Point cloud registration is invariably an essential and challenging task in the fields of photogrammetry and computer vision to align multiple point clouds to a united reference frame. In this paper, we propose a novel global registration method using a robust phase correlation method for registration of low-overlapping point clouds, which is less sensitive to noise and outliers than feature-based registration methods. The proposed point cloud registration is achieved by converting the estimation of rotation, scaling, and translation in the spatial domain to a problem of correlating low-frequency components in the frequency domain. Specifically, it consists of three core steps: transformation from the spatial domain to the frequency domain, decoupling of rotation, scaling, and translation, and adapted phase correlation for robust shift estimation. In the first step, unstructured and unordered 3D points are transformed from the spatial domain to the frequency domain via 3D Fourier transformation, following a voxelization and binarization process. In the second step, rotation, scaling, and translation are decoupled by sequential operations, including Fourier transform, resampling strategies, and Fourier-Mellin transform. In the third step, the estimation of transformation parameters is transformed into shift estimation tasks. The shift estimation task is solved by a robust phase correlation method, in which low-frequency components are matched by decomposing the normalized cross-power spectrum and linearly fitting the decomposed signals with a closed-form solution by a $\ell$1-norm-based robust estimator. Experiments were conducted using three different datasets of urban and natural scenarios. Results demonstrate the efficiency of the proposed method, with the majority of rotation and translation errors reaching less than 0.2 degree and 0.5 m, respectively. Additionally, it is also validated by experiments that the proposed method is robust to noise and versatile to datasets with wide ranges of overlaps and various geometric characteristics.

在摄影测量学和计算机视觉领域，要使多个点云与一个统一的参考系对齐，点云配准始终是必不可少且具有挑战性的任务。在本文中，我们提出了一种新的全局注册方法，该方法使用鲁棒的相位相关方法注册低重叠点云，它比基于特征的注册方法对噪声和离群值的敏感性低。通过将空间域中旋转，缩放和平移的估计转换为与频域中低频分量相关的问题，可以实现建议的点云配准。具体来说，它包括三个核心步骤：从空间域到频域的转换，旋转，缩放和平移的解耦，以及用于鲁棒移位估计的自适应相位相关性。第一步，在体素化和二值化过程之后，通过3D傅里叶变换将非结构化和无序的3D点从空间域转换到频域。在第二步中，旋转，缩放和平移通过包括傅立叶变换，重采样策略和傅立叶-梅林变换在内的顺序操作进行解耦。在第三步中，将变换参数的估计转换为移位估计任务。偏移估计任务通过鲁棒的相位相关方法解决，其中低频分量通过分解归一化的交叉功率谱并通过线性拟合将分解后的信号与闭式解进行匹配。在体素化和二值化过程之后，通过3D傅里叶变换将非结构化和无序的3D点从空间域转换到频域。在第二步中，旋转，缩放和平移通过包括傅立叶变换，重采样策略和傅立叶-梅林变换在内的顺序操作进行解耦。在第三步中，将变换参数的估计转换为移位估计任务。偏移估计任务通过鲁棒的相位相关方法解决，其中低频分量通过分解归一化的交叉功率谱并通过线性拟合将分解后的信号与闭式解进行匹配。在体素化和二值化过程之后，通过3D傅里叶变换将非结构化和无序的3D点从空间域转换到频域。在第二步中，旋转，缩放和平移通过包括傅立叶变换，重采样策略和傅立叶-梅林变换在内的顺序操作进行解耦。在第三步中，将变换参数的估计转换为移位估计任务。偏移估计任务通过鲁棒的相位相关方法解决，其中低频分量通过分解归一化的交叉功率谱并通过线性拟合将分解后的信号与闭式解进行匹配。通过顺序操作（包括傅立叶变换，重采样策略和傅立叶-梅林变换）将翻译和翻译解耦。在第三步中，将变换参数的估计转换为移位估计任务。偏移估计任务通过鲁棒的相位相关方法解决，其中低频分量通过分解归一化的交叉功率谱并通过线性拟合将分解后的信号与闭式解进行匹配。通过顺序操作（包括傅立叶变换，重采样策略和傅立叶-梅林变换）将翻译和翻译解耦。在第三步中，将变换参数的估计转换为移位估计任务。偏移估计任务通过鲁棒的相位相关方法解决，其中低频分量通过分解归一化的交叉功率谱并通过线性拟合将分解后的信号与闭式解进行匹配。$\ell$基于1范数的鲁棒估计量。使用三个不同的城市和自然场景数据集进行了实验。结果证明了该方法的有效性，大部分旋转和平移误差分别小于0.2度和0.5 m。此外，还通过实验验证了该方法对噪声具有鲁棒性，并且对于具有宽范围的重叠和各种几何特征的数据集具有通用性。