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We present new algorithms for rapid identification and three-dimensional (3D) attitude determination of a solid object from a single image, using a model matching approach. Our scheme allows the observed object to be partially occluded. The object, as well as the model to which it is matched are represented by the 3D surface constituting their boundaries. We assume that these surfaces consist of flat faces, i.e. the object and the model are (not necessarily convex) polyhedra. We represent each by an attributed graph. The nodes of the graph denote faces on the surface and edges indicate the adjacency of faces. Attributes on the nodes are features invariant to 3D motion made up of 2D moment invariants. With this representation the recognition problem becomes a subgraph matching problem between the image of the observed object and the stored models. We present an algorithm for the matching process, furthermore the exact attitude is obtained as a byproduct of the matching procedure.