Most Bundle Adjustment (BA) solvers like the Levenberg-Marquardt algorithm require a good initialization. Instead, initialization-free BA remains a largely uncharted territory. 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. To make such initialization-free BA approaches scalable, 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 problems 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. To our knowledge, this work is the first to address the scalability of BA without initialization opening new venues for initialization-free structure-from-motion.

翻译：大多数光束法平差（BA）求解器（如Levenberg-Marquardt算法）都需要良好的初始值。相比之下，无需初始化的BA方法仍是一个尚未充分探索的领域。目前研究较少的变量投影算法（VarPro）即使在没有初始值的情况下也展现出广阔的收敛域。结合物方误差公式，近期研究已证明其能解决小规模的无初始化光束法平差问题。为使此类无需初始化的BA方法具备可扩展性，我们提出了幂次变量投影法（PoVar），该方法基于幂级数扩展了近期的一种逆展开方法。重要的是，我们将幂级数展开与黎曼流形优化联系起来。这一投影框架对于解决无需初始化的大规模光束法平差问题至关重要。通过在真实世界的BAL数据集上进行实验，我们证明本求解器在速度和精度方面均达到了最先进水平。据我们所知，本研究首次解决了无需初始化的BA方法的可扩展性问题，为无需初始化的运动恢复结构技术开辟了新途径。