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Faster Two Dimensional Scaled Matching

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Abstract

The rapidly growing need for analysis of digitized images in multimedia systems has lead to a variety of interesting problems in multidimensional pattern matching. One of the problems is that of scaled matching, finding all appearances of a pattern, proportionally enlarged according to an arbitrary real-sized scale, in a given text.

The currently fastest known algorithm for this problem uses techniques from dictionary matching to solve the problem in O(nm 3+n 2 mlog m) time using O(nm 3+n 2) space, where T is a two-dimensional n×n text array and P is a two-dimensional m×m pattern array.

We present a new approach for solving the scaled matching problem improving both the running time and the space requirements. Our algorithm runs in O(n 2 m) time and uses O(n 2) space.

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References

  1. Amir, A., Benson, G., Farach, M.: An alphabet independent approach to two dimensional pattern matching. SIAM J. Comput. 23(2), 313–323 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Amir, A., Butman, A., Crochemore, M., Landau, G.M., Schaps, M.: Two-dimensional pattern matching with rotations. In: Proc. 14th Annual Symposium on Combinatorial Pattern Matching (CPM 2003). LNCS, vol. 2676, pp. 17–31. Springer, Berlin (2003)

    Chapter  Google Scholar 

  3. Amir, A., Butman, A., Lewenstein, M.: Real scaled matching. Inf. Process. Lett. 70(4), 185–190 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Amir, A., Butman, A., Lewenstein, M., Porat, E.: Real two dimensional scaled matching. In: Proc. 8th Workshop on Algorithms and Data Structures (WADS’03), pp. 353–364 (2003)

  5. Amir, A., Butman, A., Lewenstein, M., Porat, E., Tsur, D.: Efficient one dimensional real scaled matching. In: Proc. 11th Symposium on String Processing and Information Retrieval (SPIRE’04), pp. 1–9 (2004)

  6. Amir, A., Calinescu, G.: Alphabet independent and dictionary scaled matching. In: Proc. 7th Annual Symposium on Combinatorial Pattern Matching (CPM 96), pp. 320–334 (1996)

  7. Amir, A., Farach, M.: Efficient 2-dimensional approximate matching of half-rectangular figures. Inf. Comput. 118(1), 1–11 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Amir, A., Landau, G.: Fast parallel and serial multidimensional approximate array matching. Theor. Comput. Sci. 81, 97–115 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Amir, A., Landau, G.M., Vishkin, U.: Efficient pattern matching with scaling. J. Algorithms 13(1), 2–32 (1992)

    Article  MATH  Google Scholar 

  10. Amir, A., Tsur, D., Kapah, O.: Faster two dimensional pattern matching with rotations. In: Proc. 15th Annual Symposium on Combinatorial Pattern Matching (CPM’04), pp. 409–419 (2004)

  11. Fredriksson, K., Mäkinen, V., Navarro, G.: Rotation and lighting invariant template matching. In: Proceedings of the 6th Latin American Symposium on Theoretical Informatics (LATIN’04). LNCS, pp. 39–48. Springer, Berlin (2004)

    Google Scholar 

  12. Fredriksson, K., Navarro, G., Ukkonen, E.: An index for two dimensional string matching allowing rotations. In: Prof. IFIP International Conference on Theoretical Computer Science (IFIP TCS). LNCS, vol. 1872, pp. 59–75. Springer, Berlin (2000)

    Google Scholar 

  13. Fredriksson, K., Navarro, G., Ukkonen, E.: Optimal exact and fast approximate two dimensional pattern matching allowing rotations. In: Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching (CPM 2002). LNCS, vol. 2373, pp. 235–248. Springer, Berlin (2002)

    Chapter  Google Scholar 

  14. Fredriksson, K., Ukkonen, E.: A rotation invariant filter for two-dimensional string matching. In: Proc. 9th Annual Symposium on Combinatorial Pattern Matching (CPM’98). LNCS, vol. 1448, pp. 118–125. Springer, Berlin (1998)

    Chapter  Google Scholar 

  15. Fredriksson, K., Ukkonen, E.: Combinatorial methods for approximate pattern matching under rotations and translations in 3D arrays. In: Proc. 7th Symposium on String Processing and Information Retrieval (SPIRE’2000), pp. 96–104. IEEE Comput. Soc., Los Alamitos (2000)

    Chapter  Google Scholar 

  16. Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. 16th ACM Symposium on Theory of Computing, 67, pp. 135–143 (1984)

  17. Krithivansan, K., Sitalakshmi, R.: Efficient two dimensional pattern matching in the presence of errors. Inf. Sci. 13, 169–184 (1987)

    Article  Google Scholar 

  18. Landau, G.M., Vishkin, U.: Pattern matching in a digitized image. Algorithmica 12(3/4), 375–408 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pentland, A.: Invited talk. NSF Institutional Infrastructure Workshop (1992)

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Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Amihood Amir & Eran Chencinski

  2. Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218, USA

    Amihood Amir

Authors
  1. Amihood Amir
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  2. Eran Chencinski
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Correspondence to Amihood Amir.

Additional information

Research of A. Amir was partly supported by ISF grant 35/05.

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Amir, A., Chencinski, E. Faster Two Dimensional Scaled Matching. Algorithmica 56, 214–234 (2010). https://doi.org/10.1007/s00453-008-9173-3

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  • DOI: https://doi.org/10.1007/s00453-008-9173-3

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