Advertisement

An Affine Optical Flow Model for Dynamic Surface Reconstruction

  • Tobias Schuchert
  • Hanno Scharr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5604)

Abstract

In this paper we develop a differential model for simultaneous estimation of geometry and dynamics of a surface patch. To do so we combine a surface patch model in local 3D coordinates, a pinhole camera grid model and a brightness change model analogous to the brightness constancy constraint equation for optical flow. It turns out to be an extension of the well known affine optical flow model to higher dimensional data sets. Each of the translational and affine components of the optical flow is a term consisting of a mixture of surface patch parameters like its depth, slope, velocities etc. We evaluate the model by comparing estimation results using a simple local estimation scheme to available ground-truth. This simple estimation scheme already allows to get results in the same accuracy range one can achieve using range flow, i.e. a model for the estimation of 3D velocities of a surface point given a measured surface geometry. Consequently the new model allows direct estimation of additional surface parameters range flow is not capable of, without loss of accuracy in other parameters. What is more, it allows to design estimators coupling shape and motion estimation which may yield increased accuracy and/or robustness in the future.

Keywords

Structure Tensor Dynamic Surface Surface Patch Pinhole Camera Brightness Constancy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adiv, G.: Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Trans. on Pattern Analysis and Machine Intelligence 7(4), 384–401 (1985)CrossRefGoogle Scholar
  2. 2.
    Barron, J., Fleet, D., Beauchemin, S.: Performance of optical flow techniques. International Journal of Computer Vision 12(1), 43–77 (1994)CrossRefGoogle Scholar
  3. 3.
    Bigün, J., Granlund, G.H.: Optimal orientation detection of linear symmetry. In: International Conference On Computer Vision, pp. 433–438 (1987)Google Scholar
  4. 4.
    Black, M., Fleet, D., Yacoob, Y.: Robustly estimating changes in image appearence. Computer Vision and Image Understanding 7(1), 8–31 (2000)CrossRefGoogle Scholar
  5. 5.
    Bruhn, A., Weickert, J., Schnörr, C.: Lucas/kanade meets horn/schunck: Combining local and global optic flow methods. International Journal of Computer Vision 61(3), 211–231 (2005)CrossRefGoogle Scholar
  6. 6.
    Carceroni, R., Kutulakos, K.: Multi-view 3d shape and motion recovery on the spatio-temporal curve manifold. In: International Conference On Computer Vision, vol. (1), pp. 520–527 (1999)Google Scholar
  7. 7.
    Cason, C.: Persistence of vision ray tracer (POV-Ray), version 3.6, Windows (2005)Google Scholar
  8. 8.
    Denney, T.S.J., Prince, J.L.: Optimal brightness functions for optical flow estimation of deformable motion. IEEE Trans. Im. Proc. 3(2), 178–191 (1994)CrossRefGoogle Scholar
  9. 9.
    Farid, H., Simoncelli, E.P.: Optimally rotation-equivariant directional derivative kernels. In: 7th Int’l Conf. Computer Analysis of Images and Patterns, Kiel (1997)Google Scholar
  10. 10.
    Farnebäck, G.: Fast and accurate motion est. using orient. tensors and param. motion models. In: International Conference on Pattern Recognition, pp. 135–139 (2000)Google Scholar
  11. 11.
    Fleet, D., Black, M., Yacoob, Y., Jepson, A.: Design and use of linear models for image motion analysis. International Journal of Computer Vision 36(3), 171–193 (2000)CrossRefGoogle Scholar
  12. 12.
    Fleet, D., Langley, K.: Recursive filters for optical flow. Pattern Analysis and Machine Intelligence 17(1), 61–67 (1995)CrossRefGoogle Scholar
  13. 13.
    Fleet, D., Weiss, Y.: Optical flow estimation. In: Mathematical models for Computer Vision: The Handbook, Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  15. 15.
    Haußecker, H., Fleet, D.: Computing optical flow with physical models of brightness variation. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(6), 661–673 (2001)CrossRefGoogle Scholar
  16. 16.
    Haußecker, H., Spies, H.: Motion. In: Jähne, B., Haußecker, H., Geißler, P. (eds.) Handbook of Computer Vision and Applications, Academic Press, London (1999)Google Scholar
  17. 17.
    Horn, B., Schunck, B.: Determining optical flow. Artificial Intelligence 17, 185–204 (1981)CrossRefGoogle Scholar
  18. 18.
    Jähne, B., Scharr, H., Körkel, S.: Principles of filter design. In: Handbook of Computer Vision and Applications, Academic Press, London (1999)Google Scholar
  19. 19.
    Kanatani, K.: Structure from motion without correspondence: general principle. In: Proc. Image Understanding Workshop, pp. 10711–10716 (1985)Google Scholar
  20. 20.
    Matthies, L.H., Szeliski, R., Kanade, T.: Kalman filter-based algorithms for estimating depth from image sequences. International Journal of Computer Vision 3, 209–236 (1989)CrossRefGoogle Scholar
  21. 21.
    Li, G., Zucker, S.: Differential geometric consistency extends stereo to curved surfaces. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 44–57. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Longuet-Higgins, H., Prazdny, K.: The interpretation of a moving retinal image. In: Proceedings of The Royal Society of London B, vol. 208, pp. 385–397 (1980)Google Scholar
  23. 23.
    Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proc. Seventh International Joint Conference on Artificial Intelligence, Vancouver, Canada, August 1981, pp. 674–679 (1981)Google Scholar
  24. 24.
    Nakamura, Y., Matsuura, T., Satoh, K., Ohta, Y.: Occlusion detectable stereo–occlusion patterns in camera matrix. In: International Conference on Computer Vision and Pattern Recognition, pp. 371–378 (1996)Google Scholar
  25. 25.
    Nestares, O., Fleet, D., Heeger, D.: Likelihood functions and confidence bounds for total-least-squares problems. In: IEEE Conference on Computer Vision and Pattern Recognition, Hilton Head, South Carolina, vol. I, pp. 523–530 (2000)Google Scholar
  26. 26.
    Papenberg, N., Bruhn, A., Brox, T., Didas, S., Weickert, J.: Highly accurate optic flow computation with theoretically justified warping. International Journal of Computer Vision 67(2), 141–158 (2006)CrossRefGoogle Scholar
  27. 27.
    Scharr, H.: Optimal Operators in Digital Image Processing. PhD thesis, Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany (2000)Google Scholar
  28. 28.
    Scharr, H.: Towards a multi-camera generalization of brightness constancy. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds.) IWCM 2004. LNCS, vol. 3417, pp. 78–90. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  29. 29.
    Scharr, H.: Optimal filters for extended optical flow. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds.) IWCM 2004. LNCS, vol. 3417, pp. 14–29. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  30. 30.
    Scharr, H., Schuchert, T.: Simultaeous estimation of depth, motion and slopes using a camera grid. In: Kobbelt, T.A.L., Kuhlen, T., Westermann, R. (eds.) Vision Modeling and Visualization 2006, Aachen, pp. 81–88 (2006)Google Scholar
  31. 31.
    Schuchert, T., Aach, T., Scharr, H.: Range flow for varying illumination. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 509–522. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  32. 32.
    Schuchert, T., Scharr, H.: Simultaneous estimation of surface motion, depth and slopes under changing illumination. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 184–193. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  33. 33.
    Spies, H., Jähne, B., Barron, J.: Range Flow Estimation. Computer Vision and Image Understanding 85(3), 209–231 (2002)zbMATHCrossRefGoogle Scholar
  34. 34.
    Spies, H., Jähne, B.: A general framework for image sequence analysis. In: Fachtagung Informationstechnik, pp. 125–132 (2001), http://citeseerx.ist.psu.edu/viewdoc/summary?, doi:10.1.1.21.1678
  35. 35.
    Szeliski, R.: A multi-view approach to motion and stereo. In: International Conference on Computer Vision and Pattern Recognition (1999)Google Scholar
  36. 36.
    Vedula, S., Baker, S., Rander, P., Collins, R., Kanade, T.: Threedimensional scene flow. In: International Conference On Computer Vision 1999, pp. 722–729 (1999)Google Scholar
  37. 37.
    Vedula, S., Baker, S., Seitz, S., Collins, R., Kanade, T.: Shape and motion carving in 6d. In: International Conference on Computer Vision and Pattern Recognition 2000, pp. 592–598 (2000)Google Scholar
  38. 38.
    Waxman, A., Kamgar Parsi, B., Subbarao, M.: Closed-form solutions to image flow equations for 3d structure and motion. International Journal on Computer Vision 1(3), 239–258 (1987)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tobias Schuchert
    • 1
  • Hanno Scharr
    • 1
  1. 1.Institute for Chemistry and Dynamics of the Geosphere, ICG-3, Forschungszentrum Jülich GmbHJülichGermany

Personalised recommendations