Algorithmica

, Volume 53, Issue 3, pp 314–336 | Cite as

Real Two Dimensional Scaled Matching

  • Amihood Amir
  • Ayelet Butman
  • Moshe Lewenstein
  • Ely Porat
Article
First Online:
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Accepted:

Abstract

Scaled Matching refers to the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Scaled matching is an important problem that was originally inspired by Computer Vision.

Finding a combinatorial definition that captures the concept of real scaling in discrete images has been a challenge in the pattern matching field. No definition existed that captured the concept of real scaling in discrete images, without assuming an underlying continuous signal, as done in the image processing field. We present a combinatorial definition for real scaled matching that scales images in a pleasing natural manner. We also present efficient algorithms for real scaled matching.

The running times of our algorithms are as follows. For T, a two-dimensional n×n text array, and P, an m×m pattern array, we find in T all occurrences of P scaled to any real value in time O(nm 3+n 2 mlog m).

Keywords

Design and analysis of algorithms Combinatorial algorithms on words Pattern matching Scaled pattern matching Approximate pattern matching Generalized pattern matching 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Amihood Amir
    • 1
    • 2
  • Ayelet Butman
    • 3
  • Moshe Lewenstein
    • 1
  • Ely Porat
    • 1
  1. 1.Bar-Ilan UniversityRamat-GanIsrael
  2. 2.John Hopkins UniversityBaltimoreUSA
  3. 3.Holon Academic Institute of TechnologyHolonIsrael

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