Initialization-free bundle adjustment (BA) remains largely uncharted. While
Levenberg-Marquardt algorithm is the golden method to solve the BA problem, it
generally relies on a good initialization. In contrast, the under-explored
Variable Projection algorithm (VarPro) exhibits a wide convergence basin even
without initialization. Coupled with object space error formulation, recent
works have shown its ability to solve (small-scale) initialization-free bundle
adjustment problem. We introduce Power Variable Projection (PoVar), extending a
recent inverse expansion method based on power series. Importantly, we link the
power series expansion to Riemannian manifold optimization. This projective
framework is crucial to solve large-scale bundle adjustment problem without
initialization. Using the real-world BAL dataset, we experimentally demonstrate
that our solver achieves state-of-the-art results in terms of speed and
accuracy. In particular, our work is the first, to our knowledge, that
addresses the scalability of BA without initialization and opens new venues for
initialization-free Structure-from-Motion.

基于初始化的无初始化捆绑调整问题的求解方法相对较少，与 Levenberg-Marquardt 算法相比，未充分探索的 Variable Projection 算法展现了宽广的收敛区域，结合对象空间误差构建，最近的研究已经展示了其无初始化捆绑调整问题求解的能力，本研究引入了基于幂级数的反转扩展方法来扩展 Power Variable Projection，将幂级数扩展与 Riemannian 流形优化相连，这一投影框架对于无初始化的大规模捆绑调整问题求解至关重要，实验证明，使用真实世界的 BAL 数据集，我们的求解器在速度和准确度方面达到了最先进的结果，特别地，我们的工作是首次解决了无初始化 BA 的可扩展性，并为无初始化的结构运动打开了新的研究方向。