Shape Recovery of a Strictly Convex from n-Views solid

In this paper we consider the problem of extracting the shape of a smooth convex solid, V⊂ R 3 , from a set of N photographs. The method begins by extracting the edges of each photograph. These edges are used to form a cone whose apex is the camera centre, which is guaranteed to enclose V. For a strictly convex solid any two such cones will most likely touch at two places (Collings et al., 2004), whose coordinates then give two data points which lie on V along with the orientation of the surface at these points. A set of cameras observing V yields a cloud of such points and normals. A new type of implicit surface is fitted to both the points and their normals. The implicit surface has the property of minimising a linear combination of first, second and third order energies, as in (Dinh et al., 2002), but with the added refinement of incorporating information about the surface orientation at each constraint point.