What Do N Photographs Tell Us about 3D Shape?

Abstract

In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarily-shaped scene from multiple color photographs taken at known but arbitrarily-distributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a special member of this class, the maximal photo-consistent shape, that (1) can be computed from an arbitrary volume that contains the scene, and (2) subsumes all other members of this class. We then give a provably-correct algorithm for computing this shape and present experimental results from applying it to the reconstruction of a real 3D scene from several photographs. The approach is specifically designed to (1) build 3D shapes that allow faithful reproduction of all input photographs, (2) resolve the complex interactions between occlusion, parallax, shading, and their effects on arbitrary collections of photographs of a scene, and (3) follow a "least commitment" approach to 3D shape recovery.