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Real Two Dimensional Scaled Matching

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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).

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Authors and Affiliations

  1. Bar-Ilan University, Ramat-Gan, Israel

    Amihood Amir, Moshe Lewenstein & Ely Porat

  2. John Hopkins University, Baltimore, USA

    Amihood Amir

  3. Holon Academic Institute of Technology, Holon, Israel

    Ayelet Butman

Authors
  1. Amihood Amir
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  2. Ayelet Butman
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  3. Moshe Lewenstein
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  4. Ely Porat
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Corresponding author

Correspondence to Amihood Amir.

Additional information

Research of A. Amir partially supported by ISF grant 282/01 and NSF grant CCR-01-04494.

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Amir, A., Butman, A., Lewenstein, M. et al. Real Two Dimensional Scaled Matching. Algorithmica 53, 314–336 (2009). https://doi.org/10.1007/s00453-007-9021-x

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  • DOI: https://doi.org/10.1007/s00453-007-9021-x

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