Paracatadioptric Camera Calibration Using Lines

Paracatadioptric sensors combine a parabolic shaped mirror and a camera inducing an orthographic projection. Such a configuration provides a wide field of view while keeping a single effective viewpoint. Previous work in central catadioptric sensors proved that a line projects into a conic curve and that three line images are enough to calibrate the system. However the estimation of the conic curves where lines are mapped is hard to accomplish. In general only a small arc of the conic is visible in the image and conventional conic fitting techniques are unable to correctly estimate the curve. The present work shows that a set of conic curves corresponds to paracatadioptric line images if, and only if, certain properties are verified. These properties are used to constraint the search space and correctly estimate the curves. The accurate estimation of a minimum of three line images allows the complete calibration of the paracatadioptric camera. If the camera is skewless and the aspect ratio is known then the conic fitting problem is solved naturally by an eigensystem. For the general situation the conic curves are estimated using non-linear optimization.