  This paper addresses the problem of mirror surface reconstruction, and
proposes a solution based on observing the reflections of a moving reference
plane on the mirror surface. Unlike previous approaches which require tedious
calibration, our method can recover the camera intrinsics, the poses of the
reference plane, as well as the mirror surface from the observed reflections of
the reference plane under at least three unknown distinct poses. We first show
that the 3D poses of the reference plane can be estimated from the reflection
correspondences established between the images and the reference plane. We then
form a bunch of 3D lines from the reflection correspondences, and derive an
analytical solution to recover the line projection matrix. We transform the
line projection matrix to its equivalent camera projection matrix, and propose
a cross-ratio based formulation to optimize the camera projection matrix by
minimizing reprojection errors. The mirror surface is then 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.
