A Subspace-Constrained Tyler's Estimator and its Applications to
  Structure from Motion
Feng Yu Teng Zhang Gilad Lerman
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.