# HiGoReg: A Hierarchical Grouping Strategy for Point Cloud Registration
## 1 Introduction  
Owing to its exceptional efficiency and precision in data acquisition, point cloud data obtained through three-dimensional (3D) laser scanners has found widespread application across various domains, including autonomous driving [1], deformation monitoring [2], industrial inspection [3], and 3D reconstruction [4]. Despite notable progress in acquisition techniques, the massive volume of collected data presents ongoing challenges for point cloud registration (PCR), particularly in terms of computational efficiency and parameter estimation accuracy [5, 6, 7, 8, 9]. PCR arises from the inherent limitation whereby a single scan typically fails to capture complete information about a target object or scene. To obtain a comprehensive representation, multiple point clouds acquired from different viewpoints, at different times, or using different sensors may be integrated. The primary goal of PCR is to spatially align these datasets by estimating a six-degree-of-freedom (6-DOF) transformation between the source and target point clouds. Considerable efforts have been devoted to designing PCR approaches that jointly address efficiency, reliability, and structural integrity [10, 11]. One fundamental approach to this problem is the reduction of data volume while retaining essential geometric and structural features. Recently, adaptive downsampling strategies have been investigatedin this regard. For instance, [PERSON] et al. [12] introduced the Box Improved Moving Average (BIMA) method, which dynamically adjusts the downsampling window size based on local point density variations, enabling efficient and adaptive data simplification. Complementing this, [PERSON] et al. [13] proposed a dynamic voxel-filtering algorithm that integrates edge-aware mechanisms to preserve salient structural details during the downsampling process, thereby maintaining the fidelity of critical geometric features. In addition to data simplification, efficient and robust feature extraction methods are paramount for reducing the computational burden during registration. Contemporary advances in feature extraction for PCR fall into two main strategies. The first leverages geometric projections to utilize structural regularities within 3D data. For example, [PERSON] et al. [14] projected point clouds onto a horizontal plane, extracting precise feature points at structural line intersections. This reduced the problem to 2D transformation estimation, which was later combined with vertical displacement to restore full 3D alignment, effectively lowering computational complexity while maintaining accuracy. The second strategy emphasizes robust descriptor design to capture salient, scale-invariant features in 3D space. [PERSON] et al. [15] applied 3D Scale-Invariant Feature Transform (3D-SIFT) descriptors, which ensured scale robustness and reduced the number of points involved in registration without sacrificing precision. To accelerate feature-matching, histogram-based descriptors have gained widespread adoption. [PERSON] et al. [16] presented a novel 3D Binary Shape Context (BSC) descriptor that encodes local surface geometry through binary spatial histograms, optimizing parameter settings to balance descriptiveness and efficiency. The Fast Point Feature Histogram (FPFH) method introduced by [PERSON] et al. [17] significantly reduces computational complexity by computing Simplified Point Feature Histograms (SPFHs) within local neighborhoods and applying weighted fusion, bringing the complexity down to \(\mathcal{O}(nk)\). Building on this foundation, [PERSON] et al. [18] enhanced the approach by employing k-kernel based graph-theoretic pruning techniques to efficiently reject outlier correspondences, thereby improving both robustness and speed. Furthermore, [PERSON] et al. [19] applied a graph-based correspondence optimization strategy that assessed the reliability of correspondence graphs by integrating both loose and compact constraint functions.