Plane Catadioptric Camera Calibration By Symmetry Of Plane Mirror Imaging And The Pole-Polar Relationship

The plane catadioptric camera consists of a pinhole camera and double plane mirrors.When the angle between the two plane mirrors changes,one-time or multiple-times internal reflections may occur between two plane mirrors.The object will be reflected by the two mirrors one-time or multiple-times.When two plane mirrors have one-time internal reflection,an object in the double plane mirrors device will form four reflected virtual images.By analyzing the imaging properties of the object in the plane mirror,two methods for calibrating the parameters in the camera are proposed.In the double plane mirrors device,the three-dimensional point and its reflection points lie on a circle that is a coaxial parallel circle.By the symmetry of plane mirror imaging,the connection of a plurality of spatial points and corresponding reflection points forms a plurality of straight lines.These lines are parallel to each other and intersect at an infinite point.The polar lines of an infinite point with respect to parallel circles are parallel to each other,and intersect at another infinite point.According to the nature of the conjugate diameter,the two infinity points are a set of infinity points in the orthogonal direction.The pair of orthogonal vanishing points can be obtained by the projective invariance on the image plane,thereby solving the camera internal parameters.The infinite line which connected by two infinity points intersects the circle at circular points.The imaged circular points can be obtained in the image plane,by the projective invariance on the image plane.Thereby the camera internal parameters are solved.The robustness of the algorithms were demonstrated through a number of experiments with simulations and experiments with real data,by using MATLAB.Noise is considered in the simulation experiment.In the experiments,the 3D information was reconstructed in the real experiments.The experiments demonstrated that the proposed calibration methods have strong robustness.