caa a22 4500 467914524 CHVBK 20180406152858.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s11263-005-3962-9 doi (NATIONALLICENCE)springer-10.1007/s11263-005-3962-9 A Closed-Form Solution to Non-Rigid Shape and Motion Recovery [Elektronische Daten] [Jing Xiao, Jinxiang Chai, Takeo Kanade] 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. Springer Science + Business Media, Inc., 2006 non-rigid structure from motion nationallicence shape bases nationallicence rotation constraint nationallicence ambiguity nationallicence basis constraints nationallicence closed-form solution nationallicence Xiao Jing Epson Palo Alto Laboratory, 3145 Porter Drive, 94304, Palo Alto, CA, USA aut Chai Jinxiang Robotics Institute, CMU, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA aut Kanade Takeo Robotics Institute, CMU, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA aut International Journal of Computer Vision Kluwer Academic Publishers 67/2(2006-04-01), 233-246 0920-5691 67:2<233 2006 67 11263 https://doi.org/10.1007/s11263-005-3962-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-005-3962-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Xiao Jing Epson Palo Alto Laboratory, 3145 Porter Drive, 94304, Palo Alto, CA, USA aut NATIONALLICENCE 700 1- Chai Jinxiang Robotics Institute, CMU, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA aut NATIONALLICENCE 700 1- Kanade Takeo Robotics Institute, CMU, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 67/2(2006-04-01), 233-246 0920-5691 67:2<233 2006 67 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer