UAV based traffic monitoring holds distinct advantages over traditional traffic sensors, such as loop detectors, as UAVs have higher mobility, wider field of view, and less impact on the observed traffic. For traffic monitoring from UAV images, the essential but challenging task is vehicle detection. This paper extends the framework of Faster R-CNN for car detection from low-altitude UAV imagery captured over signalized intersections. Experimental results show that Faster R-CNN can achieve promising car detection results compared with other methods. Our tests further demonstrate that Faster R-CNN is robust to illumination changes and cars' in-plane rotation. Besides, the detection speed of Faster R-CNN is insensitive to the detection load, that is, the number of detected cars in a frame; therefore, the detection speed is almost constant for each frame. In addition, our tests show that Faster R-CNN holds great potential for parking lot car detection. This paper tries to guide the readers to choose the best vehicle detection framework according to their applications. Future research will be focusing on expanding the current framework to detect other transportation modes such as buses, trucks, motorcycles, and bicycles.