We propose a novel hierarchical approach for multiple rotation averaging, dubbed HARA. Our method incrementally initializes the rotation graph based on a hierarchy of triplet support. The key idea is to build a spanning tree by prioritizing the edges with many strong triplet supports and gradually adding those with weaker and fewer supports. This reduces the risk of adding outliers in the spanning tree. As a result, we obtain a robust initial solution that enables us to filter outliers prior to nonlinear optimization. With minimal modification, our approach can also integrate the knowledge of the number of valid 2D-2D correspondences. We perform extensive evaluations on both synthetic and real datasets, demonstrating state-of-the-art results.

We propose a novel method for estimating the global rotations of the cameras independently of their positions and the scene structure. When two calibrated cameras observe five or more of the same points, their relative rotation can be recovered independently of the translation. We extend this idea to multiple views, thereby decoupling the rotation estimation from the translation and structure estimation. Our approach provides several benefits such as complete immunity to inaccurate translations and structure, and the accuracy improvement when used with rotation averaging. We perform extensive evaluations on both synthetic and real datasets, demonstrating consistent and significant gains in accuracy when used with the state-of-the-art rotation averaging method.

In this paper, we study closed-form optimal solutions to two-view triangulation with known internal calibration and pose. By formulating the triangulation problem as L1and L∞minimization of angular reprojection errors, we derive the exact closed-form solutions that guarantee global optimality under respective cost functions. To the best of our knowledge, we are the first to present such solutions. Since the angular error is rotationally invariant, our solutions can be applied for any type of central cameras, be it perspective, fisheye or omnidirectional. Our methods also require significantly less computation than the existing optimal methods. Experimental results on synthetic and real datasets validate our theoretical derivations.