Mirror Symmetry => 2-View Stereo Geometry

Alexandre R.J. Francois


Abstract

We address the problem of 3-D reconstruction from a single perspective view of a mirror symmetric scene. We establish the fundamental result that it is geometrically equivalent to observing the scene with two cameras, the cameras being symmetrical with respect to the unknown 3-D symmetry plane.

All traditional tools of classical 2-view stereo can then be applied, and the concepts of fundamental/essential matrix, epipolar geometry, rectification and disparity hold. However, the problems are greatly simplified here, as the rectification process and the epipolar geometry can be easily computed from the original view only. If the camera is calibrated, we show how to synthesize the symmetric image generated by the same physical camera. An Euclidean reconstruction of the scene can then be computed from the resulting stereo pair. To validate this novel formulation, we have processed many real images, and show examples of 3-D reconstruction.


Maintained by Philippos Mordohai