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The classical case of morphological segmentation is based on the watershed transform, constructed by flooding the gradient image, which is seen as a topographic surface, with constant height speed. Changing the flooding criteria, (e.g. constant-speed height, area or volume) yields different segmentation results. In the field of PDEs and curve evolution the classic watershed transform can be modelled as the solution of an eikonal PDE. In this paper we model the watershed segmentation based on a volume flooding criterion via a different eikonal PDE. Then we solve this PDE using the fast marching method, which is a specific algorithm from the methodology of level sets. In addition, we attempt to exploit the advantages of image segmentation using PDE-based volume flooding over the classic height flooding.