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We address the problem of finding a wombling boundary in point data generatedby a general Poisson point process, a specific example of which is an LHC eventsample distributed in the phase space of a final state signature, with thewombling boundary created by some new physics. We discuss the use of Voronoiand Delaunay tessellations of the point data for estimating the local gradientsand investigate methods for sharpening the boundaries by reducing thestatistical noise. The outcome from traditional wombling algorithms is a set ofboundary cell candidates with relatively large gradients, whose spatialproperties must then be scrutinized in order to construct the boundary andevaluate its significance. Here we propose an alternative approach where wesimultaneously form and evaluate the significance of all possible boundaries interms of the total gradient flux. We illustrate our method with several toyexamples of both straight and curved boundaries with varying amounts of signalpresent in the data.

Finding Wombling Boundaries in LHC Data with Voronoi and Delaunay Tessellations