Camera self-calibration based on circular points with two planar mirrors using silhouettes

Abstract

Multiple images of an object can be obtained from a catadioptric system consisting of a pinhole camera and two planar mirrors. In this paper, we present two types of algorithm for obtaining the intrinsic parameters of a camera by computing the imaged circular points. First, according to the geometric features of the two planar mirror images, the vanishing points along the normal directions of the planar mirrors are obtained, and the vanishing points along the directions of the planar mirrors are computed using the cross-ratio invariability. Subsequently, we propose two methods of solving for the imaged circular points: one uses the inference of the Laguerre theorem, and the other uses the intersection points of the conic image and the vanishing line. Finally, the camera's intrinsic parameters are obtained by applying the constraints on imaging the circular points to the image of the absolute conic. A simulation, real data, and a 3D reconstruction are presented to show the feasibility and validity of the proposed approaches.