Applications such as traffic surveillance require a real-time and accurate method for object tracking. We propose to represent scene observations with parabola segments with an algorithm that allows us to fit parabola segments in real-time to edge pixels. The motion vectors for these parabola segments are obtained in consecutive frames by a matching technique based on distance and intensity. Furthermore, moving rigid objects are detected by an original method that clusters comparable motion vectors. The result is a robust detection and tracking method, which can cope with small changes in viewpoint on the moving rigid object.