Curve and Surface Duals and the Recognition of Curved 3D Objects from their Silhouettes

This article addresses the problem of recognizing a solid bounded by a smooth surface in a single image. The proposed approach is based on a new representation for two- and three-dimensional shapes, called their signature, that exploits the close relationship between the dual of a surface and the dual of its silhouette in weakperspective images. Objects are modeled by rotating them in front of a camera without any knowledge of or constraints on their motion. The signatures of their silhouettes are concatenated into a single object signature. To recognize an object from novel viewpoint other than those used during modeling, the signature of the contours extracted from a test photograph is matched to the signatures of all modeled objects signatures. This approach has been implemented, and recognition examples are presented.