4D Numerical Schemes for Cell Image Segmentation and Tracking

  • K. Mikula
  • N. Peyriéeras
  • M. Remešíková
  • M. Smíšek
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

Abstract

The paper introduces new techniques for 4D (space-time) segmentation and tracking in time sequences of 3D images of zebrafish embryogenesis. Instead of treating each 3D image individually, we consider the whole time sequence as a single 4D image and perform the extraction of objects and cell tracking in four dimensions. The segmentation of the spatiotemporal objects corresponding to the time evolution of the individual cells is realized by using the generalized subjective surface model [1], that is discretized by a new 4D finite volume scheme. Afterwards, we use the distance functions to the borders of the segmented spatiotemporal objects and to the initial cell center positions in order to backtrack the cell trajectories that can be understood as 4D parametrized curves. The distance functions are obtained by numerical solution of the time relaxed eikonal equation.

Keywords

Cell tracking image segmentation finite volume method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

This work was supported by the grant VEGA 1/0733/10.

References

  1. 1.
    Bourgine, P., Čunderlík, R., Drblíková-Stašová, O., Mikula, O., Peyriéras, N., Remešíková, M., Rizzi, M., Sarti, A.: 4D embryogenesis image analysis using PDE methods of image processing. Kybernetika 46 (2), 226–259 (2010).MathSciNetMATHGoogle Scholar
  2. 2.
    Bourgine, P., Frolkovič, P., Mikula, K., Peyriéras, N., Remešíková, M.: Extraction of the intercellular skeleton from 2D microscope images of early embryogenesis. In Lecture Notes in Computer Science 5567 (Proceeding of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision, Voss, Norway, June 2009) (Springer, 2009), p. 38–49.Google Scholar
  3. 3.
    Krivá, Z., Mikula, K., Peyriéras, N., Rizzi, B., Sarti, A., Stašová, O.: Zebrafish early embryogenesis 3D image filtering by nonlinear partial differential equations. Medical Image Analysis, 14 (4), 510–526 (2010).CrossRefGoogle Scholar
  4. 4.
    Mikula, K., Remešíková, M.: Finite volume schemes for the generalized subjective surface equation in image segmentation. Kybernetika 45 (4), 646–656 (2009).MathSciNetMATHGoogle Scholar
  5. 5.
    Rouy, E., Tourin, A.: Viscosity solutions approach to shape-from-shading. SIAM Journal on Numerical Analysis 29 (3), 867–884 (1992).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Zanella, C., Campana, M., Rizzi, B., Melani, C., Sanguinetti, G., Bourgine, P., Mikula, K., Peyriéras, N., Sarti, A.: Cells Segmentation from 3-D Confocal Images Of Early Zebrafish Embryogenesis. IEEE Transactions on Image Processing 19 (2), (2010).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • K. Mikula
    • 1
  • N. Peyriéeras
    • 2
  • M. Remešíková
    • 1
  • M. Smíšek
    • 1
  1. 1.Slovak University of TechnologyBratislavaSlovakia
  2. 2.CNRS-DEPSNGif sur YvetteFrance

Personalised recommendations