 256 257 260 200
  • 14. Graph of “touchings” between “steep” polygons
  • 15.  
  • 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 Δ 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