$3$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.

本文提出了一种对于相机姿态和方向估计的新方法，结合了对偏差方向的强鲁棒性和凸优化技术，有效地从二维图像集合中恢复三维结构。