A combinatorial geometrical approach to two-dimensional robust pattern matching with scaling and rotation

  • Authors:

  • Christian Hundt;Maciej Likiewicz;Ragnar Nevries

  • Affiliations:

  • Institut für Informatik, Universität Rostock, Germany;Institut für Theoretische Informatik, Universität zu Lübeck, Germany;Institut für Informatik, Universität Rostock, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

The problem of two-dimensional pattern matching invariant under a given class of admissible transformations F is to find matches of transformed versions f(P) of a pattern P in a given text T, for all f in F. In this paper, pattern matching invariant under compositions of real valued scaling and rotation are investigated. We give a new discretization technique for this class of transformations and prove sharp lower and upper bounds on the number of different possibilities to transform a pattern in this way. Subsequently, we present the first efficient pattern matching algorithm invariant under compositions of scaling and rotation. The algorithm works in time O(m^2n^6) for patterns of size m^2 and texts of size n^2. We conclude with an experimental section to support the practical use of our results.