Fast Marching 3D Reconstruction of Interphase Chromosomes

  • Pavel Matula
  • Jan Hubený
  • Michal Kozubek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3117)

Abstract

Reliable 3D reconstruction of interphase chromosomes imaged using confocal microscopy is an important task in cell biology. Computer model of chromosome territories enables performing necessary measurements and consequently making morphological studies. A large number of processed objects is necessary to ensure statistical significance of the results. Therefore an automated procedure is needed. We have developed a successful algorithm for 3D reconstruction of chromosome territories on the basis of well-known fast marching algorithm. The fast marching algorithm solves front evolution problem similarly to deformable models but in an effective way with the time complexity \({\cal O}(n\log n)\).

Keywords

fast marching method deformable models 3D object reconstruction biomedical application interphase chromosome 

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References

  1. 1.
    Adalsteinsson, D., Sethian, J.A.: A fast level set method for propagating interfaces. Journal of Computational Physics 118, 269–277 (1995)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bertin, E., Parazza, F., Chassery, J.M.: Segmentation and meassurement based on 3D Voronoi diagram: application to confocal microscopy. Computerized Medical Imaging and Graphics 17(3), 175–182 (1993)CrossRefGoogle Scholar
  3. 3.
    Cohen, L.D.: On active contour models and balloons. CVGIP: Image Understanding 53(2), 211–218 (1991)MATHCrossRefGoogle Scholar
  4. 4.
    Cohen, L.D., Cohen, I.: Finite element methods for active contour models and balloons for 2D and 3D images. IEEE Transactions on Pattern Analysis and Machine Inteligence 15(11), 1131–1147 (1993)CrossRefGoogle Scholar
  5. 5.
    Cremer, T., Cremer, C.: Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nature reviews genetics 2(4), 292–301 (2001)CrossRefGoogle Scholar
  6. 6.
    Cremer, T., Kurz, A., Zirbel, R., Dietzel, S., Rinke, B., Schröck, E., Speicher, M.R., Mathieu, U., Jauch, A., Emmerich, P., Scherthan, H., Reid, T., Cremer, C., Lichter, P.: Role of chromosome territories in the functional compartmentalization of the cell nucleus. Cold Spring Harbor Symp. Quantitative Biology 58, 777–792 (1993)Google Scholar
  7. 7.
    Eils, R., Bertin, E., Saracoglu, K., Rinke, B., Schröck, E., Parazza, F., Usson, Y., Robert-Nicoud, M., Stelzer, E.H.K., Chassery, J.M., Cremer, T., Cremer, C.: Application of confocal laser microscopy and treee-dimensional Voronoi diagrams for volume and surface estimates of interphase chromosomes. Journal of Microscopy 177(2), 150–161 (1995)Google Scholar
  8. 8.
    Eils, R., Dietzel, S., Bertin, E., Schröck, E., Speicher, M.R., Ried, T., Robert- Nicoud, M., Cremer, T., Cremer, C.: Three-dimensional reconstruction of painted human interphase chromosomes: active and inactive X chromosome territories have similar volumes but differ in shape and surface structure. Journal of Cell Biology 135(6), 1427–1440 (1996)CrossRefGoogle Scholar
  9. 9.
    Kass, M., Witkin, A., Terzopoulos, D.: Active contour models. International Journal of Computer Vision 1(4), 133–144 (1987)Google Scholar
  10. 10.
    Kozubek, M., Kozubek, S., Bártová, E., Lukášová, E., Skalníková, M., Matula, P., Matula, P., Jirsová, P., Cafourková, A., Koutná, I.: Combined confocal and wide-field high-resolution cytometry of FISH-stained cells. Cytometry 45, 1–12 (2001)CrossRefGoogle Scholar
  11. 11.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. In: Computer Graphics (SIGGRAPH 1987), vol. 21, pp. 163–169 (1987)Google Scholar
  12. 12.
    Malladi, R., Sethian, J.A.: An O(N log N) algorithm for shape modeling. Proceedings of the National Academy of Science 93, 9389–9392 (1996)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: a level set approach. IEEE Transactions on Pattern Analysis and Machine Inteligence 17(2), 158–175 (1995)CrossRefGoogle Scholar
  14. 14.
    Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Nat’l Academy of Sciences 93, 1591–1595 (1996)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 2nd edn. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pavel Matula
    • 1
  • Jan Hubený
    • 1
  • Michal Kozubek
    • 1
  1. 1.Faculty of Informatics, Laboratory of Optical MicroscopyMasaryk UniversityBrnoCzech Republic

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