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.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
S. Akl, The Design of Parallel Algorithms, Prentice-Hall (1989).
M. Brady, Computational Approaches to Image Understanding, ACM Computing Surveys, vol. 14, no. 1(1982)3–72.
M. Brainerd, Tree Generatin Regular Systems, Information and Control, vol. 14, (1969)217–231.
L.S. Davis and A. Rosenfeld, Cooperating processes for low-level vision: A survey, Artif. Intell. 17(1981)245–265.
R.D. Dyer, A. Rosenfeld and H. Samet, Region Representation: Boudary code from Quadtrees, Communications of the ACM, vol. 23(1979)171–179.
K.Inoue and A. Nakamura, Some Topological Properties of ∑-structure automata, S-C-C 7 (1982)19–27.
C. L. Jackins and S. L. Tanimoto, Oct-trees and their use in representing Three dimensional objects, Computer Graphics and Image Processing, 14(1980)249–270.
M. Nivat and A. Saoudi, On Parallel Recognition Algorithms for High Dimensional Images, The 1st Int. Conf. on Parallel Image Processing, Paris (1991).
S. Ranade, A. Rosenfeld and J.M. Prewitt, Use of Quadtrees for Image Segmentation, Computer Science Dept., University of Maryland, TR-878 (1980).
A. Rosenfeld and A. C. Kak, Digital Picture Processing, vol. 1 and 2, (The second edition) Academic Press (1982).
A. Rosenfeld, Array, Tree and Graph Grammars, in ”Syntactic and Structural Pattern Recognition: Theory and Applications ”,(H. Bunke and A. Sanfeliu, Eds.), World Scientific (1990).
H. Samet and A. Rosenfeld, Quadtreee Representations of Binary Images, Proc. 5th Int. Conf. on Pattern Recognition, Miami(1980)815–818.
H. Samet, The Design and Analysis of Spatial Data Structures, Addison Wesley (1990).
A. Saoudi and W. Rytter, Parallel Algorithms for 2D-Image Recognition, Int. Conf. on Pattern Recognition (1992).
J. W. Thatcher, Tree Automata:an informal survey, in ”Currents in Theory of Computing”(ed; A.V. Ano), Prentice-Hall(1973).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-56346-6_41
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56346-4
Online ISBN: 978-3-540-47538-5
eBook Packages: Springer Book Archive