Estimate of the cell number growth rate using PDE methods of image processing and time series analysis

We introduce a method how to estimate mathematically and computationally and how to analyse statistically the growth rate of the num- ber of cells in development of the zebrafish embryo. Our method is based on analysis of 3D confocal image sequences and consists of four basic steps. First, we filter images by the geodesic mean curvature flow (GMCF) method. Then we use the flux-based level set center detection (FBLSCD) to find the approximate positions and number of the nuclei centers. In the third step we correct FBLSCD result by image segmentation algorithm based on the subjective surface (SUBSURF) method. Finally, we understand the nuclei numbers extracted by the image processing algoritmic chain as a measure- ments and apply the statistical methods of the time series analysis to estimate trend of the cell number growth rate. We apply the developed method to the sequences of real 3D images acquised in vivo at early stages of zebrafish embryogenesis.