Robust outlier removal using penalized linear regression in multiview geometry

In multiview geometry, it is crucial to remove outliers before the optimization since they are adverse factors for parameter estimation. Some efficient and very popular methods for this task are RANSAC, MLESAC and their improved variants. However, Olsson et al. have pointed that mismatches in longer point tracks may go undetected by using RANSAC or MLESAC. Although some robust and efficient algorithms are proposed to deal with outlier removal, little concerns on the masking (an outlier is undetected as such) and swamping (an inlier is misclassified as an outlier) effects are taken into account in the community, which probably makes the fitted model biased. In the paper, we first characterize some typical parameter estimation problems in multiview geometry, such as triangulation, homography estimate and shape from motion (SFM), into a linear regression model. Then, a non-convex penalized regression approach is proposed to effectively remove outliers for robust parameter estimation. Finally,we analyze the robustness of non-convex penalized regression theoretically. We have validated our method on three representative estimation problems in multiview geometry, including triangulation, homography estimate and the SFM with known camera orientation. Experiments on both synthetic data and real scene objects demonstrate that the proposed method outperforms the state-of-the-art methods. This approach can also be extended to more generic problems that within-profile correlations exist.