Abstract
The chapter focuses on the problem of nonrigid structure and motion factorization under perspective projection. Many previous methods are based on affine assumption that may be invalid and cause large reconstruction errors when the object is close to the camera. In this chapter, we propose two algorithms to extend these methods to full perspective projection model. The first one is a linear recursive algorithm, which updates the solution from weak-perspective to perspective projection by refining the projective depth scales. The second one is a nonlinear optimization scheme that minimizes the perspective reprojection residuals. Extensive experiments on synthetic and real image sequences are performed to validate the effectiveness of the algorithms.
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
David Hilbert (1862–1943)
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References
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)
Christy, S., Horaud, R.: Euclidean shape and motion from multiple perspective views by affine iterations. IEEE Trans. Pattern Anal. Mach. Intell.18(11), 1098–1104 (1996)
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)
Dementhon, D.F., Davis, L.S.: Model-based object pose in 25 lines of code. Int. J. Comput. Vis.15(1–2), 123–141 (1995)
Fujiki, J., Kurata, T.: Recursive factorization method for the paraperspective model based on the perspective projection. In: Proc. of International Conference on Pattern Recognition, vol. 1, pp. 406–410 (2000)
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004). ISBN: 0521540518
Li, T., Kallem, V., Singaraju, D., Vidal, R.: Projective factorization of multiple rigid-body motions. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition (2007)
Lladó, X., Del Bue, A., de Agapito, L.: Non-rigid 3D factorization for projective reconstruction. In: Proc. of British Machine Vision Conference (2005)
Oliensis, J., Hartley, R.: Iterative extensions of the Sturm/Triggs algorithm: Convergence and nonconvergence. IEEE Trans. Pattern Anal. Mach. Intell.29(12), 2217–2233 (2007)
Ozden, K.E., Schindler, K., Van Gool, L.: Multibody structure-from-motion in practice. IEEE Trans. Pattern Anal. Mach. Intell.32(6), 1134–1141 (2010)
Poelman, C., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell.19(3), 206–218 (1997)
Pollefeys, M., Koch, R., Van Gool, L.: Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters. Int. J. Comput. Vis.32(1), 7–25 (1999)
Quan, L.: Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis.19(1), 93–105 (1996)
Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: a factorization method. Int. J. Comput. Vis.9(2), 137–154 (1992)
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)
Tresadern, P., Reid, I.: Articulated structure from motion by factorization. In: Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 1110–1115 (2005)
Triggs, B.: Factorization methods for projective structure and motion. In: Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 845–851 (1996)
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., Hu, Z.: Structure and motion of nonrigid object under perspective projection. Pattern Recogn. Lett.28(4), 507–515 (2007)
Xiao, J., Chai, J.X., Kanade, T.: A closed-form solution to non-rigid shape and motion recovery. In: Proc. of European Conference on Computer Vision, vol. 4, pp. 573–587 (2004)
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)
Yan, J., Pollefeys, M.: A factorization-based approach for articulated nonrigid shape, motion and kinematic chain recovery from video. IEEE Trans. Pattern Anal. Mach. Intell.30(5), 865–877 (2008)
Yao, J., Cham, W.: Feature matching and scene reconstruction from multiple widely separated views. Tech. Rep., Chinese University of Hong Kong (2005)
Zelnik-Manor, L., Machline, M., Irani, M.: Multi-body factorization with uncertainty: Revisiting motion consistency. Int. J. Comput. Vis.68(1), 27–41 (2006)
Zhang, Z.: A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell.22(11), 1330–1334 (2000)
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Wang, G., Wu, Q.M.J. (2011). Perspective 3D Reconstruction of Nonrigid Objects. 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_6
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DOI: https://doi.org/10.1007/978-0-85729-046-5_6
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