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：我们提出了首个对噪声和离群点均具有鲁棒性的多视图三角化凸松弛方法。为此，我们将现有半定松弛方法扩展至包含截断最小二乘代价函数的损失函数，以处理离群点。我们提出两种公式化形式：一种基于对极约束，另一种基于分数重投影方程。前者维度较低，在中等噪声和离群点水平下仍保持紧致性；后者维度较高因而计算较慢，但即使在极端噪声和离群点水平下也能保持紧致性。通过大量实验证明，所提方法能够计算可证明最优的重建结果，且经验表明即使存在显著噪声和大量离群点时，松弛仍保持紧致性。