3D cell image segmentation by modified subjective surface method: Applied Mathematics ´19

Year, pages: 2020, 147 - 162

In this work, we focused on $3$D image segmentation where the segmented surface is reconstructed by the use of $3$D digital image information and information from thresholded $3$D image in a local neighbourhood. To this end, we applied a mathematical model based on the level set formulation and numerical method which is based on the so-called reduced diamond cell approach. The segmentation approach is based on surface evolution governed by a nonlinear PDE, the modified subjective surface equation. This is done by defining the input to the edge detector function as the weighted sum of norm of presmoothed $3$D image and norm of presmoothed thresholded $3$D image in a local neighbourhood. For the numerical discretization, we used a semi-implicit finite volume scheme. The method was applied to real data representing $3$D microscopy images of cell nuclei within the zebrafish pectoral fin.

Uba, M., Mikula, K., Krivá, Z., Nguyen, C., Savy, T., Kardash, E., Peyriéras, N. 2020. 3D cell image segmentation by modified subjective surface method: Applied Mathematics ´19. In Tatra Mountains Mathematical Publications, vol. 75, no.1, pp. 147-162. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0010

Uba, M., Mikula, K., Krivá, Z., Nguyen, C., Savy, T., Kardash, E., Peyriéras, N. (2020). 3D cell image segmentation by modified subjective surface method: Applied Mathematics ´19. Tatra Mountains Mathematical Publications, 75(1), 147-162. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0010

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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