A Survey of Structure from Motion

The structure from motion (SfM) problem in computer vision is the problem of recovering the three-dimensional ($3$D) structure of a stationary scene from a set of projective measurements, represented as a collection of two-dimensional ($2$D) images, via estimation of motion of the cameras corresponding to these images. In essence, SfM involves the three main stages of (1) extraction of features in images (e.g., points of interest, lines, etc.) and matching these features between images, (2) camera motion estimation (e.g., using relative pairwise camera positions estimated from the extracted features), and (3) recovery of the $3$D structure using the estimated motion and features (e.g., by minimizing the so-called reprojection error). This survey mainly focuses on relatively recent developments in the literature pertaining to stages (2) and (3). More specifically, after touching upon the early factorization-based techniques for motion and structure estimation, we provide a detailed account of some of the recent camera location estimation methods in the literature, followed by discussion of notable techniques for $3$D structure recovery. We also cover the basics of the simultaneous localization and mapping (SLAM) problem, which can be viewed as a specific case of the SfM problem. Further, our survey includes a review of the fundamentals of feature extraction and matching (i.e., stage (1) above), various recent methods for handling ambiguities in $3$D scenes, SfM techniques involving relatively uncommon camera models and image features, and popular sources of data and SfM software.