Abstract

The shapes of many natural and man-made objects have curved con- tours. The images of such contours usually do not have sufficient distinctive fea- tures to apply conventional feature-based reconstruction algorithms. This paper shows that both the shape of curves in 3-D space and the camera poses can be accu- rately reconstructed from their perspective images with unknown point correspon- dences given that the curves have certain invariant properties such as symmetry. We show that in such cases the minimum number of views needed for a solution is remarkably small: one for planar curves and two for nonplanar curves (of ar- bitrary shapes), which is signi ficantly less than what is required by most existing algorithms for general curves. Our solutions rely on minimizing the L2 -distance between the shapes of the curves reconstructed via the “epipolar geometry” of sym- metric curves. Both simulations and experiments on real images are presented to demonstrate the effectiveness of our approach.