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Register a new userHybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach
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Added by
Yu Chen
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We address rotation averaging (RA) and its application to real-world 3D reconstruction. Local optimisation based approaches are the de facto choice, though they only guarantee a local optimum. Global optimisers ensure global optimality in low noise conditions, but they are inefficient and may easily deviate under the influence of outliers or elevated noise levels. We push the envelope of rotation averaging by leveraging the advantages of a global RA method and a local RA method. Combined with a fast view graph filtering as preprocessing, the proposed hybrid approach is robust to outliers. We further apply the proposed hybrid rotation averaging approach to incremental Structure from Motion (SfM), the accuracy and robustness of SfM are both improved by adding the resulting global rotations as regularisers to bundle adjustment. Overall, we demonstrate high practicality of the proposed method as bad camera poses are effectively corrected and drift is reduced.
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A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and structure-from-motion, averaging rotations is both a non-convex and high-dimensional optimization problem. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel initialization-free primal-dual method which we show empirically to converge to the global optimum. Further, we derive what is to our knowledge, the first optimal closed-form solution for rotation averaging in cycle graphs and contextualize this result within spectral graph theory. Our proposed methods achieve a significant gain both in precision and performance.
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We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems with restarting mechanisms. From this family of dynamics, we synthesize four fast algorithms for the solution of convex, strongly convex, constrained, and unconstrained optimization problems. In each case, we establish robust semi-global practical asymptotic or exponential stability results, and we show how to obtain well-posed discretized algorithms that retain the main properties of the original dynamics. Given that existing averaging theorems for singularly perturbed hybrid systems are not directly applicable to our setting, we derive a new averaging theorem that relaxes some of the assumptions made in the literature, allowing us to make a clear link between the KL bounds that characterize the rates of convergence of the hybrid dynamics and their average dynamics. We also show that our results are applicable to non-hybrid algorithms, thus providing a general framework for accelerated dynamics based on averaging theory. We present different numerical examples to illustrate our results.
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