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SOLVING THE INVERSE PROBLEM FOR FUNCTION/IMAGE APPROXIMATION USING ITERATED FUNCTION SYSTEMS II: ALGORITHM AND COMPUTATIONS
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1994
Year
Mathematical ProgrammingNumerical AnalysisEngineeringComputational ComplexitySemidefinite ProgrammingNumerical ComputationComputational GeometryApproximation TheoryCollage DistanceLinear OptimizationContinuous OptimizationReconstruction TechniqueIfsm ApproximationsInverse ProblemsComputer ScienceLocal IfsmInteger ProgrammingQuadratic ProgrammingConstructive ApproximationOptimization ProblemConvex OptimizationApproximation MethodLinear Programming
In this paper, we provide an algorithm for the construction of IFSM approximations to a target set [Formula: see text], where X ⊂ R D and µ = m (D) (Lebesgue measure). The algorithm minimizes the squared "collage distance" [Formula: see text]. We work with an infinite set of fixed affine IFS maps w i : X → X satisfying a certain density and nonoverlapping condition. As such, only an optimization over the grey level maps ϕ i : R + → R + is required. If affine maps are assumed, i.e. ϕ i = α i t + β i , then the algorithm becomes a quadratic programming (QP) problem in the α i and β i . We can also define a "local IFSM" (LIFSM) which considers the actions of contractive maps w i on subsets of X to produce smaller subsets. Again, affine ϕ i maps are used, resulting in a QP problem. Some approximations of functions on [0,1] and images in [0, 1] 2 are presented.