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Reductions in the search space for deriving a fractal set of an arbitrary shape

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Abstract

At present, the problem of finding a quick and efficient way of representing an arbitrary shape as a set of contraction mappings (an iterated function system) is unresolved. Such a representation is particularly useful in shape representation since the primitives used to construct the shape will automatically have the correct morphology. Several attempts have been made to solve this problem and some of these are discussed. The main difficulty with these approaches is the large size and great complexity of the search space. This paper examines several constraints, all of a low computational complexity, which can be placed on each of the mappings which make up a possible solution. These constraints reduce the search space of four of the six coefficients of a mapping by between 20% and 85%, and of the other two by between 75% and 95% (the size of the reduction depends only on the size of the bounding box of the shape). Since these constraints apply to each mapping of an IFS, their cumulative effect on the search space is substantial. It is anticipated that these reductions in the search space can be used to aid a variety of search algorithms.

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  1. Laboratory for Natural Language Engineering, Department of Computer Science, University of Durham Science Site, Stockton Road, DH1 3LE, Durham, UK

    David John Nettleton & Roberto Garigliano

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  1. David John Nettleton
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  2. Roberto Garigliano
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Nettleton, D.J., Garigliano, R. Reductions in the search space for deriving a fractal set of an arbitrary shape. J Math Imaging Vis 6, 379–392 (1996). https://doi.org/10.1007/BF00123353

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