We propose a fast and correspondence-free local point cloud registration method that leverages geometric surface structure and reproducing kernel Hilbert space (RKHS) embeddings. The method represents point clouds as continuous functions with point-wise anisotropic kernels that encode local geometry. This formulation improves alignment along surface normals while relaxing alignment along tangential directions. To solve the resulting registration problem, we propose a second-order on-manifold optimization scheme with approximate Riemannian Hessians, achieving a speedup of up to 10x over the first-order solvers used in prior correspondence-free RKHS-based methods. We demonstrate improved frame-to-frame LiDAR and RGB-D tracking accuracy across diverse indoor and outdoor datasets. On a LiDAR tracking registration task in the driving domain, we achieve a reduction of $>55\%$ in both translational and rotational drift in challenging feature-sparse environments. On object registration benchmarks, we show improved robustness over ICP-based methods and further gains when refining global initialization, particularly under moderate misalignment.

翻译：我们提出了一种快速且无须对应关系的局部点云配准方法，该方法利用几何表面结构与再生核希尔伯特空间(RKHS)嵌入。该方法将点云表示为具有逐点各向异性核的连续函数，这些核编码了局部几何特性。该公式在沿表面法线方向增强对齐效果的同时，放松了沿切线方向的对齐约束。为解决由此产生的配准问题，我们提出了一种基于近似黎曼海森矩阵的二阶流形优化方案，相较于先前基于无对应RKHS方法中使用的一阶求解器，实现了最高达10倍的加速。我们在多样化的室内外数据集上展示了改进的帧到帧LiDAR与RGB-D跟踪精度。在驾驶领域的LiDAR跟踪配准任务中，我们在具有挑战性的特征稀疏环境下实现了平移与旋转漂移均降低>55%的效果。在物体配准基准测试中，我们展示了相较于基于ICP方法的鲁棒性提升，并在优化全局初始化的过程中（特别是在中等程度错位情况下）取得了进一步改进。