Improved cuckoo search with Luus-Jakoola heuristics for the IFS inverse problem of binary self-similar fractal images

Abstract

This paper addresses the following problem: how to reconstruct a given binary self-similar fractal image through iterated functions systems. This means to obtain an iterated function system (IFS) whose attractor is a good approximation of the input image. This problem is known to be a very difficult multivariate nonlinear continuous optimization problem. To tackle this issue, this paper introduces a new hybrid method comprised of a modification of the original cuckoo search method for global optimization called improved cuckoo search (ICS) along with the Luus-Jakoola heuristics for local search. This hybrid methodology is applied to three fractal examples with 3, 4, and 26 contractive functions. Our experimental results show that the method performs very well and provides visually satisfactory solutions for the instances in our benchmark. The numerical values of the similarity index used in this work also show that the results are not optimal yet, suggesting that the method might arguably be further improved.