Consistency of Silhouettes and Their Duals

Silhouettes provide rich information on three-dimensional shape, since the intersection of the associated visual cones generates the "visual hull", which encloses and approximates the original shape. However, not all silhouettes can actually be projections of the same object in space: this simple observation has implications in object recognition and multi-view segmentation, and has been (often implicitly) used as a basis for camera calibration. In this paper, we investigate the conditions for multiple silhouettes, or more generally arbitrary closed image sets, to be geometrically "consistent". We present this notion as a natural generalization of traditional multi-view geometry, which deals with consistency for points. After discussing some general results, we present a "dual" formulation for consistency, that gives conditions for a family of planar sets to be sections of the same object. Finally, we introduce a more general notion of silhouette "compatibility" under partial knowledge of the camera projections, and point out some possible directions for future research.