Reestablishing consistency of uncertain geometric relations in digital images

Authors:
Peter Veelaert
Affiliations:
Hogent, Ghent, Belgium
Venue:
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Year:
2002

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Abstract

In uncertain geometry in the 2D plane, points are replaced by uncertainty regions. By allowing uncertainty several geometric notions such as parallelism and concurrency become inconsistent with Euclidean geometry. In previous work we explained how consistency can be partially restored by graph-theoretical grouping algorithms. In this paper we study inconsistencies at a higher-level, e.g., the violation of Desargues's Theorem or Pappus's Theorem. We provide a simple algorithm that completely restores Euclidean consistency. Although the algorithm may not give optimal results with respect to grouping, it shows a way to develop more sophisticated algorithms to obtain global consistency in uncertain geometry.