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Road intersections are important components of urban road system. It is the traffic flow characteristics representing the current traffic situation that provide a basis for the planning, designing and management of intersections. In this paper, we constructed an automatic processing framework on traffic flow characteristics analysis and understanding the traffic state at the urban road intersections, based on the collected raw vehicle motion trajectories. Our proposed method is basically attributed to identifying distinct vehicle motion patterns at intersections hierarchically using raw trajectory. Firstly, the fundamental assumption in traditional approaches that the trajectory set of high quality are readily available after manual rectification is not taken for granted any more. And by fully analyzing the local characteristics of trajectories, we figure out and explain various patterns behind traffic flow as well as yielded higher accuracy in motion trajectory clustering under the multi-layer spectral clustering method. At last, coupling the analyzing results with the surrounding characteristics of the intersection, the examples computing traffic flow features and predicting vehicle activity illustrates the potential of applying vehicle trajectories to traffic study, which are all suggested by experimental results.