On Shapes

An important problem in vision is to detect the presence of a known rigid, 3-d object. The general 3-d object recognition task can be thought of as building a description of the object that must have at least two parts: (1) the internal description of the object itself (with respect to an object-centered frame); and (2) the transformation of the object-centered frame to the viewer-centered (image) frame. The reason for this decomposition is parsimony: different views of the object should have minimal impact on its decription. This is achieved by factoring the object's description into two sets of parameters, one which is view-independent (the object-centered component) and one which is view-varying (the viewing transformation). Often a description of the object is known beforehand and the task reduces to finding the object-frame to viewer-frame transformation. This paper describes a method for handling this case: a known object is detected by finding changes in orientation, translation, and scale of the object from its canonical description