Abstract
We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts simultaneously all subpictures of the same size from the input picture and sends them to the second subnetwork. The second subnetwork checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterwards, we present a solution based on networks containing both evolutionary and hiding processors running in \({\cal O}(n+m+kl+k)\) computational (processing and communication) steps, where the input picture and the pattern are of size (n,m) and (k,l), respectively.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adleman, L.M., Cheng, Q., Goel, A., Huang, M.: Running time and program size for self-assembled squares. In: Proc. 33rd ACM STOC, pp. 740–748 (2001)
Aggarwal, G., et al.: Complexities for generalized models of self-assembly. SIAM Journal on Computing 34, 1493–1515 (2005)
Amir, A., Benson, G., Farach, M.: Alphabet independent two dimensional matching. In: Proc. 24th ACM STOC, pp. 59–68 (1992)
Bottoni, P., Labella, A., Mitrana, V.: Networks of evolutionary picture processors. Fundamenta Informaticae 131, 337–349 (2014)
Bozapalidis, S., Grammatikopoulou, A.: Recognizable picture series. J. of Automata, Languages and Combinatorics 10, 159–183 (2005)
Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Handbook of Formal Languages, pp. 215–267. Springer (1997)
Giammarresi, D., Restivo, A.: Recognizable picture languages. Int. J. Pattern Recognition and Artificial Intelligence 6, 241–256 (1992)
Inoue, I., Takanami, I.: A survey of two-dimensional automata theory. In: Dassow, J., Kelemen, J. (eds.) IMYCS 1988. LNCS, vol. 381, pp. 72–91. Springer, Heidelberg (1989)
Manea, F., Martín-Vide, C., Mitrana, V.: Accepting networks of evolutionary word and picture processors: A survey. In: Scientific Applications of Language Methods. Mathematics, Computing, Language, and Life: Frontiers in Mathematical Linguistics and Language Theory, vol. 2, pp. 523–560. World Scientific (2010)
Margenstern, M., Mitrana, V., Jesús Pérez-Jímenez, M.: Accepting Hybrid Networks of Evolutionary Processors. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 235–246. Springer, Heidelberg (2005)
Marriott, K., Meyer, B.E.: Visual Language Theory. Springer (1998)
Maürer, I.: Characterizations of recognizable picture series. Theoretical Computer Science 374, 214–228 (2007)
Rosenfeld, A., Kak, A.C.: Digital Picture Processing. Academic Press, New York (1982)
Rosenfeld, A., Siromoney, R.: Picture languages – a survey. Languages of Design 1, 229–245 (1993)
Siromoney, G., Siromoney, R., Krithivasan, K.: Abstract families of matrices and picture languages. Computer Graphics and Image Processing 1, 284–307 (1972)
Siromoney, G., Siromoney, R., Krithivasan, K.: Picture languages with array rewriting rules. Information and Control 22, 447–470 (1973)
Subramanian, K.G., Siromoney, R.: On array grammars and languages. Cybernetics and Systems 18, 77–98 (1987)
Wang, P.S.: Hierarchical structure and complexities of parallel isometric patterns. IEEE Trans. PAM I 5, 92–99 (1983)
Wang, P.S.: Sequential/parallel matrix array languages. Journal of Cybernetics 5, 19–36 (1975)
Wang, P.S., Bunke, H. (eds.): Handbook on Optical Character Recognition and Document Image Analysis. World Scientific (1996)
Zhu, R.F., Takaoka, T.: A technique for two-dimensional pattern matching. Communications of the ACM 32, 1110–1120 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bordihn, H., Bottoni, P., Labella, A., Mitrana, V. (2014). Solving 2D-Pattern Matching with Networks of Picture Processors. In: Dediu, AH., Lozano, M., Martín-Vide, C. (eds) Theory and Practice of Natural Computing. TPNC 2014. Lecture Notes in Computer Science, vol 8890. Springer, Cham. https://doi.org/10.1007/978-3-319-13749-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-13749-0_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13748-3
Online ISBN: 978-3-319-13749-0
eBook Packages: Computer ScienceComputer Science (R0)