Hybrid GA-PSO method with local search and image clustering for automatic IFS image reconstruction of fractal colored images

Abstract

Over the past few decades, the application of iterated function systems (IFS) in reconstructing fractal images has been a challenging research area. Numerous methods have been proposed to address this issue. However, they generally focus on binary or grayscale images, neglecting the color component of the process. Consequently, they are unsuitable for reconstructing colored images. In a previous paper presented at the ISCMI 2021 conference, the authors introduced a novel approach that utilizes the cuckoo search algorithm and k-means clustering for IFS fractal reconstruction of colored images. Building upon that work, this paper introduces an enhanced and extended method by combining genetic algorithms (GAs) and particle swarm optimization (PSO) with local search and image clustering. In this approach, GA and PSO are mutually coupled to automatically determine the color of the contractive functions and the IFS parameters, respectively. The output of each method serves as the input for the other in an iterative manner. Main contributions of this method are: (1) it computes automatically the optimal number and IFS code of the contractive functions; (2) the color of the contractive functions is determined automatically through an optimization process using GA; (3) a local refinement step is performed to further enhance the final solution. Overall, this new method yields highly accurate results in reconstructing the geometry and color of input fractal images, without requiring any additional information about the target beyond the bitmap image.