On megaparsec scales the Universe is permeated by an intricate filigree of clusters,
filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical
and hierarchical history it is crucial to identify objectively its complex morphological
components. One of the most characteristic aspects is that of the dominant underdense
Voids, the product of a hierarchical process driven by the collapse of minor voids
in addition to the merging of large ones. In this study we present an objective void
finder technique which involves a minimum of assumptions about the scale, structure
and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based
upon the Watershed Transform, a well-known technique for the segmentation of images.
Importantly, the technique has the potential to trace the existing manifestations
of a void hierarchy. The basic watershed transform is augmented by a variety of correction
procedures to remove spurious structure resulting from sampling noise. This study
contains a detailed description of the WVF. We demonstrate how it is able to trace
and identify, relatively parameter free, voids and their surrounding (filamentary
and planar) boundaries. We test the technique on a set of Kinematic Voronoi models,
heuristic spatial models for a cellular distribution of matter. Comparison of the
WVF segmentations of low noise and high noise Voronoi models with the quantitatively
known spatial characteristics of the intrinsic Voronoi tessellation shows that the
size and shape of the voids are succesfully retrieved. WVF manages to even reproduce
the full void size distribution function.