Efficient and Robust Point Cloud Registration via Heuristics-guided
  Parameter Search
Tianyu Huang Haoang Li Liangzu Peng Yinlong Liu Yun-Hui Liu
Estimating the rigid transformation with 6 degrees of freedom based on a
putative 3D correspondence set is a crucial procedure in point cloud
registration. Existing correspondence identification methods usually lead to
large outlier ratios ($>$ 95 $\%$ is common), underscoring the significance of
robust registration methods. Many researchers turn to parameter search-based
strategies (e.g., Branch-and-Bround) for robust registration. Although related
methods show high robustness, their efficiency is limited to the
high-dimensional search space. This paper proposes a heuristics-guided
parameter search strategy to accelerate the search while maintaining high
robustness. We first sample some correspondences (i.e., heuristics) and then
just need to sequentially search the feasible regions that make each sample an
inlier. Our strategy largely reduces the search space and can guarantee
accuracy with only a few inlier samples, therefore enjoying an excellent
trade-off between efficiency and robustness. Since directly parameterizing the
6-dimensional nonlinear feasible region for efficient search is intractable, we
construct a three-stage decomposition pipeline to reparameterize the feasible
region, resulting in three lower-dimensional sub-problems that are easily
solvable via our strategy. Besides reducing the searching dimension, our
decomposition enables the leverage of 1-dimensional interval stabbing at all
three stages for searching acceleration. Moreover, we propose a valid sampling
strategy to guarantee our sampling effectiveness, and a compatibility
verification setup to further accelerate our search. Extensive experiments on
both simulated and real-world datasets demonstrate that our approach exhibits
comparable robustness with state-of-the-art methods while achieving a
significant efficiency boost.