Recent technological advances have led to the rapid development of Intelligent Surveillance Systems (ISSs), ubiquitously present in modern urban spaces are constantly generating streams of raw data. As most of the actual Internet traffic is nowadays constituted by visual data streams, often originated by ISSs, it is important to properly manage these avalanches of data so as to support sustainability of this technological trend, which will very likely saturate the current network bandwidth in few years. This paper aims to combine existing technologies and paradigms from the Internet of Things, Cloud, Edge Computing and Big Data into a common framework to enable a shared approach for ISSs at a wide geographical scale, thus envisioning a Global ISS. The proposed solution is based on the idea of pushing data processing tasks as close to data sources as possible, thus increasing security and performance levels, usually critical to surveillance systems. To demonstrate the feasibility and the effectiveness of the proposed approach, the paper presents a case study based on a distributed ISS scenario in a crowded area, implemented on clustered edge devices able to offload tasks in a 'horizontal' manner.