Abstract
For motivation purpose, imagine the following continuous pattern matching problem. Given are two continuous pictures, each consisting of unicolor regions; one picture is called the scene and the other the pattern. The problem is to find all occurrences of the pattern in the scene.
As a step towards efficient algorithmic handling of the continuous pattern matching problem by computers, where discretized representations are involved, we consider in this paper a two-dimensional pattern matching problem where the pattern and the text are specified in terms of exemplar digitized images.
From the wider perspective of areas such as computer vision or image processing, our problem definitions identify an important gap in the fundamental theory of image formation and image processing — how to determine, even in the absence of noise, if a digitized image of a scene could contain an image of a given pattern?
Partially supported by the New York State Science and Technology Foundation Center for Advanced Technology.
Partially supported by NSF grants CCR-8906949 and CCR-9111348.
Preview
Unable to display preview. Download preview PDF.
References
K. Abrahamson, “Generalized string matching,” SIAM J. Comput., 17:1039–1051, 1987.
A. Amir and G.M. Landau, “Fast parallel and serial multi dimensional approximate array matching,” Theoretical Computer Science, 81:97–115, 1991.
D.H. Ballard, and C.M. Brown, Computer Vision, Prentice-Hall, 1982.
S. Ben-Yehuda and R.Y. Pinter, “Symbolic layout improvement using string matching based local transformation,” Proc. of the Decennial Caltech Conf. on VLSI, 227–239, 1989.
M.B. Clowes, “On seeing things,” Artificial Intelligence, 2:79–116, 1971.
M. Dubiner, Z. Galil, and E. Magen, “Faster tree pattern Matching,” Proc. 31th IEEE Symp. Foundations of Computer Science, 145–150, 1990.
S. Even, A Itai and A. Shamir, “On the complexity of timetables and multicommodity flow problems,” SIAM I. Computing, 5(4):691–703, 1976.
M.J. Fischer and M.S. Paterson, “String Matching and Other Products,” Complexity of Computation, R.M. Karp (editor), SIAM-AMS Proceedings, 7:113–125, 1974.
D.A. Huffman, “Impossible objects as nonsense sentences,” Machine Intelligence, 6:295–323, 1971, B. Meltzer and D. Michie (Eds.), Edinburgh University Press.
S.R. Kosaraju, “Efficient tree pattern Matching,” Proc. 30th IEEE Symp. Foundations of Computer Science, 178–183, 1989.
E.S. Lander, R. Langridge, and D.M. Saccocio, “A report on computing in Molecular Biology: mapping and interpreting Biological information,” CACM, 34,11: 33–39, 1991.
G.M. Landau and U. Vishkin, “Pattern matching in a digitized image,” Proc. 3rd ACM-SIAM Symposium on Discrete Algorithms, 453–462, 1992.
G.M. Landau and U. Vishkin, “Pattern matching in a digitized image,” Algorithmica, to appear. Also, Technical Report UMIACS-TR-92-132, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, 1992. This paper is journal version of [LV-92a] and the present paper.
R. Y. Pinter, “Efficient string matching with don't-care patterns,” in A. Apostolico and Z. Galil (editors), Combinatorial Algorithms on Words, NATO ASI Series, Series F: Computer and System Sciences, Vol. 12, Springer-Verlag, 97–107, 1985.
H. Samet, The Design and Analysis of Spatial Data Structures, Addison-Wesley, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Landau, G.M., Vishkin, U. (1993). Two dimensional pattern matching in a digitized image. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1993. Lecture Notes in Computer Science, vol 684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029802
Download citation
DOI: https://doi.org/10.1007/BFb0029802
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56764-6
Online ISBN: 978-3-540-47732-7
eBook Packages: Springer Book Archive