COMPUTING THE PERSPECTIVE PROJECTION ASPECT GRAPH OF SOLIDS OF REVOLUTION

A number of researchers have recently described algorithms for computing different versions of the aspect graph for various classes of objects. This paper presents the first (only) implemented algorithm to compute the aspect graph for a class of curved-surface objects based on an exact parcellation of 3-D viewpoint space. The object class considered is solids of revolution. A detailed analysis of the visual events for this object class is given, as well as an algorithm to construct the aspect graph. Numerical search techniques, based on a geometric interpretation of the visual events, have been devised to determine those visual event surfaces that cannot be calculated directly. The worst-case complexity of the number of cells in the parcellation of 3-D viewpoint space, and, hence, the number of nodes in the aspect graph, is O(N4), where N is the degree of a polynomial that defines the object shape. A summary of the results for 20 different object descriptions is presented, along with a detailed example for a flower vase. The implementation (in C, using X-windows) is available to interested research groups.