When is it possible to identify 3D objects from single images using class constraints?

One approach to recognizing objects seen from arbitrary viewpoint is by ext racting invariant properties of the objects from single images. Such proper ties are found in images of 3D objects only when the objects are constraine d to belong to certain classes (e.g., bilaterally symmetric objects). Exist ing studies that follow this approach propose how to compute invariant repr esentations for a handful of classes of objects. A fundamental question reg arding the invariance approach is whether it can be applied to a wide range of classes. To answer this question it is essential to study the set of cl asses for which invariance exists. This paper introduces a new method for d etermining the existence of invariant functions for classes of objects toge ther with the set of images from which these invariants can be computed. We develop algebraic tests that determine whether the objects in a given clas s can be identified from single images. These tests apply to classes of obj ects undergoing affine projection. In addition, these tests allow us to det ermine the set of views of the objects which are degenerate. We apply these tests to several classes of objects and determine which of them is identif iable and which of their views are degenerate.