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2016 | OriginalPaper | Chapter

ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

Authors : Thomas Goldstein, Paul Hand, Choongbum Lee, Vladislav Voroninski, Stefano Soatto

Published in: Computer Vision – ECCV 2016

Publisher: Springer International Publishing

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Abstract

We introduce a new method for location recovery from pairwise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth.

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The standard pipeline stands in opposition to direct methods that minimize the discrepancy between the measured images and the images predicted by a forward rendering model with respect to the (infinite-dimensional) shape of the scene, which gives rise to a variational optimization problem which we do not address here.

\(p = \varOmega (f(n))\) means that there exists a universal constant C such that \(p \ge C f(n)\).

shrink\((x, \lambda ) = \text {sign}(x) \max (0,|x| - \lambda )\).

Six of these can be seen in Table 1, and two can be seen in the monopartite \(k=50\) case in the Supplemental Materials.

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Title: ShapeFit and ShapeKick for Robust, Scalable Structure from Motion
Authors: Thomas Goldstein
Paul Hand
Choongbum Lee
Vladislav Voroninski
Stefano Soatto
Publisher: Springer International Publishing
Book: Computer Vision – ECCV 2016
Print ISBN: 978-3-319-46477-0

Electronic ISBN: 978-3-319-46478-7

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-46478-7_18

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