Geodesic
Counting number of cells and cell segmentation using advection-diffusion equations
Kybernetika, Tome 43 (2007) no. 6, pp. 817-829.

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We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical advection-diffusion equation which gives us at a certain scale the desired information on the number of cells. For solving the problems computationally we use flux-based finite volume level set method developed by Frolkovič and Mikula in [FM1] and semi-implicit co-volume subjective surface method given in [CMSSg, MSSgCVS, MSSgchapter]. Computational experiments on testing and real 2D and 3D embryogenesis images are presented and the results are discussed.
Classification : 35K55, 35K57, 65M60, 74S10, 92C37, 92C55
Keywords: image processing; partial differential equations; nonlinear advection-diffusion equations; flux-based level set method; subjective surface method; embryogenesis 
@article{KYB_2007__43_6_a6,
     author = {Frolkovi\v{c}, Peter and Mikula, Karol and Peyri\'eras, Nadine and Sarti, Alex},
     title = {Counting number of cells and cell segmentation using advection-diffusion equations},
     journal = {Kybernetika},
     pages = {817--829},
     publisher = {mathdoc},
     volume = {43},
     number = {6},
     year = {2007},
     mrnumber = {2388396},
     zbl = {1140.35468},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a6/}
}
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Frolkovič, Peter; Mikula, Karol; Peyriéras, Nadine; Sarti, Alex. Counting number of cells and cell segmentation using advection-diffusion equations. Kybernetika, Tome 43 (2007) no. 6, pp. 817-829. http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a6/