A Closed-Form Solution to Non-Rigid Shape and Motion Recovery

Jing Xiao, Jinxiang Chai, and Takeo Kanade
The 8th European Conference on Computer Vision (ECCV 2004), May, 2004.


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Abstract
Recovery of three dimensional (3D) shape and motion of non-static scenes from a monocular video sequence is important for applications like robot navigation and human computer interaction. If every point in the scene randomly moves, it is impossible to recover the non-rigid shapes. In practice, many non-rigid objects, e.g. the human face under various expressions, deform with certain structures. Their shapes can be regarded as a weighted combination of certain shape bases. Shape and motion recovery under such situations has attracted much interest. Previous work on this problem utilized only orthonormality constraints on the camera rotations (rotation constraints). This paper proves that using only the rotation constraints results in ambiguous and invalid solutions. The ambiguity arises from the fact that the shape bases are not unique because their linear transformation is a new set of eligible bases. To eliminate the ambiguity, we propose a set of novel constraints, basis constraints, which uniquely determine the shape bases. We prove that, under the weak-perspective projection model, enforcing both the basis and the rotation constraints leads to a closed-form solution to the problem of non-rigid shape and motion recovery. The accuracy and robustness of our closed-form solution is evaluated uantitatively on synthetic data and qualitatively on real video sequences.

Keywords
Non-rigid Structure from Motion, factorization, 3D reconstruction

Notes
Associated Center(s) / Consortia: Vision and Autonomous Systems Center
Associated Lab(s) / Group(s): Human Identification at a Distance
Associated Project(s): 2D->3D Face Model Construction
Number of pages: 12

Text Reference
Jing Xiao, Jinxiang Chai, and Takeo Kanade, "A Closed-Form Solution to Non-Rigid Shape and Motion Recovery," The 8th European Conference on Computer Vision (ECCV 2004), May, 2004.

BibTeX Reference
@inproceedings{Xiao_2004_4608,
   author = "Jing Xiao and Jinxiang Chai and Takeo Kanade",
   title = "A Closed-Form Solution to Non-Rigid Shape and Motion Recovery",
   booktitle = "The 8th European Conference on Computer Vision (ECCV 2004)",
   month = "May",
   year = "2004",
}