Continuous Choquet integrals with respect to random sets with applications to landmine detection

Abstract

A hit-miss transform is defined using Choquet integrals with respect to random sets. In this context, random sets represent random shapes defined on the plane. Random sets are characterised by their capacity functional. Capacity functional is fuzzy measures. Choquet integrals with respect to random sets are interpreted as stochastic morphological operations. Specifically, the integrals represent the average probability that sets either intersect or are contained in the random sets. Formulas are defined for random erosions and dilations of disks and annuli with Gaussian radii. Applications to landmine detection are given.