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2016 | OriginalPaper | Buchkapitel

Symmetric Non-rigid Structure from Motion for Category-Specific Object Structure Estimation

verfasst von : Yuan Gao, Alan L. Yuille

Erschienen in: Computer Vision – ECCV 2016

Verlag: Springer International Publishing

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Abstract

Many objects, especially these made by humans, are symmetric, e.g. cars and aeroplanes. This paper addresses the estimation of 3D structures of symmetric objects from multiple images of the same object category, e.g. different cars, seen from various viewpoints. We assume that the deformation between different instances from the same object category is non-rigid and symmetric. In this paper, we extend two leading non-rigid structure from motion (SfM) algorithms to exploit symmetry constraints. We model the both methods as energy minimization, in which we also recover the missing observations caused by occlusions. In particularly, we show that by rotating the coordinate system, the energy can be decoupled into two independent terms, which still exploit symmetry, to apply matrix factorization separately on each of them for initialization. The results on the Pascal3D+ dataset show that our methods significantly improve performance over baseline methods.

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We assume symmetric deformations because our problem involves deformations from one symmetric object to another. But it also can be extended to non-symmetric deformations straightforwardly.

We set hard constraints on \(\mathbb {\bar{S}}\) and \(\mathbb {\bar{S}}^{\dag }\), i.e. replace \(\mathbb {\bar{S}}^{\dag }\) by \(\mathcal {A}_P \mathbb {\bar{S}}\) in Eq. (5), because it can be guaranteed by the Sym-RSfM initialization in our companion paper [26]. While the initialization on \(\mathbf {V}\) and \(\mathbf {V}^{\dag }\) by PCA cannot guarantee such a desirable property, thus a Language multiplier term is used for the constraint on \(\mathbf {V}\) and \(\mathbf {V}^{\dag }\) in Eq. (9).

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Titel: Symmetric Non-rigid Structure from Motion for Category-Specific Object Structure Estimation
verfasst von: Yuan Gao
Alan L. Yuille
Verlag: Springer International Publishing
Buch: Computer Vision – ECCV 2016
Print ISBN: 978-3-319-46474-9

Electronic ISBN: 978-3-319-46475-6

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-46475-6_26

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