Extension of affine shape

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to more general sets. It turns out to be possible to generalize most of the theory. The extension makes it possible to reconstruct, for example, 3D-curves up to projective transformations, from a number of their 2D-projections. An algorithm is presented, which is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that a solution is given to the aperture problem of finding point correspondences between curves.