  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.
