Résumé: 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

Langue: Anglais