Stable and Scalable Bundle Adjustment of Holistic 3D Structures

Abstract

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.