Two-Dimensional Pattern Matching with Combined Scaling and Rotation

  • Christian Hundt
  • Maciej Liśkiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5029)


The problem of two-dimensional pattern matching invariant under a given class of admissible transformations \(\mathcal{F}\) is to find in text T matches of transformed versions f(P) of the pattern P, for all f in \(\mathcal{F}\). In this paper, pattern matching invariant under compositions of real 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 2 n 6) for patterns of size m 2 and texts of size n 2. Our method can also be applied to the image matching problem, the well known issue in the image processing research.


combinatorial pattern matching digital image matching discrete rotations and scalings discrete algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christian Hundt
    • 1
  • Maciej Liśkiewicz
    • 2
  1. 1.Institut für InformatikUniversität RostockGermany
  2. 2.Institut für Theoretische InformatikUniversität zu LübeckGermany

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