# HiGoReg: A Hierarchical Grouping Strategy for Point Cloud Registration
## 1 Introduction
Furthermore, some methods enhanced registration accuracy by imposing constraint conditions based on known prior information of parameters based on the GH model [38]. Beyond the aforementioned efforts, researchers have further investigated the enhancement of parameter estimation accuracy through diverse approaches, such as feature extraction [39; 40], geometric representation [41; 42], matching strategies [43; 44; 45], and the integration of physical attributes [46; 47]. Invariably, the above methods adopt a batch estimation framework that incorporates all features simultaneously into the mathematical model. This results in a computational complexity of \(\mathcal{O}(n^{3})\), limiting scalability in large-scale scenarios. For the specific details, refer to the contents in Table 1. High-performance computing platforms can partially alleviate this burden [48; 49], but they come with trade-offs such as higher deployment costs, increased energy consumption, and greater system complexity. More importantly, such hardware-based solutions do not reduce the algorithm's intrinsic complexity, they merely offset it through brute-force computation. Therefore, beyond optimizing peripheral components, it is essential to rethink the core structure of registration algorithms to achieve true scalability. Recently, deep learning-based PCR methods have gained considerable attention due to their high accuracy in parameter estimation and strong inference capabilities [3; 11; 55; 56; 57]. Despite these advantages, several challenges remain. These methods often exhibit sensitivity to hyperparameter tuning, require large volumes of labeled data, and struggle to generalize effectively to unseen scenarios. Moreover, they typically involve substantial computational costs and prolonged training times. Thus, while many studies boost early-stage computational efficiency, the adjustment process for registration parameter estimation stays slow, failing to break the core computational bottleneck in algorithm design. Hence, under the premise of ensuring stable and reliable results, further reducing PCR parameter estimation time remains a pressing issue. In this paper, a novel PCR methodology rooted in the hierarchical grouping framework is presented with the designation HiGoReg. Here, \"hierarchical\" emphasizes the iterative parameter estimation used to refine the progress of the source point cloud pose tuning, whereas \"grouping\" involves the systematic division of observations into groups within a single layer. Drawing inspiration from the effectiveness of Recursive Least Squares (RLS) in filtering contexts [58; 59; 60; 61; 62] and the solid performance of the GH model, our objective is to harmoniously blend their respective strengths. The proposed method not only guarantees the accuracy of the results, which is consistent with the batch solution (BS), but also significantly improves the computational time cost. Specifically, the filtered point pairs are first divided into groups by slicing. For the first group, a linearized version of the GH model is used to estimate the parameters. Subsequently, the parameter estimates and parameter cofactor matrices of the previous group, as well as the observations of the current group, are modeled together to predict new parameter values, facilitating a seamless association between groups. Since the amount of data involved in the computation of each group