Semidefinite Relaxations for Robust Multiview Triangulation

TL;DR

This paper introduces convex relaxation methods for robust multiview triangulation, enabling certifiably optimal 3D reconstructions even with high noise and many outliers.

Contribution

It extends existing relaxation techniques by incorporating a truncated least squares cost, offering two formulations with different trade-offs in complexity and robustness.

Findings

Methods achieve provably optimal reconstructions under high noise.

Approaches remain tight and effective with large outlier percentages.

Two formulations provide options for different computational needs.

Abstract

We propose an approach based on convex relaxations for certifiably optimal robust multiview triangulation. To this end, we extend existing relaxation approaches to non-robust multiview triangulation by incorporating a truncated least squares cost function. We propose two formulations, one based on epipolar constraints and one based on fractional reprojection constraints. The first is lower dimensional and remains tight under moderate noise and outlier levels, while the second is higher dimensional and therefore slower but remains tight even under extreme noise and outlier levels. We demonstrate through extensive experiments that the proposed approaches allow us to compute provably optimal reconstructions even under significant noise and a large percentage of outliers.