Faster two dimensional scaled matching

  • Authors:

  • Amihood Amir;Eran Chencinski

  • Affiliations:

  • Department of Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel and College of Computing, Georgia Tech, Atlanta, GA;Dept. of Computer Science, Bar-Ilan U., Ramat-Gan, Israel

  • Venue:
  • CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
  • Year:
  • 2006

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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 best known algorithm for this problem uses techniques from dictionary matching to solve the problem in O(nm3+n2m logm) time using O(nm3+n2) space, where the text is a two-dimensional n ×n array and the pattern is a two-dimensional m ×m array. We present a new approach for solving the scaled matching problem improving both the running times and the space requirements. Our algorithm runs in O(n2m) time and uses O(n2) space. This time includes the preprocessing (O(m3) time and O(m2) space), since the problem is only defined for m ≤n.