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Abstract

This paper studies the problem of 3D non-rigid shape and motion recovery from a monocular video sequence, under the degenerate deformations. The shape of a deformable object is regarded as a linear combination of certain shape bases. When the bases are non-degenerate, i.e. of full rank 3, a closed-form solution exists by enforcing linear constraints on both the camera rotation and the shape bases [18]. In practice, degenerate deformations occur often, i.e. some bases are of rank 1 or 2. For example, cars moving or pedestrians walking independently on a straight road refer to rank-1 deformations of the scene. This paper quantitatively shows that, when the shape is composed of only rank-3 and rank-1 bases, i.e. the 3D points either are static or independently move along straight lines, the linear rotation and basis constraints are sufficient to achieve a unique solution. When the shape bases contain rank-2 ones, imposing only the linear constraints results in an ambiguous solution space. In such cases, we propose an alternating linear approach that imposes the positive semi-definite constraint to determine the desired solution in the solution space. The performance of the approach is evaluated quantitatively on synthetic data and qualitatively on real videos.

Keywords

structure from Motion, degenerate deformations, factorization

Notes

Sponsor: National Institute of Mental Health

Grant ID: R01 MH51435

Associated Center(s) / Consortia: Vision and Autonomous Systems Center

Associated Lab(s) / Group(s): Vision for Safe Driving, People Image Analysis Consortium, Human Identification at a Distance, Face Group, Component Analysis

Associated Project(s): Facial Expression Analysis, Face Model Building and Fitting, AAM Fitting Algorithms, 2D->3D Face Model Construction

Number of pages: 8

Text Reference

Jing Xiao and Takeo Kanade, "Non-Rigid Shape and Motion Recovery: Degenerate Deformations," Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, June, 2004, pp. 668 - 675.

BibTeX Reference

@inproceedings{Xiao_2004_4661,
   author = "Jing Xiao and Takeo Kanade",
   title = "Non-Rigid Shape and Motion Recovery: Degenerate Deformations",
   booktitle = "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition",
   pages = "668 - 675",
   month = "June",
   year = "2004",
   volume = "1",
}

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