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Counting number of cells and cell segmentation using advection-diffusion equations

Peter Frolkovič, Karol Mikula, Nadine Peyriéras, Alex Sarti (2007)

Kybernetika

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...

Curvature flows on surfaces

Michael Struwe (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Prompted by recent work of Xiuxiong Chen, a unified approach to the Hamilton-Ricci and Calabi flows on a closed, compact surface is presented, recovering global existence and exponentially fast asymptotic convergence from concentration-compactness results for conformal metrics.

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