Efficient Algorithms for Global Outlier Removal in Large-scale Structure-from-Motion

Fei Wen, Danping Zou, Ruihang Miao, Rendong Ying, Peilin Liu

Abstract: This work addresses the outlier removal problem in large-scale global structure-from-motion. In such applications, outlier removal is very useful to mitigate the deterioration caused by mismatches in the feature point matching step. Unlike existing outlier removal methods, we exploit the structure in multiview geometry problems to propose a dimension reduced formulation, based on which two efficient methods have been developed. The first method considers a convex relaxed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization and is solved by a single linear programming (LP). The second method approximately solves the ideal ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> minimization by an iteratively reweighted method. The dimension reduction results in a significant speedup of the new algorithms. Further, the iteratively reweighted method can significantly reduce the possibility of removing true inliers. Results show that, compared with state-of-the-art algorithms (e.g., the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> method), the proposed algorithms are more than three times faster and meanwhile produce better consensus sets. Matlab code for reproducing the results is available at https://github.com/FWen/OUTLR.git.