Geodesic
4D Embryogenesis image analysis using PDE methods of image processing
Kybernetika, Tome 46 (2010) no. 2, pp. 226-259.

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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.
Classification : 35A99, 35L60, 65D18, 65M08, 68U10, 74S10, 92C55, 94A08
Keywords: image processing; embryogenesis; image analysis; finite volume method; image filtering; object counting; segmentation; partial differential equation 
@article{KYB_2010__46_2_a2,
     author = {Bourgine, Paul and \v{C}underl{\'\i}k, R\'obert and Drbl{\'\i}kov\'a-Sta\v{s}ov\'a, Olga and Mikula, Karol and Reme\v{s}{\'\i}kov\'a, Mariana and Peyri\'eras, Nadine and Rizzi, Barbara and Sarti, Alessandro},
     title = {4D {Embryogenesis} image analysis using {PDE} methods of image processing},
     journal = {Kybernetika},
     pages = {226--259},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2010},
     mrnumber = {2663599},
     zbl = {1198.94020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a2/}
}
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
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%0 Journal Article
%A Bourgine, Paul
%A Čunderlík, Róbert
%A Drblíková-Stašová, Olga
%A Mikula, Karol
%A Remešíková, Mariana
%A Peyriéras, Nadine
%A Rizzi, Barbara
%A Sarti, Alessandro
%T 4D Embryogenesis image analysis using PDE methods of image processing
%J Kybernetika
%D 2010
%P 226-259
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a2/
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Bourgine, Paul; Čunderlík, Róbert; Drblíková-Stašová, Olga; Mikula, Karol; Remešíková, Mariana; Peyriéras, Nadine; Rizzi, Barbara; Sarti, Alessandro. 4D Embryogenesis image analysis using PDE methods of image processing. Kybernetika, Tome 46 (2010) no. 2, pp. 226-259. http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a2/