Consistency of silhouettes and their duals
Résumé
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.
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