Robustness in Motion Averaging

A Pose-Only Solution to Visual Reconstruction and Navigation

Visual navigation and three-dimensional (3D) scene reconstruction are essential for robotics to interact with the surrounding environment. Large-scale scenarios and computational robustness are great challenges facing the research community to achieve this goal. This paper raises a pose-only imaging geometry representation and algorithms that might help solve these challenges. The pose-only representation, equivalent to the classical multiple-view geometry, is discovered to be linearly related to camera global translations, which allows for efficient and robust camera motion estimation. As a result, the spatial feature coordinates can be analytically reconstructed and do not require nonlinear optimization. Comprehensive experiments demonstrate that the computational efficiency of recovering the scene and associated camera poses is significantly improved by 2-4 orders of magnitude.

Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that outperforms general purpose numerical solvers by a large margin and compares favourably to current state-of-the-art. Further, our approach is able to handle the large problem instances commonly occurring in structure from motion settings and it is trivially parallelizable. Experiments are presented for a number of different instances of both synthetic and real-world data.

Robust Relative Rotation Averaging

This paper addresses the problem of robust and efficient relative rotation averaging in the context of large-scale Structure from Motion. Relative rotation averaging finds global or absolute rotations for a set of cameras from a set of observed relative rotations between pairs of cameras. We propose a generalized framework of relative rotation averaging that can use different robust loss functions and jointly optimizes for all the unknown camera rotations. Our method uses a quasi-Newton optimization which results in an efficient iteratively reweighted least squares (IRLS) formulation that works in the Lie algebra of the 3D rotation group. We demonstrate the performance of our approach on a number of large-scale data sets. We show that our method outperforms existing methods in the literature both in terms of speed and accuracy.