Abstract
The chapter proposes a stratification approach to recover the structure of nonrigid objects under the assumption that the object is composed of separable rigid features and deformed ones. First, we propose a deformation weight constraint for the problem and prove the invariability between the recovered structure and shape bases under this constraint. Second, we propose a constrained power factorization (CPF) algorithm to recover the deformation structure in affine space. Third, we propose to segment the rigid features from the deformed ones in 3D affine space which makes segmentation more accurate and robust. Finally, we recover the stratification matrix from the rigid features and upgrade the structure from affine to the Euclidean space.
What remains to be resolved is the question of knowing to what extent and up to what point these hypotheses are found to be confirmed by experience.
Bernhard Riemann (1826–1866)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brand, M.: Morphable 3D models from video. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 456–463 (2001)
Brand, M.: A direct method for 3D factorization of nonrigid motion observed in 2D. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 122–128 (2005)
Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3D shape from image streams. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 690–696 (2000)
Del Bue, A., Lladó, X., de Agapito, L.: Non-rigid face modelling using shape priors. In: Proc. of Second International Workshop on Analysis and Modelling of Faces and Gestures, pp. 97–108 (2005)
Del Bue, A., Lladó, X., de Agapito, L.: Non-rigid metric shape and motion recovery from uncalibrated images using priors. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 1191–1198 (2006)
Fischler, M.A., Bolles, R.C.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM24(6), 381–395 (1981)
Han, M., Kanade, T.: Creating 3D models with uncalibrated cameras. In: Proc. of IEEE Computer Society Workshop on the Application of Computer Vision (2000)
Hartley, R., Schaffalizky, F.: Powerfactorization: 3D reconstruction with missing or uncertain data. In: Proc. of Australia-Japan Advanced Workshop on Computer Vision (2003)
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004). ISBN: 0521540518
Poelman, C., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell.19(3), 206–218 (1997)
Quan, L.: Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis.19(1), 93–105 (1996)
Torresani, L., Hertzmann, A., Bregler, C.: Learning non-rigid 3D shape from 2D motion. In: Proc. of Advances in Neural Information Processing Systems (2004)
Torresani, L., Hertzmann, A., Bregler, C.: Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors. IEEE Trans. Pattern Anal. Mach. Intell.30(5), 878–892 (2008)
Torresani, L., Yang, D.B., Alexander, E.J., Bregler, C.: Tracking and modeling non-rigid objects with rank constraints. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 493–500 (2001)
Wang, G., Tian, Y., Sun, G.: Modelling nonrigid object from video sequence under perspective projection. In: Lecture Notes in Computer Science, vol. 3784, pp. 64–71 (2005)
Wang, G., Tsui, H.T., Wu, J.: Rotation constrained power factorization for structure from motion of nonrigid objects. Pattern Recogn. Lett.29(1), 72–80 (2008)
Wang, G., Wu, J.: Stratification approach for 3-D Euclidean reconstruction of nonrigid objects from uncalibrated image sequences. IEEE Trans. Syst. Man Cybern., Part B38(1), 90–101 (2008)
Xiao, J., Chai, J., Kanade, T.: A closed-form solution to non-rigid shape and motion recovery. Int. J. Comput. Vis.67(2), 233–246 (2006)
Xiao, J., Kanade, T.: Uncalibrated perspective reconstruction of deformable structures. In: Proc. of the International Conference on Computer Vision, vol. 2, pp. 1075–1082 (2005)
Yao, J., Cham, W.: Feature matching and scene reconstruction from multiple widely separated views. Tech. Rep., Chinese University of Hong Kong (2005)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Wang, G., Wu, Q.M.J. (2011). Stratified Euclidean Reconstruction. In: Guide to Three Dimensional Structure and Motion Factorization. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-0-85729-046-5_8
Download citation
DOI: https://doi.org/10.1007/978-0-85729-046-5_8
Publisher Name: Springer, London
Print ISBN: 978-0-85729-045-8
Online ISBN: 978-0-85729-046-5
eBook Packages: Computer ScienceComputer Science (R0)