Viewpoint-invariant representation of generalized cylinders using the symmetry set

Abstract

We demonstrate that viewpoint-invariant representations can be obtained from images for a useful class of 3D smooth object. The class of surfaces are those generated as the envelope of a sphere of varying radius swept along an axis. This class includes canal surfaces and surfaces of revolution. The representations are computed, using only image information, from the symmetry set of the object's outline. They are viewpoint-invariant under weak-perspective imaging, and quasi-invariant to an excellent approximation under perspective imaging. To this approximation, the planar axis of a canal surface is recovered up to an affine ambiguity from perspective images. Examples are given of the representations obtained from real images, which demonstrate stability and object discrimination, for both canal surfaces and surfaces of revolution. Finally, the representations are used as the basis for a model-based object recognition system.