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Exploiting qualitative spatial reasoning for topological adjustment of spatial data

Published:06 November 2012Publication History

ABSTRACT

Formal models of spatial relations such as the 9-Intersection model or RCC-8 have become omnipresent in the spatial information sciences and play an important role to formulate constraints in many applications of spatial data processing. A fundamental problem in such applications is to adapt geometric data to satisfy certain relational constraints while minimizing the changes that need to be made to the data. We address the problem of adjusting geometric objects to meet the spatial relations from a qualitative spatial calculus, forming a bridge between the areas of qualitative spatial representation and reasoning (QSR) and of geometric adjustment using optimization approaches. In particular, we explore how constraint-based QSR techniques can be beneficially employed to improve the optimization process. We discuss three different ways in which QSR can be utilized and then focus on its application to reduce the complexity of the optimization problem in terms of variables and equations needed. We propose two constraint-based problem simplification algorithms and evaluate them experimentally. Our results demonstrate that exploiting QSR techniques indeed leads to a significant performance improvement.

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  1. Exploiting qualitative spatial reasoning for topological adjustment of spatial data

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        Ernest Davis

        Suppose you have collected geographic information about a collection of objects and their positions. Their shapes are recorded accurately, but their positions may be misrecorded or misperceived. You additionally have information constraining the topological relations between the objects. For instance, you know that a building is entirely on an island and not leaking off of it, and you know that one end of a bridge is on the island and the other is on the mainland. Suppose that, due to the misrecorded positions of the objects, these constraints are not satisfied. The problem is finding the minimal number of repositionings for each object that will bring the system into a state where the constraints are satisfied. The author of this paper developed a system that solves this problem for 2D convex objects with constraints stated in the region connection calculus (RCC) language known as RCC8. The system works by converting the problem into a mixed integer programming problem and then applying an existing solver for such problems. The author further experimented with computing a transitive reduction of the constraint network (that is, a set-minimal subnetwork with the same solution space as the original network), and using the transitive reduction to generate the system of equations. Unsurprisingly, fewer equations were generated. More interestingly, the overall computation time decreased by a factor of more than two. There was no difference between using a simple greedy method for computing transitive reduction and using a more sophisticated method. In the extensive literature on qualitative spatial reasoning using RCC8, there are surprisingly few papers that deal with generating geometric instantiations, so this paper is a welcome addition. However, the results here are very limited by considering only two dimensions, convex objects, and the translation of objects, and the techniques do not generalize in any obvious way. Finally, there is a significant gap in the presentation. The experimentation was carried out over scenarios that were generated randomly. However, the paper does not say what random process was used. Since there is no standard probability distribution over polygons, and since the choice of random process can strongly affect the results of this kind of experiment, any paper that experimentally tests spatial computation using randomly generated instances should always specify the probability distribution or random process used. Online Computing Reviews Service

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        • Published in

          cover image ACM Conferences
          SIGSPATIAL '12: Proceedings of the 20th International Conference on Advances in Geographic Information Systems
          November 2012
          642 pages
          ISBN:9781450316910
          DOI:10.1145/2424321

          Copyright © 2012 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 6 November 2012

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