Reconstruction of canal surfaces from single images under exact perspective

This paper addresses the reconstruction of canal surfaces from single images. A canal surface is obtained as the envelope of a family of spheres of constant radius, whose center is swept along a space curve, called axis. Previous studies either used approximate relationships (quasi-invariants), or they addressed the recognition based on a geometric model. In this paper we show that, under broad conditions, canal surfaces can be reconstructed from single images under exact perspective. In particular, canal surfaces with planar axis can even be reconstructed from a single fully-uncalibrated image. An automatic reconstruction method has been implemented. Simulations and experimental results on real images are also presented.