3D Cell Image Segmentation by Modified Subjective Surface Method

In this work, we focused on 3D image segmentation where the segmented surface is reconstructed by the use of 3D digital image information and information from thresholded 3D 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 3D image and norm of presmoothed thresholded 3D 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 3D microscopy images of cell nuclei within the zebrafish pectoral fin.