In this paper we address the problem of robust and efficient averaging of relative 3D rotations. Apart from having an interesting geometric structure, robust rotation averaging addresses the need for a good initialization for largescale optimization used in structure-from-motion pipelines. Such pipelines often use unstructured image datasets harvested from the internet thereby requiring an initialization method that is robust to outliers. Our approach works on the Lie group structure of 3D rotations and solves the problem of large-scale robust rotation averaging in two ways. Firstly, we use modern 1 optimizers to carry out robust averaging of relative rotations that is efficient, scalable and robust to outliers. In addition, we also develop a twostep method that uses the 1 solution as an initialisation for an iteratively reweighted least squares (IRLS) approach. These methods achieve excellent results on large-scale, real world datasets and significantly outperform existing methods, i.e. the state-of-the-art discrete-continuous optimization method of [3] as well as the Weiszfeld method of [8]. We demonstrate the efficacy of our method on two largescale real world datasets and also provide the results of the two aforementioned methods for comparison.

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While motion estimation has been extensively studied in the computer vision literature, the inherent information redundancy in an image sequence has not been well utilised. In particular as many as

While spectral clustering has been applied successfully to problems in computer vision, their applicability is limited to pairwise similarity measures that form a probability matrix. However many geometric problems with parametric forms require more than two observations to estimate a similarity measure, e.g. epipolar geometry. In such cases we can only define the probability of belonging to the same cluster for an n-tuple of points and not just a pair, leading to an n-dimensional probability tensor. However spectral clustering methods are not available for tensors. In this paper we present an algorithm to infer a similarity matrix by decomposing the n-dimensional probability tensor. Our method exploits the super-symmetry of the probability tensor to provide a randomised scheme that does not require the explicit computation of the probability tensor. Our approach is fast and accurate and its applicability is illustrated on two significant problems, namely perceptually salient geometric grouping and parametric motion segmentation (like affine, epipolar etc.

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.