Planar motion is arguably the most dominant type of motion in surveillance videos. The constraints on motion lead to a simplified factorization method for structure from planar motion when using a stationary perspective camera. Compared with methods for general motion, our approach has two major advantages: a measurement matrix that fully exploits the motion constraints is formed such that the new measurement matrix has a rank of at most 3, instead of 4; the measurement matrix needs similar scalings, but the estimation of fundamental matrices or epipoles is not needed. Experimental results show that the algorithm is accurate and fairly robust to noise and inaccurate calibration. As the new measurement matrix is a nonlinear function of the observed variables, a different method is introduced to deal with the directional uncertainty in the observed variables. Differences and the dual relationship between planar motion and planar object are also clarified. Based on our method, a fully automated vehicle reconstruction system has been designed.