Abstract: This work is an extension of a previous paper (presented at the Cyberworlds 2019 conference) introducing a new method for fractal compression of bitmap binary images. That work is now extended and enhanced through three new valuable features: (1) the bat algorithm is replaced by an improved version based on optimal forage strategy (OFS) and random disturbance strategy (RDS); (2) the inclusion of new similarity metrics; and (3) the consideration of a variable number of contractive maps, whose value can change dynamically over the population and over the iterations. The first feature improves the search capability of the method, the second one improves the reconstruction accuracy, and the third one computes the optimal number of contractive maps automatically. This new scheme is applied to a benchmark of two binary fractal images exhibiting a complex and irregular fractal shape. The graphical and numerical results show that the method performs very well, being able to reconstruct the input images with high accuracy. It also computes the optimal number of contractive maps in a fully automatic way. A comparative work with other alternative methods described in the literature is also carried out. It shows that the presented method outperforms the previous approaches significantly.

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