Calibration Method for Central Catadioptric Camera Using Multiple Groups of Parallel Lines and Their Properties

Abstract

This paper presents an approach for calibrating omnidirectional single-viewpoint sensors using the central catadioptric projection properties of parallel lines. Single-viewpoint sensors are widely used in robot navigation and driverless cars; thus, a high degree of calibration accuracy is needed. In the unit viewing sphere model of central catadioptric cameras, a line in a three-dimensional space is projected to a great circle, resulting in the projections of a group of parallel lines intersecting only at the endpoints of the diameter of the great circle. Based on this property, when there are multiple groups of parallel lines, a group of orthogonal directions can be determined by a rectangle constructed by two groups of parallel lines in different directions. When there is a single group of parallel lines in space, the diameter and tangents at their endpoints determine a group of orthogonal directions for the plane containing the great circle. The intrinsic parameters of the camera can be obtained from the orthogonal vanishing points in the central catadioptric image plane. An optimization algorithm for line image fitting based on the properties of antipodal points is proposed. The performance of the algorithm is verified using simulated setups. Our calibration method was validated though simulations and real experiments with a catadioptric camera.