Abstract
In this paper, we use tree grammars, and tree automata for representing a set of Multidimensional images. We show that the set of all full 2d-trees (Quadtrees, Octrees,...etc) is not a regular set. But every finite set of full 2d-trees can be represented by a regular tree grammar. We give optimal algorithms for solving the S-equivalence problem of two 2d-trees and the reduction (i.e. compression) problem of a full 2d-trees. We give some characterizations of regular trees sets. We present a parallel algorithm for recognizing a multidimensional image of size N in O(log(N)) time with O(N) = N/d processors on EREW-PRAM model.
This research was supported by CEFIPRA and PRC Maths-Info, France.
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© 1992 Springer-Verlag Berlin Heidelberg
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Saoudi, A. (1992). Parallel recognition of multidimensional images using regular tree grammars. In: Nakamura, A., Nivat, M., Saoudi, A., Wang, P.S.P., Inoue, K. (eds) Parallel Image Analysis. ICPIA 1992. Lecture Notes in Computer Science, vol 654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56346-6_41
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DOI: https://doi.org/10.1007/3-540-56346-6_41
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