Depth Descent Synchronization in $${{\,\mathrm{\text {SO}}\,}}(D)
We give robust recovery results for synchronization on the rotation group, [Formula omitted]. 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...
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| Published in: | International journal of computer vision Vol. 131; no. 4; pp. 968 - 986 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Springer
01.04.2023
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| Subjects: | |
| ISSN: | 0920-5691, 1573-1405 |
| Online Access: | Get full text |
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| Summary: | We give robust recovery results for synchronization on the rotation group, [Formula omitted]. 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 [Formula omitted]. This algorithm, called Depth Descent Synchronization, exactly recovers the underlying rotations up to an outlier percentage of [Formula omitted], which corresponds to 1/4 for [Formula omitted] and 1/8 for [Formula omitted]. In the case of [Formula omitted], we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We implement this algorithm for the case of [Formula omitted] and demonstrate that it performs competitively on baseline synthetic data. |
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| ISSN: | 0920-5691 1573-1405 |
| DOI: | 10.1007/s11263-022-01686-6 |