Projective pose estimation of linear and quadratic primitives in monocular computer vision
CVGIP: Image Understanding
Reconstructing ellipsoids from projections
CVGIP: Graphical Models and Image Processing
Matrix computations (3rd ed.)
The Quadric Reference Surface: Theory and Applications
International Journal of Computer Vision
Surface reconstruction from multiple views using apparent contours and surface texture
Confluence of computer vision and computer graphics
Camera Calibration from Surfaces of Revolution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ellipsoid Reconstruction from Three Perspective Views
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Quadric Reconstruction from Dual-Space Geometry
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstruction of Spheres using Occluding Contours from Stereo Images
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
Camera Calibration from Images of Spheres
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Computer Graphics and Applications
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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.