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Guide to Three Dimensional Structure and Motion Factorization pp 63–86Cite as

Introduction to Structure and Motion Factorization

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Part of the book series: Advances in Pattern Recognition ((ACVPR))

Abstract

The chapter reviews some popular algorithms for structure and motion factorization. We first introduce the problem of structure and motion recovery. Then, present the main idea of the following factorization algorithms for different kinds of scenarios under different projection models. (i) Structure and motion factorization of rigid objects under affine assumption and its extension to perspective camera model; (ii) Nonrigid factorization under both affine and perspective projection model; (iii) Structure factorization of multiple and articulated objects.

If I have been able to see further, it was only because I stood on the shoulders of giants.

Sir Isaac Newton (1643–1727)

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References

  1. Aanæs, H., Fisker, R., Åström, K., Carstensen, J.M.: Robust factorization. IEEE Trans. Pattern Anal. Mach. Intell.24(9), 1215–1225 (2002)

    Article  Google Scholar 

  2. Anandan, P., Irani, M.: Factorization with uncertainty. Int. J. Comput. Vis.49(2–3), 101–116 (2002)

    Article  MATH  Google Scholar 

  3. Bascle, B., Blake, A.: Separability of pose and expression in facial tracing and animation. In: Proc. of the International Conference on Computer Vision, pp. 323–328 (1998)

    Google Scholar 

  4. Brand, M.: Morphable 3D models from video. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 456–463 (2001)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. Buchanan, A.M., Fitzgibbon, A.W.: Damped newton algorithms for matrix factorization with missing data. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 316–322 (2005)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Costeira, J., Kanade, T.: A multibody factorization method for independent moving objects. Int. J. Comput. Vis.29(3), 159–179 (1998)

    Article  Google Scholar 

  10. Del Bue, A.: Deformable 3-D modelling from uncalibrated video sequences. Ph.D. Thesis, Queen Mary, University of London (2007)

    Google Scholar 

  11. Del Bue, A., Agapito, L.: Non-rigid stereo factorization. Int. J. Comput. Vis.66(2), 193–207 (2006)

    Article  Google Scholar 

  12. 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)

    Google Scholar 

  13. Del Bue, A., Smeraldi, F., Agapito, L.: Non-rigid structure from motion using nonparametric tracking and non-linear optimization. In: Proc. of IEEE Workshop in Articulated and Nonrigid Motion, pp. 8–15 (2004)

    Google Scholar 

  14. Gruber, A., Weiss, Y.: Multibody factorization with uncertainty and missing data using the EM algorithm. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 707–714 (2004)

    Google Scholar 

  15. Han, M., Kanade, T.: Creating 3D models with uncalibrated cameras. In: Proc. of IEEE Computer Society Workshop on the Application of Computer Vision (2000)

    Google Scholar 

  16. Hartley, R., Vidal, R.: Perspective nonrigid shape and motion recovery. In: Proc. of European Conference on Computer Vision. Lecture Notes in Computer Science, vol. 5302, pp. 276–289. Springer, Berlin (2008)

    Google Scholar 

  17. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004). ISBN: 0521540518

    Book  MATH  Google Scholar 

  18. Heyden, A., Berthilsson, R., Sparr, G.: An iterative factorization method for projective structure and motion from image sequences. Image Vis. Comput.17(13), 981–991 (1999)

    Article  Google Scholar 

  19. Kanade, T., Morris, D.D.: Factorization methods for structure from motion. Philos. Trans. R. Soc. Lond. Ser. A356, 1153–1173 (2001)

    Article  MathSciNet  Google Scholar 

  20. Kanatani, K.: Motion segmentation by subspace separation and model selection. In: Proc. of International Conference on Computer Vision, vol. 2 (2001)

    Google Scholar 

  21. 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)

    Google Scholar 

  22. Lowe, D.G.: Object recognition from local scale-invariant features. In: Proc. of the International Conference on Computer Vision, vol. 2, pp. 1150–1157 (1999)

    Google Scholar 

  23. Lucas, B.D., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proc. of International Joint Conference on Artificial Intelligence (IJCAI), pp. 674–679 (1981)

    Google Scholar 

  24. Mahamud, S., Hebert, M.: Iterative projective reconstruction from multiple views. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 430–437 (2000)

    Google Scholar 

  25. Okatani, T., Deguchi, K.: On the Wiberg algorithm for matrix factorization in the presence of missing components. Int. J. Comput. Vis.72(3), 329–337 (2007)

    Article  Google Scholar 

  26. 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)

    Article  Google Scholar 

  27. 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)

    Article  Google Scholar 

  28. Poelman, C., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell.19(3), 206–218 (1997)

    Article  Google Scholar 

  29. Quan, L.: Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis.19(1), 93–105 (1996)

    Article  Google Scholar 

  30. Quan, L., Kanade, T.: A factorization method for affine structure from line correspondences. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 803–808 (1996)

    Google Scholar 

  31. Rabaud, V., Belongie, S.: Re-thinking non-rigid structure from motion. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition (2008)

    Google Scholar 

  32. Shi, J., Tomasi, C.: Good features to track. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 593–600 (1994)

    Google Scholar 

  33. Sturm, P.F., Triggs, B.: A factorization based algorithm for multi-image projective structure and motion. In: Proc. of European Conference on Computer Vision, vol. 2, pp. 709–720 (1996)

    Google Scholar 

  34. Sugaya, Y., Kanatani, K.: Outlier removal for motion tracking by subspace separation. IEICE Trans. Inf. Syst.86, 1095–1102 (2003)

    Google Scholar 

  35. Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: A factorization method. Int. J. Comput. Vis.9(2), 137–154 (1992)

    Article  Google Scholar 

  36. 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)

    Article  Google Scholar 

  37. 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)

    Google Scholar 

  38. 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)

    Google Scholar 

  39. 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)

    Google Scholar 

  40. Vidal, R., Abretske, D.: Nonrigid shape and motion from multiple perspective views. In: Proc. of European Conference on Computer Vision. Lecture Notes in Computer Science, vol. 3952, pp. 205–218. Springer, Berlin (2006)

    Google Scholar 

  41. 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)

    Article  Google Scholar 

  42. Wang, G., Wu, J.: Quasi-perspective projection model: Theory and application to structure and motion factorization from uncalibrated image sequences. Int. J. Comput. Vis.87(3), 213–234 (2010)

    Article  Google Scholar 

  43. 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)

    Article  Google Scholar 

  44. 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)

    Google Scholar 

  45. 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)

    Google Scholar 

  46. Yan, J., Pollefeys, M.: A factorization-based approach to articulated motion recovery. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 815–821 (2005)

    Google Scholar 

  47. 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)

    Article  Google Scholar 

  48. Zaharescu, A., Horaud, R.: Robust factorization methods using a Gaussian/uniform mixture model. Int. J. Comput. Vis.81(3), 240–258 (2009)

    Article  Google Scholar 

  49. Zelnik-Manor, L., Irani, M.: Degeneracies, dependencies and their implications in multi-body and multi-sequence factorizations. In: Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, p. 287 (2003)

    Google Scholar 

  50. Zelnik-Manor, L., Irani, M.: On single-sequence and multi-sequence factorizations. Int. J. Comput. Vis.67(3), 313–326 (2006)

    Article  Google Scholar 

  51. Zelnik-Manor, L., Machline, M., Irani, M.: Multi-body factorization with uncertainty: Revisiting motion consistency. Int. J. Comput. Vis.68(1), 27–41 (2006)

    Article  Google Scholar 

  52. Zhang, Z., Deriche, R., Faugeras, O., Luong, Q.T.: A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artif. Intell.78(1–2), 87–119 (1995)

    Article  Google Scholar 

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Authors and Affiliations

    Authors
    1. Guanghui Wang
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    2. Q. M. Jonathan Wu
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    Correspondence to Guanghui Wang or Guanghui Wang .

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    © 2011 Springer-Verlag London Limited

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    Wang, G., Wu, Q.M.J. (2011). Introduction to Structure and Motion Factorization. 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_4

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    • DOI: https://doi.org/10.1007/978-0-85729-046-5_4

    • Publisher Name: Springer, London

    • Print ISBN: 978-0-85729-045-8

    • Online ISBN: 978-0-85729-046-5

    • eBook Packages: Computer ScienceComputer Science (R0)

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