This paper presents a novel solution to automatically count vehicles in a parking lot using images captured by smart cameras. Unlike most of the literature on this task, which focuses on the analysis of single images, this paper proposes the use of multiple visual sources to monitor a wider parking area from different perspectives. The proposed multi-camera system is capable of automatically estimate the number of cars present in the entire parking lot directly on board the edge devices. It comprises an on-device deep learning-based detector that locates and counts the vehicles from the captured images and a decentralized geometric-based approach that can analyze the inter-camera shared areas and merge the data acquired by all the devices. We conduct the experimental evaluation on an extended version of the CNRPark-EXT dataset, a collection of images taken from the parking lot on the campus of the National Research Council (CNR) in Pisa, Italy. We show that our system is robust and takes advantage of the redundant information deriving from the different cameras, improving the overall performance without requiring any extra geometrical information of the monitored scene.