Mirror Surface Reconstruction Under an Uncalibrated Camera

This paper addresses the problem of mirror surface reconstruction, and a solution based on observing the reflections of a moving reference plane on the mirror surface is proposed. Unlike previous approaches which require tedious work to calibrate the camera, our method can recover both the camera intrinsics and extrinsics together with the mirror surface from reflections of the reference plane under at least three unknown distinct poses. Our previous work has demonstrated that 3D poses of the reference plane can be registered in a common coordinate system using reflection correspondences established across images. This leads to a bunch of registered 3D lines formed from the reflection correspondences. Given these lines, we first derive an analytical solution to recover the camera projection matrix through estimating the line projection matrix. We then optimize the camera projection matrix by minimizing reprojection errors computed based on a cross-ratio formulation. The mirror surface is finally reconstructed based on the optimized cross-ratio constraint. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and accuracy of our method.