Reestablishing Consistency of Uncertain Geometric Relations in Digital Images

  • Peter Veelaert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)


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.


Parameter Point Uncertainty Region Parallel Pair Digital Plane Parallel Incidence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Peter Veelaert
    • 1
  1. 1.HogentGhentBelgium

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