We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation leads to extreme robustness to outliers; however, finding the maximum clique is an NP-hard problem, and therefore approximation is required in practice for large-size problems. The performance of an approximation algorithm is evaluated by its computational complexity (the lower the runtime, the better) and solution accuracy (how close the solution is to the maximum clique). Accordingly, the main contribution of CLIPPER+ is outperforming the state-of-the-art in accuracy while maintaining a relatively low runtime. CLIPPER+ builds on prior work (CLIPPER [1] and PMC [2]) and prunes the graph by removing vertices that have a small core number and cannot be a part of the maximum clique. This will result in a smaller graph, on which the maximum clique can be estimated considerably faster. We evaluate the performance of CLIPPER+ on standard graph benchmarks, as well as synthetic and real-world point cloud registration problems. These evaluations demonstrate that CLIPPER+ has the highest accuracy and can register point clouds in scenarios where over $99\%$ of associations are outliers. Our code and evaluation benchmarks are released at https://github.com/ariarobotics/clipperp.

翻译：我们提出CLIPPER+算法，该算法在无权重图中寻找最大团，用于对离群点具有鲁棒性的全局配准。该配准问题可建模为图的形式，并通过求解其最大团来解决。这一建模方式对离群点具有极强的鲁棒性；然而，寻找最大团是一个NP难问题，因此在实际处理大规模问题时需要进行近似求解。近似算法的性能通过其计算复杂度（运行时间越低越好）和解的精度（解与最大团的接近程度）来评估。据此，CLIPPER+的主要贡献在于：在保持相对较低运行时间的同时，在精度上超越了现有最优方法。CLIPPER+建立在先前工作（CLIPPER [1]和PMC [2]）的基础上，通过移除核心数较小且不可能成为最大团一部分的顶点来对图进行剪枝。这将得到一个更小的图，在该图上可以显著更快地估计最大团。我们在标准图基准测试以及合成和真实世界的点云配准问题上评估了CLIPPER+的性能。这些评估表明，CLIPPER+具有最高的精度，并且能够在超过$99\%$的关联均为离群点的场景下完成点云配准。我们的代码和评估基准已在https://github.com/ariarobotics/clipperp发布。