We present the subspace-constrained Tyler's estimator (STE) designed for
recovering a low-dimensional subspace within a dataset that may be highly
corrupted with outliers. STE is a fusion of the Tyler's M-estimator (TME) and a
variant of the fast median subspace. Our theoretical analysis suggests that,
under a common inlier-outlier model, STE can effectively recover the underlying
subspace, even when it contains a smaller fraction of inliers relative to other
methods in the field of robust subspace recovery. We apply STE in the context
of Structure from Motion (SfM) in two ways: for robust estimation of the
fundamental matrix and for the removal of outlying cameras, enhancing the
robustness of the SfM pipeline. Numerical experiments confirm the
state-of-the-art performance of our method in these applications. This research
makes significant contributions to the field of robust subspace recovery,
particularly in the context of computer vision and 3D reconstruction.

我们介绍了面向数据集中可能被严重污染的低维子空间恢复的子空间约束的 Tyler 估计器 (STE)。通过理论分析，我们发现 STE 可以有效恢复潜在的子空间，即使相对于其他鲁棒子空间恢复方法，它包含更小比例的内点。我们将 STE 应用于 Structure from Motion (SfM) 的两种方式：用于鲁棒估计基础矩阵和去除异常相机，增强 SfM 流程的鲁棒性。数值实验证实了我们方法在这些应用中的最先进性能。这项研究对于鲁棒子空间恢复领域，尤其是在计算机视觉和三维重建方面做出了重要贡献。