用凸优化实现高效全局三维重建，无需初始猜测。
Building Rome with Convex Optimization
- 将2D关键点通过学习深度升维至3D，构建可全局最优的凸优化模型。
- 在大规模数据上实现可验证的全局最优解，速度比现有方法快数倍。
- 无需初始化，适合海量图像重建，尤其适合自动化场景建模。
我们提出一种缩放后的捆绑调整（SBA）公式，通过学习到的深度将2D关键点测量值提升为3D坐标；设计了一个经验上紧致的凸半定规划（SDP）松弛，可保证求解SBA达到可验证的全局最优；采用Burer-Monteiro分解与基于CUDA的信赖域黎曼优化器（名为XM），实现了对超大规模SDP松弛的高效求解；以XM作为优化引擎构建了结构光从运动（SfM）流程，结果表明XM-SfM在重建质量上优于现有方法，同时显著更快、更可扩展且无需初始化。
原文摘要 · Abstract (English)
Global bundle adjustment is made easy by depth prediction and convex optimization. We (i) propose a scaled bundle adjustment (SBA) formulation that lifts 2D keypoint measurements to 3D with learned depth, (ii) design an empirically tight convex semidfinite program (SDP) relaxation that solves SBA to certfiable global optimality, (iii) solve the SDP relaxations at extreme scale with Burer-Monteiro factorization and a CUDA-based trust-region Riemannian optimizer (dubbed XM), (iv) build a structure from motion (SfM) pipeline with XM as the optimization engine and show that XM-SfM compares favorably with existing pipelines in terms of reconstruction quality while being significantly faster, more scalable, and initialization-free.
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