The driving behavior at urban intersections is very complex. It is thus crucial for autonomous vehicles to comprehensively understand challenging urban traffic scenes in order to navigate intersections and prevent accidents. In this paper, we introduce a stereo vision and 3D digital map based approach to spatially and temporally analyze the traffic situation at urban intersections. Stereo vision is used to detect, classify and track obstacles, while a 3D digital map is used to improve ego-localization and provide context in terms of road-layout information. A probabilistic approach that temporally integrates these geometric, semantic, dynamic and contextual cues is presented. We qualitatively and quantitatively evaluate our proposed technique on real traffic data collected at an urban canyon in Tokyo to demonstrate the efficacy of the system in providing comprehensive awareness of the traffic surroundings.