We propose a new approach to visual perception for relative localization of agents within large-scale swarms of Unmanned Aerial Vehicles (UAVs). Inspired by biological perception utilized by schools of sardines, swarms of bees, and other large groups of animals capable of moving in a decentralized yet coherent manner, our method does not rely on detecting individual neighbors by each agent and estimating their relative position, but rather we propose to regress a neighbor density over distance. This allows for a more accurate distance estimation as well as better scalability with respect to the number of neighbors. Additionally, a novel swarm control algorithm is proposed to make it compatible with the new relative localization method. We provide a thorough evaluation of the presented methods and demonstrate that the regressing approach to distance estimation is more robust to varying relative pose of the targets and that it is suitable to be used as the main source of relative localization for swarm stabilization.