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Many estimation problems in robotics, computer vision, and learning requireestimating unknown quantities in the face of outliers. Outliers are typicallythe result of incorrect data association or feature matching, and it is commonto have problems where more than 90% of the measurements used for estimationare outliers. While current approaches for robust estimation are able to dealwith moderate amounts of outliers, they fail to produce accurate estimates inthe presence of many outliers. This paper develops an approach to pruneoutliers. First, we develop a theory of invariance that allows us to quicklycheck if a subset of measurements are mutually compatible without explicitlysolving the estimation problem. Second, we develop a graph-theoretic framework,where measurements are modeled as vertices and mutual compatibility is capturedby edges. We generalize existing results showing that the inliers form a cliquein this graph and typically belong to the maximum clique. We also show that inpractice the maximum k-core of the compatibility graph provides anapproximation of the maximum clique, while being faster to compute in largeproblems. These two contributions leads to ROBIN, our approach to RejectOutliers Based on INvariants, which allows us to quickly prune outliers ingeneric estimation problems. We demonstrate ROBIN in four geometric perceptionproblems and show it boosts robustness of existing solvers while running inmilliseconds in large problems.

ROBIN: a Graph-Theoretic Approach to Reject Outliers in Robust Estimation using Invariants