Reconstruction of general curves, using factorization and bundle adjustment

In this paper, we extend the notion of affine shape, introduced by Sparr, f rom finite point sets to curves. The extension makes it possible to reconst ruct 3D-curves up to projective transformations, from a number of their 2D- projections. We also extend the bundle adjustment technique from point feat ures to curves. The first step of the curve reconstruction algorithm is based on affine sha pe. It 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, except for a small set of curves (e.g. a movin g line), a solution is given to the aperture problem of finding point corre spondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bun dle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.