arXiv:2610.34271v1 Announce Type: cross Abstract: We propose a novel method for robust point cloud registration with only one tunable parameter. Our method, dubbed TLP, uses truncated $L_p$ functions with different values of $p$ to assign priority scores to correspondences, select the hypothesis, and refine the final model. By leveraging the robustness of truncated functions, TLP effectively handles the high outlier rates commonly encountered in real-world 3D feature matching. We also exploit GPU parallelization to evaluate hypotheses efficiently, enabling registration from thousands of correspondences in under a second on average. With only one tunable parameter, our method offers greater practicality than multi-parameter methods that require dataset-specific tuning of several parameters. Evaluations on public benchmark datasets demonstrate that TLP achieves higher accuracy than state-of-the-art single-parameter methods. Furthermore, it outperforms two widely used multi-parameter methods on three of the four evaluated datasets while maintaining competitive runtime.