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.

中文翻译：

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基于自适应M估计器的几何估计技术：算法与应用


鲁棒拟合是一项基础技术，在摄影测量和遥感等几何校正等领域有着广泛的应用。众所周知，典型的鲁棒估计器（包括M估计器、S估计器、MM估计器等）在离群值率高于50%时经常失败，即使离群值是均匀分布的。在本文中，我们提出了简单而有效的估计器，称为自适应 M 估计器（AM 估计器）。它们在 80% 的异常值下仍然稳健。所提出的 AM 估计器是 M 估计器的非常重要的补充。与 M 估计器不同，我们在权重函数中使用变化参数（形状控制参数）而不是原始恒定参数。形状控制参数随着迭代重新加权最小二乘的迭代而减小，即AM估计器以从粗到细的方式优化。我们将所提出的估计器应用到经典的遥感和摄影测量任务中，包括失配消除、相机方向（或称为透视 n 点）和点集配准以展示其功能。大量的综合和真实实验表明，AM 估计器优于 M 估计器、S 估计器、MM 估计器和 RANSAC 型方法。 AM 估计器的源代码将在 https://ljy-rs.github.io/web 上公开提供。