Recognizing a polyhedron by network constraint analysis

The present paper describes a method of recognizing a polyhedron employing the notion of network constraint analysis. Typical difficulties in three-dimensional object recognition, other than shading, reflection, and hidden line problems, include the case where appearances of an object vary according to observation points and the case where an object to be recognized is occluded by other objects placed in its front, resulting in incomplete information on the object shape. These difficulties can, however, be solved to a large extent, by taking account of certain local constraints defined on a polyhedral shape. The present paper assumes a model-based vision employing an appearance-oriented model of a polyhedron which is provided by placing it at the origin of a large sphere and observing it from various positions on the surface of the sphere. The model is actually represented by the sets of adjacent faces pairs of the polyhedron observed from those positions. Since the shape of a projected face gives constraint to that of its adjacent face, this results in a local constraint relation between these faces. Each projected face of an unknown polyhedron on an acquired image is examined its match with those faces in the model, producing network constraint relations between faces in the image and faces in the model. Taking adjacency of faces into consideration, these network constraint relations are analyzed. And if the analysis finally provides a solution telling existence of one to one match of the faces between the unknown polyhedron and the model, the unknown polyhedron is understood to be one of those memorized models placed in a certain posture. In the performed experiment, a polyhedron was observed from 320 regularly arranged points on a sphere to provide its appearance model and a polyhedron with arbitrarily postured, occluded, or imposed another difficulty was successfully recognized.