A Camera moving in a plane can often simplify a computer vision job. Camera self-calibration [1] and robot self-location are good examples. In this paper, we focus on the problem camera planar motion and its application to the camera self-calibration method of Faugeras et al [1]. In this paper, we have made three new contributions to the camera planar motion detection. First, we proved that the trifocal lines in different views of the same planar motion must have the same line representation in 2D retinal plane. This conclusion greatly simplifies the planar motion detection problem. Second, we distinguished the usage of three different cases of planar motion: ordinary planar motion, co-linear planar motion and rotation planar motion. Third, we proposed the robust planar motion detection method and the method of estimation of trifocal lines in the uniform framework under the above three configurations. We had also purposed a method on how to eliminate the 2D image points whose 1D projection points are inaccurate and causing significant errors on the estimation of the 1D trifocal tensor. Experiments with our new techniques using simulated data and real images had obtained very good results, which are better than those reported in [1].