Reconstruction of 3-D symmetric curves from perspective images without discrete features

Abstract

The shapes of many natural and man-made objects have curved contours. The images of such contours usually do not have sufficient distinctive features 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 accurately reconstructed from their perspective images with unknown point correspondences 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 arbitrary shapes), which is significantly 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 symmetric curves. Both simulations and experiments on real images are presented to demonstrate the effectiveness of our approach. © Springer-Verlag 2004.