Using Symmetries For Analysis Of Shape From Contour

Abstract

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. We survey classes of techniques proposed in the past and provide a critical analysis. We propose two kinds of symmetries in figures, which we call parallel and mirror symmetries, give significant information about surface shape for a variety of objects. We show the constraints imposed by these symmetries and how to use them to infer 3-D shape. Our method is applicable to any zero-gaussian curvature surface, and also to a variety of doubly curved surfaces. One of our mathematical results is that for a cone, the surface shape can be constructed uniquely under very simple assumptions. We also show some preliminary results on extraction of symmetries from real images.