4D Embryogenesis image analysis using PDE methods of image processing

Paul Bourgine; Róbert Čunderlík; Olga Drblíková-Stašová; Karol Mikula; Mariana Remešíková; Nadine Peyriéras; Barbara Rizzi; Alessandro Sarti

Kybernetika (2010)

  • Volume: 46, Issue: 2, page 226-259
  • ISSN: 0023-5954

Abstract

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In this paper, we introduce a set of methods for processing and analyzing long time series of 3D images representing embryo evolution. The images are obtained by in vivo scanning using a confocal microscope where one of the channels represents the cell nuclei and the other one the cell membranes. Our image processing chain consists of three steps: image filtering, object counting (center detection) and segmentation. The corresponding methods are based on numerical solution of nonlinear PDEs, namely the geodesic mean curvature flow model, flux-based level set center detection and generalized subjective surface equation. All three models have a similar character and therefore can be solved using a common approach. We explain in details our semi-implicit time discretization and finite volume space discretization. This part is concluded by a short description of parallelization of the algorithms. In the part devoted to experiments, we provide the experimental order of convergence of the numerical scheme, the validation of the methods and numerous experiments with the data representing an early developmental stage of a zebrafish embryo.

How to cite

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Bourgine, Paul, et al. "4D Embryogenesis image analysis using PDE methods of image processing." Kybernetika 46.2 (2010): 226-259. <http://eudml.org/doc/196413>.

@article{Bourgine2010,
abstract = {In this paper, we introduce a set of methods for processing and analyzing long time series of 3D images representing embryo evolution. The images are obtained by in vivo scanning using a confocal microscope where one of the channels represents the cell nuclei and the other one the cell membranes. Our image processing chain consists of three steps: image filtering, object counting (center detection) and segmentation. The corresponding methods are based on numerical solution of nonlinear PDEs, namely the geodesic mean curvature flow model, flux-based level set center detection and generalized subjective surface equation. All three models have a similar character and therefore can be solved using a common approach. We explain in details our semi-implicit time discretization and finite volume space discretization. This part is concluded by a short description of parallelization of the algorithms. In the part devoted to experiments, we provide the experimental order of convergence of the numerical scheme, the validation of the methods and numerous experiments with the data representing an early developmental stage of a zebrafish embryo.},
author = {Bourgine, Paul, Čunderlík, Róbert, Drblíková-Stašová, Olga, Mikula, Karol, Remešíková, Mariana, Peyriéras, Nadine, Rizzi, Barbara, Sarti, Alessandro},
journal = {Kybernetika},
keywords = {image processing; embryogenesis; image analysis; finite volume method; image filtering; object counting; segmentation; partial differential equation; finite volume method; image processing; embryogenesis; image analysis; image filtering; object counting; segmentation; partial differential equation},
language = {eng},
number = {2},
pages = {226-259},
publisher = {Institute of Information Theory and Automation AS CR},
title = {4D Embryogenesis image analysis using PDE methods of image processing},
url = {http://eudml.org/doc/196413},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Bourgine, Paul
AU - Čunderlík, Róbert
AU - Drblíková-Stašová, Olga
AU - Mikula, Karol
AU - Remešíková, Mariana
AU - Peyriéras, Nadine
AU - Rizzi, Barbara
AU - Sarti, Alessandro
TI - 4D Embryogenesis image analysis using PDE methods of image processing
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 2
SP - 226
EP - 259
AB - In this paper, we introduce a set of methods for processing and analyzing long time series of 3D images representing embryo evolution. The images are obtained by in vivo scanning using a confocal microscope where one of the channels represents the cell nuclei and the other one the cell membranes. Our image processing chain consists of three steps: image filtering, object counting (center detection) and segmentation. The corresponding methods are based on numerical solution of nonlinear PDEs, namely the geodesic mean curvature flow model, flux-based level set center detection and generalized subjective surface equation. All three models have a similar character and therefore can be solved using a common approach. We explain in details our semi-implicit time discretization and finite volume space discretization. This part is concluded by a short description of parallelization of the algorithms. In the part devoted to experiments, we provide the experimental order of convergence of the numerical scheme, the validation of the methods and numerous experiments with the data representing an early developmental stage of a zebrafish embryo.
LA - eng
KW - image processing; embryogenesis; image analysis; finite volume method; image filtering; object counting; segmentation; partial differential equation; finite volume method; image processing; embryogenesis; image analysis; image filtering; object counting; segmentation; partial differential equation
UR - http://eudml.org/doc/196413
ER -

References

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  1. Aoyama, Y., Nakano, J., RS/6000 SP: Practical MPI Programming, IBM 1999. 
  2. Bourgine, P., Frolkovič, P., Mikula, K., Peyriéras, N., Remešíková, M., Extraction of the intercellular skeleton from 2D microscope images of early embryogenesis, (Lecture Notes in Comp. Sci., 5567.) (Proc. 2nd Internat. Conference on Scale Space and Variational Methods in Computer Vision, Voss 2009), Springer, Berlin pp. 38–49. 
  3. Caselles, V., Kimmel, R., Sapiro, G., 10.1023/A:1007979827043, Internat. J. Comput. Vision 22 (1997), 61–79. Zbl0894.68131DOI10.1023/A:1007979827043
  4. Chen, Y., Vemuri, B. C., Wang, L., 10.1016/S0898-1221(00)00050-X, Comp. Math. Appl. 39 (2000), 131–149. Zbl0951.68556MR1742478DOI10.1016/S0898-1221(00)00050-X
  5. Corsaro, S., Mikula, K. , Sarti, A., Sgallari, F., 10.1137/060651203, SIAM J. Sci. Comput. 28 (2006), 6, 2248–2265. MR2272260DOI10.1137/060651203
  6. Frolkovič, P., Mikula, K., 10.1016/j.apnum.2006.06.002, Appl. Numer. Math. 57 (2007), 4, 436–454. MR2310759DOI10.1016/j.apnum.2006.06.002
  7. Frolkovič, P., Mikula, K., Peyrieras, N., Sarti, A., A counting number of cells and cell segmentation using advection-diffusion equations, Kybernetika 43 (2007), 6, 817–829. MR2388396
  8. Huttenlocher, D. P., Klanderman, G. A., Rucklidge, W. J., Comparing images using the Hausdorff distance, IEEE Trans. Pattern Analysis and Machine Intelligence 15 (1993), 9, xxx–xxx. 
  9. Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A., 10.1007/BF00379537, Arch. Rational Mech. Anal. 134 (1996), 275–301. Zbl0937.53029MR1412430DOI10.1007/BF00379537
  10. Krivá, Z., Mikula, K., Peyriéras, N., Rizzi, B., Sarti, A., Zebrafish early embryogenesis 3D image filtering by nonlinear partial differential equations, Medical Image Analysis. Submitted for publication. 
  11. Mikula, K., Peyriéras, N., Remešíková, M., Sarti, A., 3D embryogenesis image segmentation by the generalized subjective surface method using the finite volume technique, In: Proc. FVCA5 – 5th International Symposium on Finite Volumes for Complex Applications, Hermes Publ. Paris 2008. 
  12. Mikula, K., Remešíková, M., Finite volume schemes for the generalized subjective surface equation in image segmentation, Kybernetika 45 (2009), 4, xxx–xxx. MR2588630
  13. Mikula, K., Sarti, A., Parallel co-volume subjective surface method for 3D medical image segmentation, Parametric and Geometric Deformable Models: An application in Biomaterials and Medical Imagery, Vol. II, Springer Publishers, 2007, pp. 123–160. 
  14. Sarti, A., Malladi, R., Sethian, J. A., Subjective surfaces: A method for completing missing boundaries, In: Proc. National Academy of Sciences of the United States of America 12 (2000), 97, 6258–6263. Zbl0966.68214MR1760935
  15. Tassy, O., Daian, F., Hudson, C., Bertrandt, V., Lemaire, P., 10.1016/j.cub.2005.12.044, Currrent Biology 16 (2006), 345–358. DOI10.1016/j.cub.2005.12.044
  16. Yushkevich, P. A., Piven, J., Hazlett, H. Cody, Smith, R. Gimpel, Ho, S., Gee, J. C., Gerig, G., 10.1016/j.neuroimage.2006.01.015, Neuroimage 31 (2006), 3, 1116–28. DOI10.1016/j.neuroimage.2006.01.015
  17. Zanella, C., Campana, M., Rizzi, B., Melani, C., Sanguinetti, G., Bourgine, P., Mikula, K., Peyriéras, N., Sarti, A., 10.1109/TIP.2009.2033629, IEEE Trans. Image Process. 19 (2010), 3, 770–781. MR2756569DOI10.1109/TIP.2009.2033629
  18. Zhang, J. W., Han, G. Q., Wo, Y., Image registration based on generalized and mean Hausdorff distances, In: Proc. Fourth International Conference on Machine Learning and Cybernetics, Guangzhou 2005. 

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