Abstract
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.
Supported by DFG research grant RE 672/5-1.
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Hundt, C., Liśkiewicz, M. (2008). Two-Dimensional Pattern Matching with Combined Scaling and Rotation. In: Ferragina, P., Landau, G.M. (eds) Combinatorial Pattern Matching. CPM 2008. Lecture Notes in Computer Science, vol 5029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69068-9_4
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DOI: https://doi.org/10.1007/978-3-540-69068-9_4
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