Depth Descent Synchronization in SO(D)

Tyler Maunu; Gilad Lerman

doi:10.1007/s11263-022-01686-6

Depth Descent Synchronization in SO(D)

Tyler Maunu
, Gilad Lerman

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We give robust recovery results for synchronization on the rotation group, SO(D). In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We develop a novel algorithm that exploits Tukey depth in the tangent space of SO(D). This algorithm, called Depth Descent Synchronization, exactly recovers the underlying rotations up to an outlier percentage of 1 / (D(D- 1) + 2) , which corresponds to 1/4 for SO(2) and 1/8 for SO(3). In the case of SO(2), we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We implement this algorithm for the case of SO(3) and demonstrate that it performs competitively on baseline synthetic data.

Original language	English (US)
Pages (from-to)	968-986
Number of pages	19
Journal	International Journal of Computer Vision
Volume	131
Issue number	4
DOIs	https://doi.org/10.1007/s11263-022-01686-6
State	Published - Apr 2023

Bibliographical note

Funding Information:
Gilad Lerman was supported by NSF awards DMS-1821266 and DMS-2152766.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Multiple rotation averaging
Nonconvex optimization
Robust synchronization
Structure from motion

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10.1007/s11263-022-01686-6

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title = "Depth Descent Synchronization in SO(D)",

abstract = "We give robust recovery results for synchronization on the rotation group, SO(D). In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We develop a novel algorithm that exploits Tukey depth in the tangent space of SO(D). This algorithm, called Depth Descent Synchronization, exactly recovers the underlying rotations up to an outlier percentage of 1 / (D(D- 1) + 2) , which corresponds to 1/4 for SO(2) and 1/8 for SO(3). In the case of SO(2), we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We implement this algorithm for the case of SO(3) and demonstrate that it performs competitively on baseline synthetic data.",

keywords = "Multiple rotation averaging, Nonconvex optimization, Robust synchronization, Structure from motion",

author = "Tyler Maunu and Gilad Lerman",

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N2 - We give robust recovery results for synchronization on the rotation group, SO(D). In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We develop a novel algorithm that exploits Tukey depth in the tangent space of SO(D). This algorithm, called Depth Descent Synchronization, exactly recovers the underlying rotations up to an outlier percentage of 1 / (D(D- 1) + 2) , which corresponds to 1/4 for SO(2) and 1/8 for SO(3). In the case of SO(2), we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We implement this algorithm for the case of SO(3) and demonstrate that it performs competitively on baseline synthetic data.

AB - We give robust recovery results for synchronization on the rotation group, SO(D). In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We develop a novel algorithm that exploits Tukey depth in the tangent space of SO(D). This algorithm, called Depth Descent Synchronization, exactly recovers the underlying rotations up to an outlier percentage of 1 / (D(D- 1) + 2) , which corresponds to 1/4 for SO(2) and 1/8 for SO(3). In the case of SO(2), we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We implement this algorithm for the case of SO(3) and demonstrate that it performs competitively on baseline synthetic data.

KW - Multiple rotation averaging

KW - Nonconvex optimization

KW - Robust synchronization

KW - Structure from motion

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Depth Descent Synchronization in SO(D)

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