Abstract. 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 ID 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, pl57]). 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.
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机译：抽象的。从其遮挡轮廓重建二次曲面的问题是计算机视觉中最早的问题之一，例如，参见[1,2,3]。众所周知，Cross et al。提出了从三个角度看三个轮廓的方法。在[4]中证明，只有两个轮廓，就可以得到对偶射影空间中一个ID线性解的族。在这项工作中，我们描述了一种多视图算法，该算法明确地重构了所谓的Prolate Quadrics of Revolution（PQoR，参见文本），并至少给定了两个有限的投影摄像机（请参见[5，pl57]中的术语）。特别是，我们展示了如何获得封闭形式的解决方案。这项工作的主要结果是对PQoR的双重参数化，它使用二次对偶到主焦点对和双重绝对对偶（DAQ）的7-dof“线性组合”。其中一项贡献是证明，可以从PQoR和DAQ的图像中按设定的方式恢复PQoR的主要病灶的图像。在真实图像的仿真和实验中说明了所提出算法的性能。
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