[Paper Review] ROBIN: a Graph-Theoretic Approach to Reject Outliers in Robust Estimation using Invariants

Jingnan Shi, Heng Yang+1 more|arXiv (Cornell University)|Nov 7, 2020

Anomaly Detection Techniques and Applications63 references4 citations

TL;DR

ROBIN is a graph-theoretic framework that uses invariants to rapidly detect and reject outliers in robust estimation, modeling compatible measurements as a compatibility graph where inliers form a maximum clique or k-core. It enables existing solvers like RANSAC and GNC to achieve robustness against over 95% outliers while running in milliseconds on large-scale problems.

ABSTRACT

Many estimation problems in robotics, computer vision, and learning require estimating unknown quantities in the face of outliers. Outliers are typically the result of incorrect data association or feature matching, and it is common to have problems where more than 90% of the measurements used for estimation are outliers. While current approaches for robust estimation are able to deal with moderate amounts of outliers, they fail to produce accurate estimates in the presence of many outliers. This paper develops an approach to prune outliers. First, we develop a theory of invariance that allows us to quickly check if a subset of measurements are mutually compatible without explicitly solving the estimation problem. Second, we develop a graph-theoretic framework, where measurements are modeled as vertices and mutual compatibility is captured by edges. We generalize existing results showing that the inliers form a clique in this graph and typically belong to the maximum clique. We also show that in practice the maximum k-core of the compatibility graph provides an approximation of the maximum clique, while being faster to compute in large problems. These two contributions leads to ROBIN, our approach to Reject Outliers Based on INvariants, which allows us to quickly prune outliers in generic estimation problems. We demonstrate ROBIN in four geometric perception problems and show it boosts robustness of existing solvers while running in milliseconds in large problems.

Motivation & Objective

• Address the challenge of robust estimation in the presence of extreme outlier rates (e.g., >90%) that overwhelm traditional solvers.
• Develop a fast, general-purpose method to pre-prune outliers before applying standard robust estimators.
• Enable existing fast solvers (e.g., RANSAC, GNC) to maintain accuracy and efficiency even under extreme outlier contamination.
• Provide a scalable framework applicable to diverse geometric perception problems such as pose estimation, registration, and SLAM.

Proposed method

• Introduce a theory of invariance to check mutual compatibility of small subsets of measurements without solving the full estimation problem.
• Model measurements as vertices in a compatibility graph, with edges connecting mutually compatible subsets based on invariant checks.
• Leverage the fact that inliers form a clique in the compatibility graph, and use the maximum k-core as a fast, scalable approximation of the maximum clique.
• Use the k-core structure to efficiently prune outliers while preserving inliers, reducing the effective outlier rate below the threshold where standard solvers fail.
• Integrate ROBIN as a preprocessing step before robust estimators like GNC or RANSAC to enhance their robustness.
• Utilize geometric invariants—such as cross-ratio for 2D-3D pose estimation and point-normal invariants for registration—to define compatibility checks.

Experimental results

Research questions

• RQ1 Can we design a fast, general-purpose method to detect and reject outliers in estimation problems without solving the full estimation problem?
• RQ2 How can invariants be used to define mutual compatibility between measurement subsets in a way that is both accurate and computationally efficient?
• RQ3 To what extent can the maximum k-core of a compatibility graph approximate the maximum clique, and how does this affect outlier rejection performance?
• RQ4 Can ROBIN be integrated with existing robust estimators to significantly improve their tolerance to extreme outlier rates (e.g., >95%)?
• RQ5 How does the choice of invariants (e.g., point-only vs. point-with-normal) affect the sparsity of the compatibility graph and the accuracy of the k-core approximation?

Key findings

• ROBIN successfully rejects over 95% of outliers in 2D-3D pose estimation and point cloud registration, even when inliers are embedded in highly corrupted data.
• The maximum k-core of the compatibility graph provides a strong approximation of the maximum clique, enabling fast outlier rejection with minimal loss of inliers.
• ROBIN + GNC and ROBIN* + GNC achieve near-perfect outlier rejection (nearly 100%) across all tested outlier levels, with inlier preservation rates above 90% even at 90% outlier contamination.
• ROBIN runs in 0.1 to 46 ms on large-scale problems, with the k-core variant being 2 to 3.4 times faster than the maximum clique variant.
• Using point-normal invariants leads to sparser compatibility graphs, improving the k-core’s approximation of the maximum clique and enhancing robustness.
• TEASER(ROBIN)++ fails at low overlap ratios (e.g., 5%) because the k-core alone cannot reject enough outliers, while ROBIN-based variants maintain high accuracy.