Augmented Maximum Correntropy Criterion for Robust Geometric Perception

Maximum correntropy criterion (MCC) is a robust and powerful technique to handle heavy-tailed nonGaussian noise, which has many applications in the fields of vision, signal processing, machine learning, etc. In this article, we introduce several contributions to the MCC and propose an augmented MCC (AMCC), which raises the robustness of classic MCC variants for robust fitting to an unprecedented level. Our first contribution is to present an accurate bandwidth estimation algorithm based on the probability density function (PDF) matching, which solves the instability problem of the Silverman's rule. Our second contribution is to introduce the idea of graduated nonconvexity (GNC) and a worst-rejection strategy into MCC, which compensates for the sensitivity of MCC to high outlier ratios. Our third contribution is to provide a definition of local distribution measure to evaluate the quality of inliers, which makes the MCC no longer limited to random outliers but is generally suitable for both random and clustered outliers. Our fourth contribution is to show the generalizability of the proposed AMCC by providing eight application examples in geometry perception and performing comprehensive evaluations on five of them. Our experiments demonstrate that 1) AMCC is empirically robust to 80% $-$ 90% of random outliers across applications, which is much better than Cauchy M-estimation, MCC, and GNC-GM; 2) AMCC achieves excellent performance in clustered outliers, whose success rate is 60% $-$ 70% percentage points higher than the second-ranked method at 80% of outliers; 3) AMCC can run in real-time, which is 10 $-$ 100 times faster than RANSAC-type methods in low-dimensional estimation problems with high outlier ratios. This gap will increase exponentially with the model dimension.