A calibration method for paracatadioptric camera from sphere images

For paracatadioptric camera, the estimation of intrinsic parameters from sphere images is still an open and challenging problem. In this paper, we propose a calibration method for paracatadioptric camera based on sphere images, which only requires that the projected contour of parabolic mirror is visible on the image plane in one view. We have found that, under central catadioptric camera, a sphere is projected to two conics on the image plane, which are defined as a pair of antipodal sphere images. The conic that is visible on the image plane is called the sphere image, while the other invisible conic is called the antipodal sphere image. In the other aspect, according to the image formation of central catadioptric camera, these two conics can also be considered as the projections of two parallel circles on the viewing sphere by a virtue camera. That is to say, if three pairs of antipodal sphere images are known, central catadioptric camera can be directly calibrated by the calibration method based on two parallel circles. Therefore, the problem of calibrating central catadioptric camera is transferred to the estimations of sphere images and their antipodal sphere images. Based on this idea, we first initialize the intrinsic parameters of the camera by the projected contour of parabolic mirror, and use them to initialize the antipodal sphere images. Next, we study properties of several pairs of antipodal sphere images under paracatadioptric camera. Then, these properties are used to optimize sphere images and their antipodal sphere images, so as to calibrate the paracatadioptric camera. Experimental results on both simulated and real image data have demonstrated the effectiveness of our method.