Spherical Object Reconstruction Using Star-Shaped Simplex Meshes

  • Pavel Matula
  • David Svoboda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2134)

Abstract

Spherical object reconstruction is of great importance, especially in the field of cell biology, since cells as well as cell nuclei mostly have the shape of a deformed sphere. Fast, reliable and precise procedure is needed for automatic measuring of topographical parameters of the large number of cells or cell nuclei. This paper presents a new method for spherical object reconstruction. The method springs from Delingette general object reconstruction algorithm which is based on the deformation of simplex meshes. However, the unknown surface is searched only within the subclass of simplex meshes, which have the shape of a star. Star-shaped simplex meshes are suitable for modelling of spherical or ellipsoidal objects. In our approach, the law of motion was altered so that it preserves the star-shape during deformation. The proposed method is easier than the general method and therefore faster. In addition, it uses more computationally stable expressions than a method strictly implemented according to Delingette’s paper. It is also shown how to partly avoid the occasional instability of the Delingette method. The accuracy of both methods is comparable. The star-shaped method achieves a stable state more often.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. S. Umesh Adiga and B. B. Chaudhuri. Deformable models for segmentation of CLSM tissue images and its application in FISH signal analysis. Analytical Cellular Pathology, 18(4):211–225, 1999. ISSN 0921-8912.Google Scholar
  2. 2.
    P. Bamford and B. Lovell. Unsupervised cell nucleus segmentation with active contours. Signal Processing Special Issue: Deformable Models and Techniques for Image and Signal Processing, 71(2), 1998.Google Scholar
  3. 3.
    C. Ortiz de Solórzano, E. Garcýa Rodriguez, A. Jones, D. Pinkel, J. W. Gray, D. Sudar, and S. J. Lockett. Segmentation of confocal microscope images of cell nuclei in thick tissue sections. Journal of Microscopy, 193:212–226, 1999.CrossRefGoogle Scholar
  4. 4.
    H. Delingette. Simplex meshes: a general representation for 3D shape reconstruction. Technical Report 2214, INRIA, France, 1994.Google Scholar
  5. 5.
    H. Delingette. General object reconstruction based on simplex meshes. International Journal of Computer Vision, 32(2):111–146, 1999.CrossRefGoogle Scholar
  6. 6.
    A. Fitzgibbon, M. Pilu, and R. B. Fisher. Direct least square fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Inteligence, 21(5):476–480, May 1999.Google Scholar
  7. 7.
    F. Guilak. Volume and surface area measurement of viable chondrocytes in situ using geometric modelling of serial confocal sections. Journal of Microscopy, 173(3):245–256, 1993.Google Scholar
  8. 8.
    M. Kass, A. Witkin, and D. Terzopoulos. Active contour models. International Journal of Computer Vision, 1(4): 133–144, 1987.Google Scholar
  9. 9.
    M. Kozubek, S. Kozubek, E. Lukásová, A. Marecková, E. Bártová, M. Skalnýková, and A. Jergová. High-resolution cytometry of FISH dots in interphase cell nuclei. Cytometry, 36:279–293, 1999.CrossRefGoogle Scholar
  10. 10.
    L. Kubýnová, J. Janácek, F. Guilak, and Z. Opatrný. Comparison of several digital and stereological methods for estimating surface area and volume of cell studied by confocal microscopy. Cytometry, 36:85–95, 1999.CrossRefGoogle Scholar
  11. 11.
    W. E. Lorensen and H. E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. In Computer Graphics (Proceedings of SIGGRAPH’ 87), volume 21, pages 163–169, 1987.CrossRefGoogle Scholar
  12. 12.
    H. Netten, I. T. Young, L. J. Van Vliet, H. J. Tanke, H. Vrolijk, and W. C. R. Sloos. FISH and chips: automation of fluorescent dot counting in interphase cell nuclei. Cytometry, 28:1–10, 1997.CrossRefGoogle Scholar
  13. 13.
    W. K. Pratt. Digital Image Processing. John Wiley & Sons, Inc., New York, second edition, 1991.MATHGoogle Scholar
  14. 14.
    F. P. Preparata and M. I. Shamos. Computational geometry: an introduction. Springer-Verlag, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Pavel Matula
    • 1
  • David Svoboda
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

Personalised recommendations