Robust Camera Location Estimation by Convex Programming

TL;DR

This paper introduces a robust convex programming approach for estimating camera locations from noisy and outlier-corrupted pairwise direction measurements, improving accuracy in large, irregular image collections.

Contribution

It provides a complete characterization of well-posed location estimation problems and proposes a novel two-step robust method combining direction estimation and convex optimization.

Findings

Convex formulation can recover locations exactly with partially corrupted data.

Method demonstrates robustness to outliers in direction measurements.

Experiments on Internet photo collections validate effectiveness.

Abstract

$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation part, which can be formulated as the inverse problem of estimating $n$ locations $\mathbf{t}_1, \mathbf{t}_2, \ldots, \mathbf{t}_n$ in $\mathbb{R}^3$ from noisy measurements of a subset of the pairwise directions $\frac{\mathbf{t}_i - \mathbf{t}_j}{\|\mathbf{t}_i - \mathbf{t}_j\|}$, are sensitive to outliers in direction measurements. In this paper, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by presenting its relation to the existing theory of parallel rigidity. For robust estimation of camera locations, we introduce a two-step approach, comprised of a pairwise direction estimation method robust to outliers in point correspondences between image pairs, and a convex program to maintain robustness to outlier directions. In the presence of partially corrupted measurements, we empirically demonstrate that our convex formulation can even recover the locations exactly. Lastly, we demonstrate the utility of our formulations through experiments on Internet photo collections.