Inplace 2D matching in compressed images

  • Authors:

  • Amihood Amir;Gad M. Landau;Dina Sokol

  • Affiliations:

  • Department of Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel and College of Computing, Georgia Tech;Department of Computer Science, Haifa University, Haifa 31905 Israel and Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY;Bar-Ilan University, 52900 Ramat-Gan, Israel

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2003

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Abstract

The compressed matching problem is the problem of finding all occurrences of a pattern in a compressed text. In this paper we discuss the 2-dimensional compressed matching problem in Lempel-Ziv compressed images. Given a pattern P of (uncompressed) size m × m, and a text T of (uncompressed) size n × n, both in 2D-LZ compressed form, our algorithm finds all occurrences of P in T. The algorithm is strongly inplace, that is, the amount of extra space used is proportional to the best possible compression of a pattern of size m2. The best compression that the 2D-LZ technique can obtain for a file of size m2 is O(m). The time for performing the search is O(n2) and the preprocessing time is O(m3). Our algorithm is general in the sense that it can be used for any 2D compression which can be sequentially decompressed in small space.