Paracatadioptric camera calibration based on properties of polar line of infinity point with respect to circle and line

Two linear calibration methods based on space-line projection properties for a paracatadioptric camera are presented. Considering the central catadioptric system, a straight line is projected into a circle on the viewing spherical surface for the first projection. The tangent lines in a group at antipode point pairs with respect to the circle are parallel, with the infinity point being the intersection point; therefore, the infinity line can be obtained from two groups of antipode point pairs. Further, the direction of the polar line of an infinity point with respect to the circle is orthogonal to the direction of its infinity point. Hence, on the imaging plane, images of the circular points or orthogonal vanishing points are used to determine the intrinsic parameters. On the basis of the properties of the antipodal point pairs and a least-squares fitting, a corresponding optimization algorithm for line image fitting is proposed. Experimental results demonstrate the robustness of the two calibration methods, that is, for images of the circular points and orthogonal vanishing points.