Duals, invariants, and the recognition of smooth objects from their occluding contour

Abstract

This paper presents a new geometric relation between a solid bounded by a smooth surface and its silhouette in images formed under weak perspective projection. The relation has the potential to be used for recognizing complex 3-D objects from a single image. Objects are modeled by showing them to a camera without any knowledge of their motion. The main idea is to consider the dual of the 3-D surface and the family of dual curves of the silhouettes over all viewing directions. Occluding contours correspond to planar slices of the dual surface. We introduce an affine-invariant representation of this surface that can constructed from a sequence of images and allows an object to be recognized from arbitrary viewing directions. We illustrate the proposed object representation scheme through synthetic examples and image contours detected in real images.