Introducing a new problem: Shape-from-silhouette when the relative positions of the viewpoints is unknown

Abstract

3D shapes can be reconstructed from 2D silhouettes by back-projecting them from the corresponding viewpoints and intersecting the resulting solid cones. However, in many practical cases as observing an aircraft or an asteroid, the positions of the viewpoints with respect to the object are not known. In these cases, the relative position of the solid cones is not known and the intersection cannot be performed. The purpose of this paper is introducing and stating in a theoretical framework the problem of understanding 3D shapes from silhouettes when the relative positions of the viewpoints are unknown. The results presented provide a first insight into the problem. In particular, the case of orthographic viewing directions parallel to the same plane is thoroughly discussed, and sets of inequalities are presented which allow determining objects compatible with the silhouettes.