We propose the first convex relaxation for multiview triangulation that is robust to both noise and outliers. To this end, we extend existing semidefinite relaxation approaches to loss functions that include a truncated least squares cost to account for outliers. We propose two formulations, one based on epipolar constraints and one based on the fractional reprojection equations. The first is lower dimensional and remains tight under moderate noise and outlier levels, while the second is higher dimensional and therefore slower but remains tight even under extreme noise and outlier levels. We demonstrate through extensive experiments that the proposed approach allows us to compute provably optimal reconstructions and that empirically the relaxations remain tight even under significant noise and a large percentage of outliers.

翻译：我们提出了第一个多视图三角宽放办法,该办法对噪音和外缘都有力。为此,我们将现有的半无限制放松办法扩大到损失功能,包括耗尽的最小平方块成本,以计算外缘。我们提出了两种配方,一种基于上极限制,另一种基于分数再预测方程。第一个是低维,在中度噪音和外缘水平下仍然紧紧,而第二个则较高维度,因此较慢,但即使在极端噪音和外缘水平下仍然很紧。我们通过广泛的实验表明,拟议办法使我们能够计算出最理想的重建,在经验上,即使有重大噪音和很大比例的外缘,放松也仍然很紧。