Calibration of Double-Plane-Mirror Catadioptric Camera Based on Coaxial Parallel Circles

Abstract

A catadioptric camera with a double-mirror system, composed of a pinhole camera and two planar mirrors, can capture multiple catadioptric views of an object. The catadioptric point sets (CPSs) formed by the contour points on the object lie on circles, all of which are coaxial parallel. Based on the property of the polar line of the infinity point with respect to a circle, the infinity points in orthogonal directions can be obtained using any two CPSs, and a pole and polar pair with respect to the image of the absolute conic (IAC) can be obtained through inference of the Laguerre theorem. Thus, the camera intrinsic parameters can be solved. Furthermore, as the five points needed to fit the image of a circle are not easy to obtain accurately, only sets in which five points can be located can be obtained, whereas the points on the line of intersection between the two plane mirrors and the ground plane can easily be obtained accurately. An optimization method based on the analysis of neighboring point sets to compare the intersection points with an image of the center of multiple circle images fitted using the point sets is proposed. Bundle adjustment is then applied to further optimize the camera intrinsic parameters. The feasibility and validity of the proposed calibration methods and their optimization were confirmed through simulation and experiments. Two primary innovations were obtained from the results of this study: (1) by applying coaxial parallel circles to the double-plane-mirror catadioptric camera model, a variety of calibration methods were derived, and (2) we found that the overall model could be optimized by analyzing the features of the neighboring point set and bundle adjustment.