Affine Reconstruction from Monocular Vision in the Presence of a Symmetry Plane

This paper reports a closed-form solution for reconstructing a scene up to an affine transformation from a single image in the presence of a symmetry plane. Unlike scene reconstruction in stereo vision, the affine reconstruction process discussed in this paper does not require any knowledge about camera parameters or camera orientation relative to the scene, so camera self-calibration is totally eliminated. By setting in the scene a plane mirror which creates lateral symmetric world points for an uncalibrated, perspective camera to capture, the linear equations involved in the reconstruction process can be derived from two sets of similar triangles. The affine reconstruction is relative to an arbitrary affine coordinated frame implicitly defined on the mirror plane. Also involved in the process are the estimation of the epipole and recovery of the image-tomirror plane homography. Implementation on estimating the epipole is detailed. A real experiment is presented to demonstrate the reconstruction.