3D cell image segmentation by modified subjective surface method

Abstract

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 neighborhood. 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 neighborhood.
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.