Single View 3D Reconstruction under an Uncalibrated Camera and an Unknown Mirror Sphere

In this paper, we develop a novel self-calibration method for single view 3D reconstruction using a mirror sphere. Unlike other mirror sphere based reconstruction methods, our method needs neither the intrinsic parameters of the camera, nor the position and radius of the sphere be known. Based on eigen decomposition of the matrix representing the conic image of the sphere and enforcing a repeated eignvalue constraint, we derive an analytical solution for recovering the focal length of the camera given its principal point. We then introduce a robust algorithm for estimating both the principal point and the focal length of the camera by minimizing the differences between focal lengths estimated from multiple images of the sphere. We also present a novel approach for estimating both the principal point and focal length of the camera in the case of just one single image of the sphere. With the estimated camera intrinsic parameters, the position(s) of the sphere can be readily retrieved from the eigen decomposition(s) and a scaled 3D reconstruction follows. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and accuracy of our approach.