Algebraic Characteristic and Geometric Interpretation of Planar Motions and their Applications to Camera Self-calibration

Vision tasks with constrained camera motion have been discussed for a long time since Active Vision appeared. As an example, Camera under planar motion can often simplify the works, like camera self-calibration, scene reconstruction and robot self-location. In this paper, we provide detail information on the algebraic characteristic and geometric interpretation of planar motion. It does help to build up a special vision system and make it more feasible for practical use. In this paper, an explicit algebraic analysis of the camera planar motion detection is first given. A special spatial parameterization is used to explain the geometric meaning of planar motions and for the detection of such motions. Three kinds of planar motions: non-collinear, collinear and stationary camera motion, are considered. According to this, we design a practical simplified vision system, which can be easily used for outdoor vision tasks. Lastly, we discuss the stability and uncertainty propagation, while 2D image matching points project onto a 1D virtual camera retina. It is critical for the original image matching uncertainty to be carefully handled to avoid the error blowup due to 2D to 1D projection. Experiments on camera selfcalibration and scene reconstruction using simulated data and real images show the validity and effectiveness of our method.