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

arXiv: https://arxiv.org/abs/2204.01324 · HTML: https://mlsanity.com/paper/2204.01324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 4 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Multi-view Self-supervised Deep Learning for 6D Pose Estimation in the Amazon Picking Challenge](https://mlsanity.com/paper/1609.09475/) (2016)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [SegICP: Integrated Deep Semantic Segmentation and Pose Estimation](https://mlsanity.com/paper/1703.01661/) (2017)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [In Perfect Shape: Certifiably Optimal 3D Shape Reconstruction from 2D Landmarks](https://mlsanity.com/paper/1911.11924/) (2019)
- [RANSIC: Fast and Highly Robust Estimation for Rotation Search and Point Cloud Registration using Invariant Compatibility](https://mlsanity.com/paper/2104.09133/) (2021)
- [Optimal Pose and Shape Estimation for Category-level 3D Object Perception](https://mlsanity.com/paper/2104.08383/) (2021)
- [Robust Single Rotation Averaging](https://mlsanity.com/paper/2004.00732/) (2020)
- [TriVoC: Efficient Voting-based Consensus Maximization for Robust Point Cloud Registration with Extreme Outlier Ratios](https://mlsanity.com/paper/2111.00657/) (2021)
- [Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees](https://mlsanity.com/paper/1903.11683/) (2019)

## Abstract (arXiv)

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.