Non-sequential structure from motion

Abstract

Prior work on multi-view structure from motion is dominated by sequential approaches starting from a single twoview reconstruction, then adding new images one by one. In contrast, we propose a non-sequential methodology based on rotational consistency and robust estimation using convex optimization. The resulting system is more robust with respect to (i) unreliable two-view estimations caused by short baselines, (ii) repetitive scenes with locally consistent structures that are not consistent with the global geometry and (iii) loop closing as errors are not propagated in a sequential manner. Both theoretical justifications and experimental comparisons are given to support these claims.

Robust Global Motion Estimation with Matrix Completion

“…A fraction of the available relative rotations is drawn uniformly from SO(3), simulating outliers. The probability that a given relative rotation is an outlier is inversely proportional to the number of corresponding points of the pair, which is consistent with the assumptions made in (Enqvist et al, 2011).…”

“…The authors of (Enqvist et al, 2011) consider a maximum-weight spanning tree, where the weights are the numbers of inlier correspondences, and they analyze cycles formed by the remaining edges. A cycle is kept if the cycle error, normalized by the factor 1/ √ l, where l is the cycle length, is small enough; otherwise the non-tree edge is removed.…”

“…If the cycle error is greater than the threshold, then the cycle must contain at least one inconsistent rotation. To detect such outliers, we improve the algorithm described in (Enqvist et al, 2011).…”

“…(Crosilla and Beinat, 2002)), where first stereo-models are built and co-registered, structure-and-motion methods, such as bundle block adjustment (e.g. (Triggs et al, 2000)), resection-intersection methods (Brown andLowe, 2005, Snavely et al, 2006), hierarchical methods (Gherardi et al, 2010, Ni andDellaert, 2012)), where "structure" and "motion" are solved simultaneously, and -more recently -motion-first methods (Govindu, 2001, Martinec and Pajdla, 2007, Kahl and Hartley, 2008, Enqvist et al, 2011, ArieNachimson et al, 2012, Moulon et al, 2013) that first solve for the "motion" and then recover the "structure". All these motionfirst methods are global, for they take into account the whole epipolar graph, whose nodes represent the views and edges link views having consistent matching points.…”

“…by repetitive structures in the scene. To this end, we improve an algorithm based on the notion of cycle consistency (Enqvist et al, 2011) by introducing cycle bases. * Corresponding author In order to estimate the angular attitudes of the cameras, we formulate a gradient descent algorithm based on low-rank matrix completion, that naturally copes with the case of missing data, very frequent in practice, in which the epipolar graph is hardly complete.…”