Cuckoo search with Lévy flights for reconstruction of outline curves of computer fonts with rational Bézier curves

Abstract

Cuckoo search is a powerful nature-inspired metaheuristics recently introduced by Prof. Xin-She Yang to solve difficult optimization problems. In this paper, we apply this method to solve a very difficult problem: the reconstruction of outline curves of computer fonts with single curves. In particular, we wish to obtain the underlying shape of the outline curves from a set of noisy data points assumed to lie on the boundary separating the body of the font and the (either inner or outer) background. Usually, polynomial Bezier curves are used to this task. However, there are some shapes that cannot properly described with polynomial curves. The classical solution has been to consider composite Bezier curves. This solution works well but it is not optimal, because it requires several curves working together to describe a single outline shape. In this paper, we overcome this limitation by using rational Bezier curves. As we will show, this problem is by far much more complicated than the polynomial one. Our approach is based on the application of the cuckoo search with Levy flights method to compute all relevant parameters of our approximation problem. To illustrate the applicability of our approach, it is applied to obtain the outline curves of several letters and numbers forming the name of this conference with an artistic computer vector font. Our experimental results show that this approach performs very well, and the outline curves can be reconstructed with very good accuracy. In addition, all (inner and outer) outline shapes can be obtained with just a single curve in each case.