Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search

TL;DR

This work tackles robust 6-DoF point cloud registration under heavy outliers by marrying heuristics-guided parameter search with a three-stage decomposition that reduces the problem to 3-DoF translation, 2-DoF rotation axis, and 1-DoF rotation angle. It introduces a valid-sampling strategy and spatial-compatibility verification to accelerate search and improve robustness, leveraging interval stabbing for fast 1D/2D searches at each stage. Through extensive simulations and real-world datasets, the method achieves robustness comparable to state-of-the-art approaches while delivering significant efficiency gains, often orders of magnitude faster than global-search baselines. The results suggest strong practical impact for large-scale and real-time registration tasks, with potential extensions to GPUs and other geometry-based pose estimation problems.

Abstract

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.

Figures (16)

• Figure 1: Illustration of the proposed heuristics-guided parameter search strategy. The large gray block represents the whole parameter space. Each middle blue/yellow block represents the feasible region that makes each correspondence an inlier. The small red block represents the optimal region that fits the most correspondences. (a) The parameter search-based methods yang2015goliu2018efficientchen2022deterministic generally search the whole parameter space (i.e., the large gray block) to find the optimal solution and lead to unsatisfactory efficiency. (b) Our heuristics-guided parameter search method integrates the sampling strategy into parameter search and only needs to search the yellow blocks associated with the samples.
• Figure 2: Pipeline of the proposed point cloud registration approach. Given a set of putative correspondences, we decompose the original 6-DoF transformation problem into three sub-problems and conduct progressive outlier removal by solving the sub-problems in turn. Green and red values denote the numbers of inlier and outlier correspondences, respectively.
• Figure 3: Illustration of our search strategy for solving the first sub-problem at stage I (cf. Section \ref{['subsec: te']}). (a) For the feasible region $\mathcal{S}_j$ of $\mathbf{t}$ related to each sampled ($\mathbf{x}_j$, $\mathbf{y}_j$) (i.e., the yellow shell), we discretize the 3D spherical shell $\mathcal{S}_j$ into $m$ spherical surface $\mathcal{C}_j^p$ (i.e., the orange spherical surface) (cf. Section \ref{['subsubset: t_dis']}). For each $\mathcal{C}_j^p$, we use 1D BnB to search $t_3$. (b) At each branch, when $t_3 = \dot{t}_3 \in [\underline{t_3},\overline{t_3}]$, the intersection of the circle related to ($\mathbf{x}_j$, $\mathbf{y}_j$) and each ring related to ($\mathbf{x}_i$, $\mathbf{y}_i$) leads to the interval [$\varphi_i$] (cf. Section \ref{['subsubset: t_1dbnb']}). (c) The computations of lower and upper bounds in the outer BnB module only differ in the width of intervals. We adopt interval stabbing as the inner module to compute both bounds (cf. Algorithm \ref{['alg: interval_stabbing']}).
• Figure 4: Illustration of our search strategy for solving the second sub-problem at stage II (cf. Section \ref{['subsec: re']}). (a) The constraint defined by Eq. (\ref{['eq: r_cons_simp']}) results in a girdle-like feasible region $\mathcal{G}_i$. (b) We discretize $\mathcal{G}_j$ related to the sampled ($\mathbf{x}_j$, $\mathbf{y}_j$) into $n$ half-circles $\mathcal{K}_j^q$ (cf. Section \ref{['subsubset: r_dis']}). Note that the intersection of $\mathcal{K}_j^q$ and each $\mathcal{G}_i$ leads to a interval (cf. Section \ref{['subsubset: r_search']}). Therefore we apply interval stabbing to find the candidate ${\mathbf{r}_{j}^q}'$ corresponding to each 1D $\mathcal{K}_j^q$.
• Figure 5: At stage III, each correspondence is related to an interval [$\underline{\theta_i}$, $\overline{\theta_i}$] (cf. Section \ref{['subsec: thetae']}), and we directly apply interval stabbing to get a globally optimal solution of the third sub-problem (i.e., problem (\ref{['eq: sub_theta']})).