Abstract
We investigate how the size of the compressed version of a 2-dimensional image changes when we cut off a part of it, e.g. extracting a photo of one person from a photo of a group of people. 2-dimensional compression is considered in terms of finite automata. Let n be the size of the smallest acyclic automaton which describes an image T. We show that the tight bound for the compression size of a subsegment (subimage) in the deterministic case is Θ(n 2.5) and in the weighted case is Θ(n). We also show how to construct efficiently the compressed representation of subsegments given the compressed representation of the whole image. Two applications of subsegments compression are more efficient automata-compressed pattern-matching and the first polynomial time algorithm for the fully compressed pattern-checking problem for weighted automata.
Supported by Academy of Finland under grant 14047.
Supported partially by the grant KBN 8T11C03915.
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References
A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEEE Data Compression Conference 279–288 (1992).
P. Berman, M. Karpinski, L. Larmore, W. Plandowski, W. Rytter, The compexity of pattern matching of highly compressed two-dimensional texts, Combinatorial Pattern Matching 1997, in Springer Verlag
K. Culik and J. Karhumaki, Finite automata computing real functions, SIAM J. Comp (1994).
K. Culik and J. Kari, Image compression using weighted finite automata, Computer and Graphics 17, 305–313 (1993).
D. Derencourt, J. Karhumäki, M. Letteux and A. Terlutte, On continuous functions computed by real functions, RAIRO Theor. Inform. Appl. 28, 387–404 (1994).
S. Eilenberg, Automata, Languages and Machines, Vol.A, Academic Press, New York (1974).
K. Culik and J. Kari, Fractal image compression: theory and applications, (ed. Y. Fisher, Springer Verlag 243–258 (1995).
M. Farach and M. Thorup, String matching in Lempel-Ziv compressed strings, in STOC’95, pp. 703–712.
J. Kari, P. Franti, Arithmetic coding of weighted finite automata, RAIRO Theor. Inform. Appl. 28 343–360 (1994).
L. Gąsieniec, M. Karpiński, W. Plandowski and W. Rytter, Efficient Algorithms for Compressed Strings, in SWAT’96 (1996).
J. Karhumaki, W. Plandowski, W. Rytter, Pattern matching for images generated by finite automata, FCT’97, in LNCS Springer Verlag 1997
M. Karpinski, W. Rytter and A. Shinohara, Pattern-matching for strings with short description, in CPM’95 (1995).
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© 1999 Springer-Verlag Berlin Heidelberg
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Karhumäki, J., Plandowski, W., Rytter, W. (1999). The Compression of Subsegments of Images Described by Finite Automata. In: Crochemore, M., Paterson, M. (eds) Combinatorial Pattern Matching. CPM 1999. Lecture Notes in Computer Science, vol 1645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48452-3_14
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DOI: https://doi.org/10.1007/3-540-48452-3_14
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