Invariant-based recognition of complex curved 3D objects from image contours

This paper addresses the problem of recognizing three-dimensional objects b ounded by smooth curved surfaces from image contours found in a single phot ograph. The proposed approach is based on a viewpoint-invariant relationshi p between object geometry and certain image features under weak perspective projection. The image features themselves are viewpoint-dependent. Concret ely, the set of all possible silhouette bitangents, along with the contour points sharing the same tangent direction, is the projection of a one-dimen sional set of surface points where each point lies on the occluding contour for a five-parameter family of viewpoints. These image features form a one -parameter family of equivalence classes, and it is shown that each class c an be characterized by a set of numerical attributes that remain constant a cross the corresponding five-dimensional set of viewpoints. This is the bas is for describing objects by "invariant" curves embedded in high-dimensiona l spaces. Modeling is achieved by moving an object in front of a camera and does not require knowing the object-to-camera transformation; nor does it involve implicit or explicit three-dimensional shape reconstruction. At rec ognition time, attributes computed from a single image are used to index th e model database, and both qualitative and quantitative verification proced ures eliminate potential false matches. The approach has been implemented a nd examples are presented. (C) 1998 Academic Press.