  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 paper, 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. Generally, RANSIC starts with randomly selecting small subsets
from the correspondence set, then seeks potential inliers as graph vertices
from the random subsets through the compatibility tests of invariants
established in each problem, and eventually returns the eligible inliers when
there exists at least one K-degree vertex (K is automatically updated depending
on the problem) and the residual errors satisfy a certain termination condition
at the same time. In multiple synthetic and real experiments, we demonstrate
that RANSIC is fast for use, robust against over 95% outliers, and also able to
recall approximately 100% inliers, outperforming other state-of-the-art solvers
for both the rotation search and the point cloud registration problems.
