Mirror symmetry⇒2-view stereo geometry

摘要

We address the problem of 3D 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 3D 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 computation of epipolar geometry can be easily performed from the original view only. If the camera is calibrated, we show how to synthesize the symmetric image generated by the same physical camera. A 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 3D reconstruction.