Object recognition using property spheres
György Fekete, Larry Steven Davis · 1988
Most three dimensional recognition systems do not consider a problem of organizing the large collection of object models into some structure that would support a strategy other than the brute force comparison of images to object models. The work described in this dissertation introduces a new approach to recognizing three-dimensional objects from two-dimensional images based on a representation called property spheres. A property sphere is a representation for solid objects that encodes properties of the image of the object as a function of viewing direction. Property spheres are implemented in a generalized form of the quadtree, allowing the organization of the modeled objects in a multiresolution data structure that supports logarithmic search strategies for object recognition. A special case of the property sphere, the property circle, is used to demonstrate the strategic choice of the viewing position in a case where one cannot determine both the identity and the orientation of the object in the field of view from a single image. The property circle restricts the set of possible viewpoints to a circle. All objects that are considered for modeling share the property having a fixed number of stable positions, hence they can be modeled as a collection of property circles. This dissertation develops the theory for implementing the data structure to represent the property sphere, defines and implements basic topological and geometrical operations on the property sphere, and introduces and implements an algorithm for generating the property sphere as a multiresolution data structure from a geometrical model. Furthermore, it develops a theory to handle ambiguity by selecting alternate viewing positions and demonstrates its use through examples using (not necessarily convex) polyhedral objects.