  We address the problem of finding a wombling boundary in point data generated
by a general Poisson point process, a specific example of which is an LHC event
sample distributed in the phase space of a final state signature, with the
wombling boundary created by some new physics. We discuss the use of Voronoi
and Delaunay tessellations of the point data for estimating the local gradients
and investigate methods for sharpening the boundaries by reducing the
statistical noise. The outcome from traditional wombling algorithms is a set of
boundary cell candidates with relatively large gradients, whose spatial
properties must then be scrutinized in order to construct the boundary and
evaluate its significance. Here we propose an alternative approach where we
simultaneously form and evaluate the significance of all possible boundaries in
terms of the total gradient flux. We illustrate our method with several toy
examples of both straight and curved boundaries with varying amounts of signal
present in the data.
