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Register a new userRotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs
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Added by
Gabriel Moreira
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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 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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