Optical Flow on Evolving Surfaces with an Application to the Analysis of 4D Microscopy Data

  • Clemens Kirisits
  • Lukas F. Lang
  • Otmar Scherzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7893)

Abstract

We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are defined on an evolving surface. Volumetric microscopy images depicting a live zebrafish embryo serve as both biological motivation and test data.

Keywords

Computer Vision biomedical imaging optical flow variational methods evolving surfaces zebrafish laser-scanning microscopy 

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References

  1. 1.
    Baker, S., Scharstein, D., Lewis, J.P., Roth, S., Black, M.J., Szeliski, R.: A Database and Evaluation Methodology for Optical Flow. Int. J. Comput. Vision 92(1), 1–31 (2011)CrossRefGoogle Scholar
  2. 2.
    Cermelli, P., Fried, E., Gurtin, M.E.: Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. J. Fluid Mech. 544, 339–351 (2005)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Courant, R., Hilbert, D.: Methods of mathematical physics, vol. I. Interscience Publishers, Inc., New York (1953)Google Scholar
  4. 4.
    Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer, Berlin (2001), Reprint of the 1998 editionGoogle Scholar
  5. 5.
    Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)CrossRefGoogle Scholar
  6. 6.
    Hubený, J., Ulman, V., Matula, P.: Estimating large local motion in live-cell imaging using variational optical flow. In: VISAPP: Proc. of the Second International Conference on Computer Vision Theory and Applications, pp. 542–548. INSTICC (2007)Google Scholar
  7. 7.
    Imiya, A., Sugaya, H., Torii, A., Mochizuki, Y.: Variational analysis of spherical images. In: Gagalowicz, A., Philips, W. (eds.) CAIP 2005. LNCS, vol. 3691, pp. 104–111. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Kimmel, C.B., Ballard, W.W., Kimmel, S.R., Ullmann, B., Schilling, T.F.: Stages of embryonic development of the zebrafish. Devel. Dyn. 203(3), 253–310 (1995)CrossRefGoogle Scholar
  9. 9.
    Lee, J.M.: Riemannian Manifolds. An Introduction to Curvature. Graduate Texts in Mathematics, vol. 176. Springer, New York (1997)Google Scholar
  10. 10.
    Lefèvre, J., Baillet, S.: Optical flow and advection on 2-Riemannian manifolds: A common framework. IEEE Trans. Pattern Anal. Mach. Intell. 30(6), 1081–1092 (2008)CrossRefGoogle Scholar
  11. 11.
    Megason, S.G., Fraser, S.E.: Digitizing life at the level of the cell: high-performance laser-scanning microscopy and image analysis for in toto imaging of development. Mech. Dev. 120(11), 1407–1420 (2003)CrossRefGoogle Scholar
  12. 12.
    Melani, C., Campana, M., Lombardot, B., Rizzi, B., Veronesi, F., Zanella, C., Bourgine, P., Mikula, K., Peyriéras, N., Sarti, A.: Cells tracking in a live zebrafish embryo. In: Proceedings of the 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS 2007), pp. 1631–1634 (2007)Google Scholar
  13. 13.
    Miura, K.: Tracking Movement in Cell Biology. In: Rietdorf, J. (ed.) Microscopy Techniques. Advances in Biochemical Engineering/Biotechnology, vol. 95, pp. 267–295. Springer (2005)Google Scholar
  14. 14.
    Mizoguchi, T., Verkade, H., Heath, J.K., Kuroiwa, A., Kikuchi, Y.: Sdf1/Cxcr4 signaling controls the dorsal migration of endodermal cells during zebrafish gastrulation. Development 135(15), 2521–2529 (2008)CrossRefGoogle Scholar
  15. 15.
    Quelhas, P., Mendonça, A.M., Campilho, A.: Optical flow based arabidopsis thaliana root meristem cell division detection. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010, Part II. LNCS, vol. 6112, pp. 217–226. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Torii, A., Imiya, A., Sugaya, H., Mochizuki, Y.: Optical Flow Computation for Compound Eyes: Variational Analysis of Omni-Directional Views. In: De Gregorio, M., Di Maio, V., Frucci, M., Musio, C. (eds.) BVAI 2005. LNCS, vol. 3704, pp. 527–536. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Warga, R.M., Nüsslein-Volhard, C.: Origin and development of the zebrafish endoderm. Development 126(4), 827–838 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Clemens Kirisits
    • 1
  • Lukas F. Lang
    • 1
  • Otmar Scherzer
    • 1
    • 2
  1. 1.Computational Science CenterUniversity of ViennaViennaAustria
  2. 2.Radon Institute of Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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