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Correspondence-based rotation search and point cloud registration are two fundamental problems in robotics and computer vision. However, the presence of outliers, sometimes even occupying the great majority of the putative correspondences, can make many existing algorithms either fail or have very high computational cost. In this letter, we present RANSIC (RANdom Sampling with Invariant Compatibility), a fast and highly robust method applicable to both problems based on a new paradigm combining random sampling with invariance and compatibility. RANSIC starts with randomly selecting small subsets from the correspondence set, then seeks potential inliers as the graph vertices from random subsets through the compatibility tests based on invariants established in each problem, and eventually returns the eligible inliers when there exists a <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula>-degree vertex (where <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula> is initially set and updated during the algorithm) and the residual errors satisfy a certain termination condition at the same time. In synthetic and real experiments, we show that RANSIC is fast for use, robust against over 95&#x0025; outliers, and also able to recall approximately 100&#x0025; inliers, outperforming other state-of-the-art solvers for both the rotation search and point cloud registration problems.

RANSIC: Fast and Highly Robust Estimation for Rotation Search and Point Cloud Registration Using Invariant Compatibility