A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion
This work addresses robust subspace recovery for computer vision and 3D reconstruction, offering incremental improvements in handling outliers in applications like Structure from Motion.
The paper tackles robust subspace recovery in datasets with many outliers by introducing the subspace-constrained Tyler's estimator (STE), which effectively recovers low-dimensional subspaces even with a smaller fraction of inliers compared to other methods, and applies it to Structure from Motion for tasks like fundamental matrix estimation and outlier camera removal, achieving state-of-the-art performance in numerical experiments.
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.