Geodesic
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Michael Keane1 ; K. Károly2 ; Boris Solomyak3
1 Mathematics Department Wesleyan University Middletown, CT 06459, U.S.A. and CWI University of Amsterdam Amsterdam, The Netherlands
2 Institute of Mathematics Technical University of Budapest P.O. Box 91 H-1529 Budapest, Hungary
3 Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350, U.S.A.
Fundamenta Mathematicae, Tome 180 (2003) no. 3, pp. 279-292.

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Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
DOI : 10.4064/fm180-3-5
Keywords: consider graph directed iterated function system gifs line which consists similarities assuming neither separation conditions nor restrictions contractions compute almost sure dimension attractor apply result partial answer problem field fractal image recognition concerning self affine graph directed attractors space

Michael Keane 1 ; K. Károly 2 ; Boris Solomyak 3

1 Mathematics Department Wesleyan University Middletown, CT 06459, U.S.A. and CWI University of Amsterdam Amsterdam, The Netherlands
2 Institute of Mathematics Technical University of Budapest P.O. Box 91 H-1529 Budapest, Hungary
3 Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350, U.S.A. 
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Michael Keane; K. Károly; Boris Solomyak. The dimension of graph directed
attractors with 
overlaps on the line, with an application to a
problem in fractal image recognition. Fundamenta Mathematicae, Tome 180 (2003) no. 3, pp. 279-292. doi : 10.4064/fm180-3-5. http://geodesic.mathdoc.fr/articles/10.4064/fm180-3-5/

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