Linear Reconstruction from Dual Multilinear Constraints

This paper deals with the problem of reconstruction from a sequence of images, by linear methods. The reconstruction is made directly, without calculating the fundamental matrices or the trilinear tensors. In a general setting it is shown that it is possible to do such a reconstruction of six points from four images up to a projective transformation. Furthermore, when more point matches are available, it is possible to reconstruct subsets of six points linearly and then make a linear reconstruction of the whole scene. This can be done in the same way using more than four images. The possibility to make direct shape recovery was pointed out in 1], where it was shown that there is a duality between reconstruction of the object and reconstruction of the motion of the camera. A similar approach has been outlined in 6], with the diierence that they are using seven points each time. Furthermore, we are using an aanely reduced framework, introduced in 3], which simpliies our approach.