Dual Representations for Vision-Based 3D Reconstruction

We consider the problem of representing sets of 3D points in the context of 3D reconstruction from point matches. We present a new representation for sets of 3D points, which is general, compact and expressive : any set of points can be represented; geometric relations that are often present in manmade scenes, such as coplanarity, alignment and orthogonality, are explicitly expressed. In essence, we propose to define each 3D point by three independent linear constraints that it verifies, and exploit the fact that coplanar points verify a common constraint. We show how to use the dual representation in Maximum Likelihood estimation, and that it substantially improves the precision of 3D reconstruction.