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International Journal of Computer Vision

Erschienen in:

01.05.2016

Complex Non-rigid 3D Shape Recovery Using a Procrustean Normal Distribution Mixture Model

verfasst von: Jungchan Cho, Minsik Lee, Songhwai Oh

Erschienen in: International Journal of Computer Vision | Ausgabe 3/2016

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Abstract

Recovering the 3D shape of a non-rigid object is a challenging problem. Existing methods make the low-rank assumption and do not scale well with the increased degree of freedom found in complex non-rigid deformations or shape variations. Moreover, in general, the degree of freedom of deformation is assumed to be known in advance, which limits the applicability of non-rigid structure from motion algorithms in a practical situation. In this paper, we propose a method for handling complex shape variations based on the assumption that complex shape variations can be represented probabilistically by a mixture of primitive shape variations. The proposed model is a generative probabilistic model, called a Procrustean normal distribution mixture model, which can model complex shape variations without rank constraints. Experimental results show that the proposed method significantly outperforms existing methods.

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http://mocap.cs.cmu.edu/subjects.php.

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In this paper, we use \({\mathbf {0}}\) to denote both matrices and vectors of zeros.

Let \({\mathbf {R}}_i^f\) be a rotation matrix obtained from the factorization method. Then \({\mathbf {R}}_i\) in (32) is a transpose of \({\mathbf {R}}^f\).

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Naming convention: \(p \langle n \rangle \_\langle a \rangle \_\langle k \rangle \), where n is the number of persons, a is the action type, and k is the take number.

The maximum number of shape basis vectors is limited up to \(\lfloor \frac{15}{3}\rfloor \) for 15 landmarks (Gotardo and Martinez 2011).

In this table, we denote six sequences as only action types.

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The viewpoint of each video sequence is assigned to one of four coarse camera viewpoints, i.e., front, back, left, and right.

We select a more plausible result between the reconstructed 3D shape and its depth inverted version to remove the sign ambiguity. Also, we made two virtual 3D landmarks of a torso, i.e., upper body and lower body, for the purpose of visualization, since the Penn Action dataset does not give torso landmark positions.

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Titel: Complex Non-rigid 3D Shape Recovery Using a Procrustean Normal Distribution Mixture Model
verfasst von: Jungchan Cho
Minsik Lee
Songhwai Oh
Publikationsdatum: 01.05.2016
Verlag: Springer US
Erschienen in: International Journal of Computer Vision / Ausgabe 3/2016
Print ISSN: 0920-5691
Elektronische ISSN: 1573-1405
DOI: https://doi.org/10.1007/s11263-015-0860-7

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