Paracatadioptric Camera Is Calibrated By The Antipodal Ralation Of The Spheral Image

In computer vision study,a catadioptric imaging system is constructed by combining a reflective mirror and a common camera to increase the imaging field of view.The application of catadioptric system is on the basis of the estimation to parameters of the system,i.e.the calibration of catadioptric camera.The reasonable and accurate calibration method are affected by the result of system application directly.In view of the superior geometric characteristics of sphere projection,the calibration method of based on the properties of sphere projection are more common.Therefore,according to the properties of sphere projection,two methods for paracatadioptric camera calibration are proposed on the basis of studying the imaging model of central catadioptric camera,one is to calibrate by using orthogonal vanishing points,and the other is to calibrate by using imaged circular points.The concrete contents of the paper are as follows:1.According to the calibration of orthogonal vanishing points,the pole and polar of the common self-polar triangle formed by parallel antipodal small circles on the image plane are obtained from the knowledge of the common self-polar triangle,and the corresponding vanishing point is determined from the position between the poles and the circle image under the unit sphere projection model.On the other hand,the intersection points of the polar with the sphere image and the position are located on the surface of the unit sphere,and the center of the unit sphere forms the image of the unit circle,thus the vanishing point in the direction of the common polar on the image is obtained according to the ratio harmonic conjugation.Then the conjugate diameter knowledge is used to prove that the vanishing point obtained from the common self-polar triangle is orthogonal to the vanishing point in the direction of common polar,thus the orthogonal vanishing points could be obtained.2.According to the calibration of imaged circlar points and the projection model of space sphere,any two pairs of antipodal points can form a plane containing unit circle,and the infinity point corresponding to each pair of antipodal point is obtained by using ratio harmonic conjugation,so as to construct an infinity line.According to the two pairs of antipodal points on the plane circle govered by the infinity line,one can calculate the other infinity points in the parallel direction.And the other points on the circle are calculated by using the ratio harmonic conjugation and antipodal relation,thus the imaged circle equation can be obtained by least square method.Finally,the imaged circular points are obtained through the relation between the image of infinite line and the circle image.3.The robustness and feasibility of the algorithm is demonstrated through simulation experiments and real experiments based on Matlab 2016a.