B. Forte, E. R. Vrscay. Solving the inverse problem for function/image approximation using iterated function systems, II. Algorithm and computations. Fractals, 2(3):335-346, 1994.
In this paper, we provide an algorithm for the construction of IFSM approximations to a target set , where and (Lebesgue measure). The algorithm minimizes the squared "collage distance" || v - Tv || 2\2162. We work with an infinite set of fixed affine IFS maps satisfying a certain density and nonoverlapping condition. As such, only an optimization over the grey level maps : R+ ( R+ is required. If affine maps are assumed, i.e. = (i t and (i , then the algorithm becomes a quadratic programming (QP) problem in the (i and (i . We can also define a "local IFSM" (LIFSM) which considers the actions of contractive maps on subsets of X to produce smaller subsets. Again, affine maps are used, resulting in a QP problem. Some approximations of functions on [0,1] and images in [0,1]2 are presented.
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@article{FoVr94b,
Author = {Forte, B. and Vrscay, E. R.},
Title = {Solving the inverse problem for function/image approximation using iterated function systems, II. Algorithm and computations},
Journal = {Fractals},
Volume = {2},
Number = {3},
Pages = {335--346},
Year = {1994}
}