Calibration Of Central Catadioptric Camera According To The Projection Properties Of Right Cone And Oblique Cone

3D objects in space can be reconstructed from 2D images according to the camera parameters,camera calibration and its accuracy play a key role in this process.Because of its isotropic properties,sphere has been widely used in camera calibration.In this thesis,the projection properties of the oblique cone and the right cone formed by the small circle and the mirror contour are analyzed according to the imaging process of the sphere under the central catadioptric unit viewing sphere model,and via the constraints of the image of circular points and orthogonal vanishing points about the intrinsic parameters of the camera,two linear calibration algorithms are proposed.Under the central catadioptric unit viewing sphere model,firstly,the sphere forms a small circle,then the small circle and the mirror contour form an oblique cone and a right cone with the camera optical center,respectively.From the generalized eigenvectors of the coefficient matrices of the right cone and the oblique cone equations,an infinity point on the plane of the mirror contour can be obtained,then two oblique cones and a right cone can obtain the infinity line on the plane of the mirror contour.According to the projective invariance,corresponding a vanishing line can be obtained on the image plane,by intersecting it with the image of mirror contour,the image of circular points can be obtained,then the camera intrinsic parameters can be obtained by three images.After obtaining an infinity point on the plane of the mirror contour,the infinity point in the orthogonal direction can be obtained according to the properties of pole-polar and conjugate diameter.On the image plane,a pair of orthogonal vanishing points can be obtained,and camera intrinsic parameters can be obtained by three images.By decomposing the equation of two images of spheres,a point and line can be found.The point and line are pole and polar not only about the sphere images but also about the image of the modified absolute conic.The modified camera intrinsic parameters can be obtained by the relationship of pole-polar with respect to the image of the modified absolute conic,combining above two methods,mirror parameter can be obtained.The feasibility and effectiveness of the proposed two algorithms are verified by simulation data experiments and real experiments.