Abstract
Rigid structure-from-motion (SfM) usually consists of two steps: First, a projective reconstruction is computed which is then upgraded to Euclidean structure and motion in a subsequent step. Reliable algorithms exist for both problems. In the case of non-rigid SfM, on the other hand, especially the Euclidean upgrading has turned out to be difficult. A few algorithms have been proposed for upgrading an affine reconstruction, and are able to obtain successful 3D-reconstructions. For upgrading a non-rigid projective reconstruction, however, either simple sequences are used, or no 3D-reconstructions are shown at all.
In this article, an algorithm is proposed for estimating the self-calibration of a projectively reconstructed non-rigid scene. In contrast to other algorithms, neither prior knowledge of the non-rigid deformations is required, nor a subsequent step to align different motion bases. An evaluation with synthetic data reveals that the proposed algorithm is robust to noise and it is able to accurately estimate the 3D-reconstructions and the intrinsic calibration. Finally, reconstructions of a challenging real image with strong non-rigid deformation are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004) ISBN: 0521540518
Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3d shape from image streams. In: IEEE Computer Vision and Pattern Recognition (CVPR), Hilton Head, SC, USA, pp. 690–696 (2000)
Triggs, B.: Autocalibration and the absolute quadric. In: Conf. Comp. Vis. and Pat. Recog. (CVPR) (1997)
Pollefeys, M., Koch, R., van Gool, L.: Self-calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters. Int. J. Comp. Vis. (IJCV) 32, 7–25 (1999)
Seo, Y., Heyden, A.: Auto-calibration by linear iteration using the DAC equation. Img. Vis. Comp. 22, 919–926 (2004)
Chandraker, M., Agarwal, S., Kahl, F., Nistér, D., Kriegman, D.: Autocalibration via rank-constrained estimation of the absolute quadric. In: Conf. Comp. Vis. and Pat. Recog. (CVPR) (2007)
Xiao, J., Chai, J., Kanade, T.: A closed-form solution to non-rigid shape and motion recovery. International Journal of Computer Vision 67, 233–246 (2006)
Brand, M.: A direct method for 3D factorization of nonrigid motion observed in 2d. In: IEEE Computer Vision and Pattern Recognition (CVPR), Washington, DC, USA, pp. 122–128 (2005)
Olsen, S., Bartoli, A.: Implicit non-rigid structure-from-motion with priors. Journal of Mathematical Imaging and Vision 31, 233–244 (2008)
Torresani, L., Hertzmann, A., Bregler, C.: Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors. IEEE Pattern Analysis and Machine Intelligence (PAMI) 30, 878–892 (2008)
Paladini, M., Del Bue, A., Stosic, M., Dodig, M., Xavier, J., Agapito, L.: Factorization for non-rigid and articulated structure using metric projections. In: IEEE Computer Vision and Pattern Recognition (CVPR), Miami, FL, USA, pp. 2898–2905 (2009)
Xiao, J., Kanade, T.: Uncalibrated perspective reconstruction of deformable structures. In: Proceedings of the 10th International Conference on Computer Vision (ICCV), vol. 2, pp. 1075–1082 (2005)
Hartley, R.I., Vidal, R.: Perspective Nonrigid Shape and Motion Recovery. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 276–289. Springer, Heidelberg (2008)
Brand, M.: Morphable 3D models from video. In: IEEE Computer Vision and Pattern Recognition (CVPR), pp. 456–463 (2001)
Heyden, A., Berthilsson, R., Sparr, G.: An iterative factorization method for projective structure and motion from image sequences. International Journal on Computer Vision 17, 981–991 (1999)
Mahamud, S., Hebert, M.: Iterative projective reconstruction from multiple views. In: The Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 430–437 (2000)
Akhter, I., Sheikh, Y., Khan, S.: In defense of orthonormality constraints for nonrigid structure from motion. In: IEEE Computer Vision and Pattern Recognition (CVPR), Miami, FL, USA, pp. 1534–1541 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ackermann, H., Rosenhahn, B. (2013). Non-rigid Self-calibration of a Projective Camera. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds) Computer Vision – ACCV 2012. ACCV 2012. Lecture Notes in Computer Science, vol 7727. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37447-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-37447-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37446-3
Online ISBN: 978-3-642-37447-0
eBook Packages: Computer ScienceComputer Science (R0)