Yunpeng Shi

Shaohan Li, Yunpeng Shi, Gilad Lerman

Group synchronization plays a crucial role in global pipelines for Structure from Motion (SfM). Its formulation is nonconvex and it is faced with highly corrupted measurements. Cycle consistency has been effective in addressing these challenges. However, computationally efficient solutions are needed for cycles longer than three, especially in practical scenarios where 3-cycles are unavailable. To overcome this computational bottleneck, we propose an algorithm for group synchronization that leverages information from cycles of lengths ranging from three to six with a time complexity of order $O(n^3)$ (or $O(n^{2.373})$ when using a faster matrix multiplication algorithm). We establish non-trivial theory for this and related methods that achieves competitive sample complexity, assuming the uniform corruption model. To advocate the practical need for our method, we consider distributed group synchronization, which requires at least 4-cycles, and we illustrate state-of-the-art performance by our method in this context.

Zhekai Fan, Wanze Li, Jinxin Wang et al.

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.

Francisco Chen, Yiran Wang, Yunpeng Shi

Pairwise translation directions are a key input to camera location estimation in global structure-from-motion. Existing estimators usually process each image pair independently, producing directions that may be locally plausible but inconsistent with the other relative directions in the viewing graph. To jointly estimate the direction, we propose TriDE, which exploits camera-triangle consistency as an efficient higher-order verification signal. Instead of solving a costly global nonlinear optimization problem that is sensitive to initialization, TriDE refines unreliable pairwise directions through message passing between directions and their incident weighted triangles. This information propagation strategy enables us to establish a strong phase-transition bound for exact recovery under a realistic random corruption model. Experiments on real image graphs show that TriDE improves direction accuracy by a large margin and yields better downstream camera locations, providing a practical link between local pairwise estimation and global camera pose geometry.

Yunpeng Shi, Shaohan Li, Tyler Maunu et al.

We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline. The statistics are based on consistency constraints that arise within the clustered structure of the graph of keypoint matches. The statistics are designed to give smaller values to corrupted matches and than uncorrupted matches. These new statistics are combined with an iterative reweighting scheme to filter keypoints, which can then be fed into any standard structure from motion pipeline. This filtering method can be efficiently implemented and scaled to massive datasets as it only requires sparse matrix multiplication. We demonstrate the efficacy of this method on synthetic and real structure from motion datasets and show that it achieves state-of-the-art accuracy and speed in these tasks.

Yunpeng Shi, Gilad Lerman

We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization. We first describe our recent theoretically guaranteed message passing algorithm that estimates the corruption levels of the measured group ratios. We then propose a novel reweighted least squares method to estimate the group elements, where the weights are initialized and iteratively updated using the estimated corruption levels. We demonstrate the superior performance of our algorithm over state-of-the-art methods for rotation synchronization using both synthetic and real data.

Yunpeng Shi, Shaohan Li, Gilad Lerman

We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares procedure. In view of these limitations, we suggest a novel and more reliable iterative reweighting strategy that incorporates information from higher-order neighborhoods by exploiting the graph connection Laplacian. We demonstrate the superior performance of our procedure over state-of-the-art methods using both synthetic and real datasets.

Gilad Lerman, Yunpeng Shi

We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently solve the synchronization problem in our setting. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. These guarantees hold as long as the ratio of corrupted cycles per edge is bounded by a reasonable constant. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further establish exact recovery with high probability under a common uniform corruption model.

Gilad Lerman, Yunpeng Shi, Teng Zhang

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Ozyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee was established for the ShapeFit algorithm by Hand, Lee and Voroninski, but with typically less corruption.