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 and experiments with real images. © Springer-Verlag 2010.
CITATION STYLE
Gurdjos, P., Charvillat, V., Morin, G., & Guénard, J. (2010). Multiple view reconstruction of a quadric of revolution from its occluding contours. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5994 LNCS, pp. 1–12). https://doi.org/10.1007/978-3-642-12307-8_1
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