Calibration Of A Paracatadioptric Camera By The Projection Properties Of A Single Sphere

Central catadioptric camera has a large field of view and a unique effective viewpoint,so it is widely used in the field of computer vision.Camera calibration is one of the key steps in computer vision.There are important research significance and great application value for the central catadioptric camera calibration.Based on analysis of the imaging geometric features of a single sphere in the paracatadioptric camera,five types of algorithms for the camera intrinsic parameters are presented by computing the imaged circular points and orthogonal vanishing points.The five algorithms as follows:For the unit sphere model,a sphere in 3D space is first projected to two parallel circles on the unit viewing sphere.Two different points are extracted on the projection circle,the two points and their antipodal points can form a rectangle according to the definition of the antipodal points.A pair of orthogonal vanishing points can be obtained in the image plane.Two different points are extracted on the projection circle,the line passing through the two points and the line passing through their antipodal points are parallel,and intersect at the point at infinity.The two parallel circles intersect at four virtual points,of which two are circular points,which are collinear with the point at infinity.Based on the geometric invariance under projective transformation,the imaged circular points can be obtained in the image plane.Given two pairs of two different points on the sphere image,two vanishing points can be obtained on the plane containing the projection circle.The line passing through the two vanishing points is the vanishing line,which and the images of sphere are intersect at the imaged circular points.Two tangents of a point and its antipode point,are parallel and intersect at the point at infinity on the two parallel circles on the unit viewing sphere.The direction of the polar of the point at infinity with respect to the circle is orthogonal to the direction of the point at infinity.A pair of orthogonal vanishing points can be obtained in the image plane.The vanishing line passes through the orthogonal vanishing points,which is on the plane containing the projection circle.The images of sphere and the vanishing line are intersect at the imaged circular points.The robustness of there algorithms were demonstrated through a number of experiments with simulations and experiments with real data,by using MATLAB R2016 a.In the experiments,we also took into account the lens distortion.The 3D information was reconstructed in the real experiments.The experiments demonstrated that the proposed calibration methods have strong robustness.