A Geometric Estimation Technique Based on Adaptive M-Estimators: Algorithm and Applications

Robust fitting is a basic technique and has been widely applied in photogrammetry and remote sensing, such as geometric correction. As known, typical robust estimators (include M-estimators, S-estimators, MM-estimators, etc.) often fail when outlier rate is higher than 50%, even if the outliers are uniformly distributed. In this article, we propose simple yet effective estimators, called adaptive M-estimators (AM-estimators). They are still robust under 80% of outliers. The proposed AM-estimators are very important supplements of M-estimators. Different from M-estimators, we use a varying parameter (shape-control parameter) instead of the original constant parameter in the weight function. The shape-control parameter decreases along with iterations in iteratively reweighted least squares, namely, AM-estimators are optimized in a coarse-to-fine manner. We adapt the proposed estimators into classical remote sensing and photogrammetry tasks, including mismatch removal, camera orientation (or called perspective-n-point), and point set registration to demonstrate their powers. Extensive synthetic and real experiments show that AM-estimators are superior to M-estimators, S-estimators, MM-estimators, and RANSAC-type methods. The source code of AM-estimators will be publicly available at https://ljy-rs.github.io/web.