Fig. 1: Comparing different shape embedding.
From: Statistical analysis of spatial patterns in tumor microenvironment images
Two set A points (in green), and three set B points (in red) are distributed over the domain Ω. Distribution of red points are analyzed within a distance of r units from A objects (in gray). a For Ripley-based spatial analysis, boundary correction is necessary because the circles can extend beyond Ω. b When shapes are individually embedded via levelsets ϕ1 and ϕ2, boundary correction is no more necessary. However, the point lying in the intersection zone is still counted twice. c This is eliminated in the ensemble representation using a single levelset function ϕ to represent the shapes as an ensemble. Moreover, standard Ripley-based analysis (a) is restricted to point objects for the set A, while (b) and (c) can embed any closed form.
