Journal Article10.1142/S0218348X94000429
Solving the inverse problem for function/image approximation using iterated function systems i: theoretical basis
Bruno Forte,Edward R. Vrscay +1 more
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TL;DR: In this paper, an N-map IFS with grey level maps (IFSM) is proposed, where each IFSM is associated with a contractive operator T with fixed point, and a rigorous solution to the following inverse problem is provided: given a target υ ∈ ℒp(X, µ) and an ∊ > 0, find an IFSm whose attractor satisfies.
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Abstract: We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over ℒp (X, µ): An N-map IFS with grey level maps (IFSM), to be denoted as (w, Φ), is a set w of N contraction maps wi: X → X over a compact metric space (X, d) (the "base space") with an associated set Φ of maps ϕi: R → R. Associated with each IFSM is a contractive operator T with fixed point . We provide a rigorous solution to the following inverse problem: Given a target υ ∈ ℒp(X, µ) and an ∊ > 0, find an IFSM whose attractor satisfies .
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Citations
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Dietmar Saupe,Raouf Hamzaoui,Hannes Hartenstein +2 more
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TL;DR: This paper has chosen the similarity to a particular variant of vector quantization as the most direct approach to fractal image compression and surveys some of the advanced concepts such as fast decoding, hybrid methods, and adaptive partitionings.
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Theory of Generalized Fractal Transforms
Bruno Forte,Edward R. Vrscay +1 more
- 01 Jan 1996
TL;DR: In this article, the authors consider the more general overlapping case, i.e., the sets w i (X) are nonoverlapping (or at least ignore any overlapping), and the question of how to combine the n(x) fractal components i k (u(w?1 i k(x))) to form a generalized fractal transform (Tu)(x).
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Iterated function systems: theory, applications and the inverse problem
Edward R. Vrscay
- 01 Jan 1991
TL;DR: In this paper, a generalized recurrent IFS is introduced, with suitably constructed measure space, from which the existence of an invariant measure follows, and the inverse problem of fractal/measure construction is discussed.
75
Continuity of Attractors and Invariant Measures for Iterated Function Systems
P. M. Centore,E. R. Vrscay +1 more
TL;DR: In this paper, it was shown that both the attractor A and invariant measure μ of an N-map Iterated Function System vary continuously with variations in the contractive IFS maps as well as the probabilities.
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