TriP: A Triangle Puzzle Approach to Robust Translation Averaging
This work addresses the ill-conditioned and corruption-sensitive problem of translation averaging in global Structure-from-Motion, offering a robust, scalable, and theoretically grounded solution.
TriP introduces a triangle-based framework for translation averaging that recovers camera locations from pairwise relative translations by inferring local edge scales from triangle geometry and synchronizing them in the logarithmic domain. It achieves state-of-the-art robustness to structured corruptions and outperforms previous methods by a large margin on synthetic and real datasets.
Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain no distance information, making the estimation problem highly ill-conditioned and highly sensitive to corrupted observations. In this paper, we propose TriP, a triangle-based framework for robust translation averaging. TriP first infers local relative edge scales from triangle geometry, and then synchronizes the scales of overlapping triangles in the logarithmic domain to recover globally consistent edge lengths and camera locations. By leveraging higher-order consistency across triangles, the proposed method is robust to adversarial, cycle-consistent, and other structured corruptions. In addition, TriP avoids the collapse issue without requiring any extra anti-collapse constraints, since log-scale synchronization excludes the degenerate zero-scale solution by construction. These structural advantages enable a particularly strong theory for exact location recovery. On the practical side, TriP is fully parallelizable, computationally efficient, and naturally scalable to graphs with millions of cameras. Moreover, it outperforms all previous translation averaging methods by a large margin on both synthetic and real datasets.