Outlier-Robust Geometric Perception: A Novel Thresholding-Based Estimator with Intra-Class Variance Maximization

TL;DR

This work tackles robust geometric perception under heavy outlier contamination by introducing TIVM, a thresholding-based estimator that leverages intra-class variance maximization to dynamically separate inliers from outliers without requiring known noise statistics. By combining a 2-group residual threshold with multi-layered thresholding and a self-adaptive layer-tuning mechanism, TIVM iteratively refines the model while progressively isolating pure inliers; a noise-statistics–aware variant further accelerates convergence when $\tau$ is known. Across rotation averaging, point cloud registration, and category-level perception, TIVM achieves robustness against $70$–$90\%$ outliers and typically converges in $3$–$15$ iterations, outperforming state-of-the-art solvers in both speed and accuracy. The method maintains robustness even when noise statistics are unknown and provides an implementation that integrates with standard non-minimal solvers, with open-source code available for reproducibility.

Abstract

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.

Figures (12)

• Figure 1: Intuitive illustration on the thresholding framework of the proposed TIVM estimator in Algorithm \ref{['algo-TIVM*']}.
• Figure 2: Illustration of the residual-error histograms with labeled thresholds in our TIVM algorithm at different iterations.
• Figure 3: Benchmarking on robust rotation averaging.
• Figure 4: Benchmarking on robust rotation averaging without inlier-noise statistics.
• Figure 5: Demonstration of the experimental setup of robust point cloud registration. Green and red lines denote inliers and outliers, respectively.