Geometric perception problems are fundamental tasks in robotics and computer vision. In real-world applications, they often encounter the inevitable issue of outliers, preventing traditional algorithms from making correct estimates. In this paper, we present a novel general-purpose robust estimator TIVM (Thresholding with Intra-class Variance Maximization) that can collaborate with standard non-minimal solvers to efficiently reject outliers for geometric perception problems. First, we introduce the technique of intra-class variance maximization to design a dynamic 2-group thresholding method on the measurement residuals, aiming to distinctively separate inliers from outliers. Then, we develop an iterative framework that robustly optimizes the model by approaching the pure-inlier group using a multi-layered dynamic thresholding strategy as subroutine, in which a self-adaptive mechanism for layer-number tuning is further employed to minimize the user-defined parameters. We validate the proposed estimator on 3 classic geometric perception problems: rotation averaging, point cloud registration and category-level perception, and experiments show that it is robust against 70--90\% of outliers and can converge typically in only 3--15 iterations, much faster than state-of-the-art robust solvers such as RANSAC, GNC and ADAPT. Furthermore, another highlight is that: our estimator can retain approximately the same level of robustness even when the inlier-noise statistics of the problem are fully unknown.

翻译：几何感知问题是机器人学和计算机视觉中的基础任务。在实际应用中，这些问题常常不可避免地遇到离群点，导致传统算法无法做出正确估计。本文提出了一种新颖的通用鲁棒估计器TIVM（基于类内方差最大化的阈值化方法），该估计器可与标准的非最小求解器协同工作，有效剔除几何感知问题中的离群点。首先，我们引入类内方差最大化技术，在测量残差上设计了一种动态二分组阈值化方法，旨在清晰地区分内点和离群点。随后，我们开发了一个迭代框架，通过采用多层动态阈值化策略作为子程序逼近纯内点组，从而鲁棒地优化模型；该框架进一步采用了层数自适应调整机制，以最小化用户定义的参数。我们在三个经典几何感知问题上验证了所提出的估计器：旋转平均、点云配准和类别级感知。实验表明，该估计器对70–90%的离群点具有鲁棒性，通常仅需3–15次迭代即可收敛，其速度远快于RANSAC、GNC和ADAPT等先进鲁棒求解器。此外，另一个突出特点是：即使在内点噪声统计特性完全未知的情况下，我们的估计器仍能保持大致相同水平的鲁棒性。