Intrinsic parameter determination of a paracatadioptric camera by the intersection of two sphere projections

In this paper, a linear calibration method is proposed for a paracatadioptric camera using the images of two spheres. Two spheres are selected in space, and the two groups of their projection circles on the unit viewing sphere are made to intersect at four points. The quadrilateral consisting of four points is a rectangle, so a group of orthogonal directions can be determined in space to obtain a group of orthogonal vanishing points in the paracatadioptric image plane. Because of the relationship between orthogonal vanishing points and intrinsic camera parameters, the intrinsic parameters of a paracatadioptric camera can be linearly solved by at least five views satisfying the above conditions. First, one estimates the sphere images and their antipodal sphere images. Second, by solving the intersection of the images of two spheres and the intersection of the images of their antipodal spheres, a group of orthogonal vanishing points can be obtained in the image plane. Finally, by taking the relationship between the orthogonal vanishing points and the intrinsic camera parameters as constraint conditions, the intrinsic parameters of the paracatadioptric camera can be obtained. Simulation results and real image data demonstrate the effectiveness of our new algorithms.