Registration of partially overlapping, featureless three-dimensional (3D) point sets with noise is a difficult problem in the applications of large-scale metrology (LSM). Existing approaches use the sparse iterative closest points (SICP) method applying the $l_p$ norm to decrease the influence of outliers during registration. However, we reveal in this study that sparse point-to-point becomes easily trapped into local minima in featureless point clouds registration, and the error landscape of sparse point-to-plane is too shallow to restrain the sliding due to the lack of constraints in the large flat areas. Also, point clouds sampled from the large flat areas cause the low-rank matrix of linear equation in estimating the transformation matrix. Hence, we propose using the point-to-point $l_p$ distance constraints to restrain the sliding along large flat areas. We further define a weighted enhanced $l_p$ distance (WELD) error metric to slacken the constraints and escape from the local minima. Moreover, WELD can improve stability with the full-rank linear equation in estimating the transformation matrix. To verify the capability of escaping from the local minima and restraining the sliding, we choose SICP and two other algorithms to be compared with our method in simulated and actual point clouds. The comparisons show that our method successfully can escape from the local minima and restrain the sliding to handle outliers and noisy featureless point clouds effectively. The source code is available at https://github.com/Timbersaw-wangzw/WES-ICP.

部分重叠、无特征的三维 (3D) 点集与噪声的配准是大规模计量 (LSM) 应用中的难题。现有方法使用稀疏迭代最近点 (SICP) 方法应用$l_p$规范以减少注册过程中异常值的影响。然而，我们在这项研究中发现，在无特征点云配准中，稀疏点对点很容易陷入局部最小值，并且由于缺乏约束，稀疏点对面的误差范围太浅而无法抑制滑动在大面积的平坦区域。此外，从大平面区域采样的点云在估计变换矩阵时会导致线性方程的低秩矩阵。因此，我们建议使用点对点$l_p$距离约束以抑制沿大平面区域的滑动。我们进一步定义了加权增强$l_p$距离（WELD）误差度量来放松约束并摆脱局部最小值。此外，WELD 在估计变换矩阵时可以提高全秩线性方程的稳定性。为了验证摆脱局部最小值和抑制滑动的能力，我们选择 SICP 和其他两种算法与我们在模拟和实际点云中的方法进行比较。比较表明，我们的方法成功地摆脱了局部最小值并抑制了滑动，从而有效地处理了异常值和嘈杂的无特征点云。源代码可在 https://github.com/Timbersaw-wangzw/WES-ICP 获得。