Inverse Problems in Fractal Construction: Hellinger Distance Method

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1994 · Volume 56 · Issue 4

DOI: 10.1111/j.2517-6161.1994.tb02008.x

Abstract

Some images can be approximated by the geometry of fractals that are attractors of iterative function systems. The inverse problems to be discussed involve searching for an iterative function system that best approximates a given image. Existing methods often assume full knowledge of the image and rely on complicated computations to avoid local optima in the distance measure being used. We propose the use of a revised Hellinger distance in addressing inverse problems. It is shown that the new method does not require full knowledge of the image to be approximated and can eliminate most of the unwanted locally optimal approximations.

Keywords

bounded lipschitz distance, collage theorem, hausdorff distance, hutchinson distance

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