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A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion

Feng Yu · Teng Zhang · Gilad Lerman

Arch 4A-E Poster #184
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Thu 20 Jun 5 p.m. PDT — 6:30 p.m. PDT
Oral presentation: Orals 4B 3D Vision
Thu 20 Jun 1 p.m. PDT — 2:30 p.m. PDT


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, offering superior computational efficiency compared to TME. 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 and speed 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.

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