Algebraic derivations of relative affine structure and applications to 3D reconstruction from 2D views
Nassir Navab, Amnon Shashua · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
We present an algebraic description of relative affine structure -- an invariant structure affinely related to the structure seen from one of the cameras. This algebraic description yields a simple canonical framework that unifies results in projective, affine, and Euclidean structure from motion. We then introduce a method for capturing the redundancy in recovering relative affine structure from a stream of perspective views. We propose a certain decomposition that on one hand involves an optimal projection of the contribution of each point at each frame onto a single bilinear equation; and on the other hand reveals a connection (bilinear) between the homography of an arbitrary plane and the translational component of motion. Given an estimation of the epipoles, which can be computed in a least squares manner for each frame separately, the decomposition equations yield a linear least squares method for solving for scene structure. The main results were applied to a real image sequence for the purpose of 3D reconstruction from 2D views, visual recognition by alignment, and image coding.