让3D重建同时优化复杂几何关系,速度不降反而更准。
Stable and Scalable Bundle Adjustment of Holistic 3D Structures

- 用2D投影误差统一建模点、线及平行共面等高级关系
- 在真实和合成数据上达到与传统方法相当的运行速度
- 适合需要高精度3D结构的视觉重建任务
Bundle Adjustment(BA)是三维计算机视觉的核心,历经数十年发展,在稀疏优化与数值方法方面持续进步。它最初用于联合优化相机内参、位姿和稀疏3D点。尽管后续扩展纳入了直线等几何基元,但引入平行、共面或线框等更丰富的几何结构时,常导致计算成本剧增且数值稳定性下降。本文提出一个统一框架,将BA扩展为同时优化几何特征与高阶关系。我们首先建立分类体系:区分具有直接2D测量值的可扩展几何特征(如点、线),以及编码高阶关系的组(如共面、平行)。我们证明这些组可作为相机类实体嵌入BA框架。基于此,我们提出组约束与跨特征关联(如点-线关联)均可通过2D重投影误差表达。通过构建组诱导与跨特征重投影误差,我们在施尔消元下保持经典点式BA的稀疏性,同时避免直接3D正则化带来的条件恶化与不稳定性。在真实与合成数据集上的实验表明,该方法运行时间与仅点式BA相当,却能生成显著更丰富的3D结构并提升几何精度。
原文摘要 · Abstract (English)
Bundle Adjustment (BA) is a cornerstone of 3D computer vision and has benefited from decades of advances in sparse optimization and numerical methods. It was originally developed for jointly optimizing camera intrinsics, poses and sparse 3D points. While extensions incorporate lines and other primitives, integrating richer geometric structures such as parallelism, coplanarity, or wireframes often introduces significantly increased computational cost and reduced numerical stability. In this paper, we propose a unified framework that extends bundle adjustment to jointly optimize geometric features and higher-order relations. We first introduce a taxonomy that distinguishes scalable geometric features with direct 2D measurements (e.g., points and lines), from groups encoding higher-order relations (e.g., coplanarity, parallelism, etc.), where we show that groups can be modeled as camera-like entities within the bundle adjustment framework. Building on this formulation, we propose that both group constraints and cross-feature relations (i.e., point-line associations) can be expressed through 2D reprojection measurements. By formulating group-induced and cross-feature reprojection errors, we preserve the sparsity structure of classical point-based BA under Schur elimination, while avoiding direct 3D regularization that degrades the conditioning and stability. Experiments on both real-world and synthetic datasets demonstrate runtime performance comparable to classical point-only bundle adjustment, while producing significantly richer 3D structures and improved geometric accuracy.
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