Topological Adjustment of Polygonal Data
Qualitative spatial relations, in particular (mereo)topological relations such as those defined in the 9-Intersection model or RCC-8 and RCC-5, play an important role as constraints in many applications of spatial data processing such as conflation and data cleaning, map generalization, and solving layout problems in general. A fundamental problem in such applications is to adjust geometric data such that certain topological constraints are satisfied, while minimizing the changes that need to be made to the geometric input data. We develop an approach to solve this problem for topological relations between polygonal objects and with displacement of the objects being the only allowed adjustment operation. Our approach is based on a formalization of these relations as sets of (in)equations which can then be translated into a MNLP program and be solved using a dedicated MNLP solver. Our suggested adjustment algorithm uses Minkowski sums of the involved polygons to achieve a linear number of (in)equations per relation.
KeywordsTopological relations Integrity constraints Adjustment theory Qualitative spatial reasoning Displacement Data cleaning
The author would like to thank Reinhard Moratz and the anonymous reviewers for valuable feedback and suggestions.
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