A New Visibility Partition for Affine Pattern Matching

  • Michiel Hagedoorn
  • Mark Overmars
  • Remco C. Veltkamp
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

Visibility partitions play an important role in computer vision and pattern matching. This paper studies a new type of visibility, reflection-visibility, with applications in affine pattern matching: it is used in the definition of the reflection metric between two patterns consisting of line segments. This metric is affine invariant, and robust against noise, deformation, blurring, and cracks. We present algorithms that compute the reflection visibility partition in O((n+k) log(n)+v) randomised time, where k is the number of visibility edges (at most O(n 2 )), and v is the number of vertices in the partition (at most O(n 2 +k 2 ). We use this partition to compute the reflection metric in O(r(n A + n B )) randomised time, for two line segment unions, with n A and n B line segments, separately, where r is the complexity of the overlay of two reflection-visibility partitions (at most O(nA 4 + nB 4)).

Keywords

Line Segment Pattern Match Computational Geometry Visibility Graph Visibility Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Michiel Hagedoorn
    • 1
  • Mark Overmars
    • 1
  • Remco C. Veltkamp
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

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