Depth-estimation-free condition for projective factorization and its application to 3D reconstruction

Abstract

This paper concerns depth-estimation-free conditions for projective factorization. We first show that, using an algebraic approach, the estimation of the projective depth is avoidable if and only if the origins of all camera coordinate systems are lying on a single plane, and optical axes of the coordinate systems point the same direction that is perpendicular to the plane. Next, we generalize the result to the case where the points are possibly restricted on a plane or on a line. The result clearly reveals the trade-off between the freedom of camera motion and that of point location. We also give a least-square-based method for Euclidean reconstruction from the result of the projective reconstruction. The proposed method is evaluated through simulation from the viewpoint of computational time. © 2013 Springer-Verlag.