Paracatadioptric camera calibration based on the projecting relationship of the relative position between two spheres

摘要

We discuss how the projecting relationship of the relative position between two spheres in space can be used to calibrate paracatadioptric cameras. The projections of two spheres under a paracatadioptric camera are classified into three cases: Intersection, tangency, and separation. Methods for obtaining the principal point are proposed for each case. When the principal point is known, an analysis of the geometric relationship of the two spheres on the unit viewing sphere model shows that their tangent lines at the antipodal points are parallel. Based on this geometric relationship, the vanishing line of the plane containing the projection circle can be determined to yield the imaged circular points and obtain the remaining intrinsic camera parameters. When the principal point is unknown, the intersection points of two groups of parallel projection circles of the two spheres on the unit viewing sphere model combine with their corresponding antipodal points to form a rectangle; hence, the vanishing point in the orthogonal directions can be determined. Finally, the intrinsic camera parameters can be obtained by applying the constraints of the vanishing points in orthogonal directions to the absolute conic. Simulation results and real image data demonstrate the effectiveness of our methods.