QuadSync：基于 Tucker 分解的四焦点张量同步
QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition
把四焦点张量当作可同步的高阶约束，用固定多线性秩 (4,4,4,4) 的 Tucker 分解从 n 个四焦点张量一次性恢复全部相机矩阵，为全局式 SfM 提供比本质矩阵更强的初始化与优化信号；其块张量与三焦点/双焦点张量的联合同步思路可直接替换现有增量式或成对同步流程中的相机位姿求解环节。
原文依据 We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论在运动恢复结构中，四焦点张量比其成对对应物（本质矩阵）携带更多信息，然而它们常被认为不实用、仅具理论意义。本文挑战这一看法，提出一个新框架，从相应的四焦点张量集合中恢复 n 个相机。我们构造块四焦点张量，并证明其具有 Tucker 分解，其因子矩阵即为堆叠的相机矩阵，因而其多线性秩为 (4,4,4,4)，与 n 无关。我们利用 Tucker 分解、交替方向乘子法与迭代重加权最小二乘，提出了首个四焦点张量同步算法。我们进一步建立块四焦点张量、三焦点张量与双焦点张量之间的关系，并引入一个联合同步这三类实体的算法。数值实验在现代数据集上验证了所提方法的有效性，表明在同步中使用高阶信息的潜力与重要性。
英文原文摘要 1106 字符
In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover n cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,4,4,4) independent of n. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.