Exact Camera Location Recovery by Least Unsquared Deviations

TL;DR

This paper proves that the Least Unsquared Deviations (LUD) algorithm can exactly recover camera locations in a probabilistic model even with significant corruption, extending previous guarantees for similar algorithms.

Contribution

It establishes the first exact recovery guarantees for the LUD algorithm under a probabilistic model with high corruption levels.

Findings

LUD algorithm achieves exact recovery with high probability.

Recovery is possible even with substantial data corruption.

The results extend previous guarantees for similar algorithms like ShapeFit.

Abstract

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Ozyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee was established for the ShapeFit algorithm by Hand, Lee and Voroninski, but with typically less corruption.