Multiple View Reconstruction of a Quadric of Revolution from Its Occluding Contours

The problem of reconstructing a quadric from its occluding contours is one of the earliest problems in computer vision e.g., see [1,2,3]. It is known that three contours from three views are required for this problem to be well-posed while Cross et al. have proved in [4] that, with only two contours, what can be obtained is a 1D linear family of solutions in the dual projective space. In this work, we describe a multiple view algorithm that unambiguously reconstructs so-called Prolate Quadrics of Revolution (PQoR's, see text), given at least two finite projective cameras (see terminology in [5, p157]). In particular, we show how to obtain a closed-form solution. The key result on which is based this work is a dual parameterization of a PQoR, using a 7-dof 'linear combination' of the quadric dual to the principal focus-pair and the Dual Absolute Quadric (DAQ). One of the contributions is to prove that the images of the principal foci of a PQoR can be recovered set-wise from the images of the PQoR and the DAQ. The performance of the proposed algorithm is illustrated on simulations anti experiments with real images.