用流匹配方法实现点云拼接，能高效处理无重叠碎片。
Equivariant Flow Matching for Point Cloud Assembly
- 基于流匹配学习等变向量场，实现点云对齐。
- 在非重叠输入下仍可完成高质量拼接，数据效率高。
- 适合3D重建、几何恢复等需要精准拼接的场景。
点云拼接的目标是通过对齐多个点云片段来重建完整的3D形状。本文提出一种基于流匹配模型的新颖等变求解器。理论上证明，通过学习相关向量场可实现等变分布的学习。据此提出等变扩散拼接（Eda）模型，其条件化于输入片段以学习相关向量场，并构建等变路径以保障训练过程的高数据效率。数值实验表明，Eda在实际数据集上表现优异，甚至能在输入片段无重叠的挑战性情况下完成拼接。
原文摘要 · Abstract (English)
The goal of point cloud assembly is to reconstruct a complete 3D shape by aligning multiple point cloud pieces. This work presents a novel equivariant solver for assembly tasks based on flow matching models. We first theoretically show that the key to learning equivariant distributions via flow matching is to learn related vector fields. Based on this result, we propose an assembly model, called equivariant diffusion assembly (Eda), which learns related vector fields conditioned on the input pieces. We further construct an equivariant path for Eda, which guarantees high data efficiency of the training process. Our numerical results show that Eda is highly competitive on practical datasets, and it can even handle the challenging situation where the input pieces are non-overlapped.
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