Abstract
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.
Abstract (translated)
我们提出了对多视角三角化的第一个凸 relaxation,该 relaxation 能够 robust 地应对噪声和异常点。为此,我们扩展了现有的半正则 relaxation 方法,将其应用于包含截断最小二乘成本的损失函数,以处理异常点。我们提出了两个 formulation,一个基于极线约束,另一个基于分块重构方程。第一个 formulation 是低维度的,在中等噪声和异常点水平下仍然非常紧,而第二个 formulation 是高维度的,因此较慢,但即使在极端噪声和异常点水平下仍然非常紧。我们通过广泛的实验表明,我们提出的方法能够计算出可证明最优重构,而且经验上,即使在大量的噪声和异常点情况下, relaxation 仍然非常紧。
URL
https://arxiv.org/abs/2301.11431
