Topological Relationships Between Complex Spatial Objects -- by Markus & Thomas

1. Topological Relationships Between Complex Spatial Objects --by Markus & Thomas Presented by: Daniel Hess, Yun Zhang

2. Outline • Motivation •Problem statement • Major contributions • Key concepts • Validation methodology • Assumptions • Recommended changes

3. Motivation • To distinguish simplified spatial objects with complex spatial objects •To define topological relationships for complex spatial objects A more complex topological relationship

4. Problem Statement • Input: spatial query (SQL), complex spatial objects • Output: query results • Objective: find correct, complete query results • Constraints: two spatial objects have only one topological relationship

5. Major contributions of this paper • Define complex points, complex lines and complex regions • Determine topological relationships for all complex spatial data types • Prove the completeness and mutual exclusion of the topological relationship predicates • Provide the users concepts of topological cluster predicates and topological predicate groups

6. Key Concept--Complex spatial objects (1/2) (Schneider and Behr, 2006, p. 46) • A complex point object may include several points • A complex line may be a spatially embedded network, possibly consisting of several components • A complex region may be a multipart region, possibly consisting of multiple faces and holes

7. Key Concept--Complex spatial objects (2/2) • Example: -A complex region with two faces in which the upper face has two holes: -A complex region with five faces and three holes: (Schneider and Behr, 2006, p. 53) (Schneider and Behr, 2006, p. 53)

8. Proposed approach • Derive topological relationships from the 9- Intersection model • Use technique ‘proof-by-constraint-and-drawing’, determine the complete sets of mutually exclusive topological relationships

9. Proof- by-constraint-and-drawing • two-step proof technique -Step 1: For each possible data type combination (e.g. point, line) ->collect topological constraint rules ->apply to the topological matrix -Step 2: Remaining assignments of the topological matrix, indicate possible topological relationships between the data types

10. Validation methodology examples • Proof example: (Schneider and Behr, 2006, p. 68) (Schneider and Behr, 2006, p. 45) (Schneider and Behr, 2006, p. 74)

11. The 82 topological relationships between two complex lines (Schneider and Behr, 2006, p. 60)

12. The 33 topological relationships between two complex regions (Schneider and Behr, 2006, p. 66)

13. Validation methodology comments • The proof technique is suitable for validating the approaches used in this paper, as it is generally abstract and precise • The proof technique may be time consuming and labor intensive

14. Assumptions • The authors assume the existence of the Euclidean distance function when making the definition for complex lines: • The spatial objects are static, and will not change with time

15. If rewrite this paper, we would… • Keep the key ideas of the approach. We would still apply the 9-intersection model to complex spatial objects • Keep the clustering of topological predicates in order to reduce the large predicates set and to make the topological relationships more manageable • Change step 2 of the proof method and apply a math formula to define valid topological relationships between specific data types, in order to improve efficiency • Extend the spatial data types to three dimensions

16. Simple Exercise • The author defines complex point, line, and region in paper MSD 6. Possible trade-off result is large numbers of predicates and the difficulty of handling them. How does this paper solve this problem?

17. Simple Exercise • Model answer: The author proposes concepts of topological cluster predicates and topological predicate groups. It reduces the number of predicates to be dealt with in a user-defined and/or application-specific manner.