Object/Image Relations in Full and Weak Perspective and 3D Reconstruction

In this paper we focus on the recovery of 3D shape (in a well defined sense) from matched features in 2D views. Our approach to shape reconstruction is invariant to pose and not dependent on knowing any of the camera parameters or the camera's location. The methods are also independent of any choice of coordinates used to represent the 2D or 3D features. We begin by examining two fundamental problems. The first problem involves determining global equations for the geometric constraints (object/image equations) that must hold between a set of object feature points and any image of those points, and using these equations to effectively reconstruct the 3D shape. The second involves describing the shape spaces for point features.