This work describes a straightforward implementation of detecting and tracking pedestrian walking across a public square using computer vision. The methodology consists of the use of the well-known YOLOv3 algorithm over videos recorded during different days of the week. The chosen location was the Piazza Duca d’Aosta in the city of Milan, Italy, in front of the main Centrale railway station, an access point for the subway. Several analyses have been carried out to investigate macroscopic parameters of pedestrian dynamics such as densities, speeds, and main directions followed by pedestrians, as well as testing strengths and weaknesses of computer-vision algorithms for pedestrian detection. The developed system was able to represent spatial densities and speeds of pedestrians along temporal profiles. Considering the whole observation period, the mean value of the Voronoi density was about 0.035 person/m2 with a standard deviation of about 0.014 person/m2. On the other hand, two main speed clusters were identified during morning/evening hours. The largest number of pedestrians with an average speed of about 0.77 m/s was observed along the exit direction of the subway entrances during both morning and evening hours. The second relevant group of pedestrians was observed walking in the opposite direction with an average speed of about 0.65 m/s. The analyses generated initial insights into the future development of a decision-support system to help with the management and control of pedestrian dynamics.