Border reconstruction is a key technology in medical image processing, where it is applied to identify and separate different tissues, organs, and tumors in diagnostic procedures. The classical approaches for this problem are based on either linear or polynomial functions to describe the border of the region of interest. However, little effort has been devoted to the more powerful case of rational functions, which extend the polynomial case by including extra degrees of freedom (the weights). As a consequence, rational functions are more difficult to compute. In this paper, we solve the problem by applying a nature-inspired swarm intelligence method called cuckoo search algorithm. The method is applied to two illustrative examples of medical images with satisfactory results.