This study investigates the impact of the invariance of feature vectors for partial-to-partial point set registration under translation and rotation of input point sets, particularly in the realm of techniques based on deep learning and Gaussian mixture models (GMMs). We reveal both theoretical and practical problems associated with such deep-learning-based registration methods using GMMs, with a particular focus on the limitations of DeepGMR, a pioneering study in this line, to the partial-to-partial point set registration. Our primary goal is to uncover the causes behind such methods and propose a comprehensible solution for that. To address this, we introduce an attention-based reference point shifting (ARPS) layer, which robustly identifies a common reference point of two partial point sets, thereby acquiring transformation-invariant features. The ARPS layer employs a well-studied attention module to find a common reference point rather than the overlap region. Owing to this, it significantly enhances the performance of DeepGMR and its recent variant, UGMMReg. Furthermore, these extension models outperform even prior deep learning methods using attention blocks and Transformer to extract the overlap region or common reference points. We believe these findings provide deeper insights into registration methods using deep learning and GMMs.

翻译：本研究探讨了在平移和旋转输入点云时，特征向量不变性对部分到部分点云配准的影响，特别是在基于深度学习和高斯混合模型（GMM）的技术领域。我们揭示了此类基于深度学习的GMM配准方法在理论和实践中的问题，尤其关注了该领域的开创性工作DeepGMR在部分到部分点云配准中的局限性。我们的主要目标是揭示此类方法失效的根本原因，并提出一种可解释的解决方案。为此，我们引入了一种基于注意力的参考点移位（ARPS）层，该层能够鲁棒地识别两个部分点云的公共参考点，从而获取变换不变特征。ARPS层利用成熟的注意力模块来寻找公共参考点，而非重叠区域。因此，它显著提升了DeepGMR及其最新变体UGMMReg的性能。此外，这些扩展模型甚至优于先前使用注意力模块和Transformer提取重叠区域或公共参考点的深度学习方法。我们相信这些发现为基于深度学习和GMM的配准方法提供了更深入的理解。