This paper addresses the problem of recognizing three-dimensional objects bounded by smooth curved surfaces from image contours found in a single photograph. The proposed approach is based on a viewpoint-invariant relationship between object geometry and certain image features under weak perspective projection. The image features themselves are viewpoint-dependent. Concretely, the set of all possible silhouette bitangents, along with the contour points sharing the same tangent direction, is the projection of a one-dimensional 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 can be characterized by a set of numerical attributes that remain constant across the corresponding five-dimensional set of viewpoints. This is the basis for describing objects by “invariant” curves embedded in high-dimensional 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 recognition time, attributes computed from a single image are used to index the model database, and both qualitative and quantitative verification procedures eliminate potential false matches. The approach has been implemented and examples are presented.