A Closed-Form Solution to Non-Rigid Shape and Motion Recovery |
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Authors: | Jing Xiao Jinxiang Chai Takeo Kanade |
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Affiliation: | (1) Epson Palo Alto Laboratory, 3145 Porter Drive, Palo Alto, CA 94304, USA;(2) Robotics Institute, CMU, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA |
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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 (Bregler, C., Hertzmann, A., and Biermann,
H. 2000. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Brand, M. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Torresani, L., Yang, D., Alexander, G., and Bregler, C. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition) 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. An arbitrary linear transformation of the bases produces another 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 quantitatively on synthetic data and qualitatively on
real video sequences. |
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Keywords: | non-rigid structure from motion shape bases rotation constraint ambiguity basis constraints closed-form solution |
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