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Hadwiger integrals employ the intrinsic volumes as measures for integrationof real-valued functions. We provide a formula for the expected values ofHadwiger integrals of Gaussian-related random fields. The expected Hadwigerintegrals of random fields are both theoretically interesting and potentiallyuseful in applications such as sensor networks, image processing, and celldynamics. Furthermore, combining the expected integrals with a functionalversion of Hadwiger's theorem, we obtain expected values of more generalvaluations on Gaussian-related random fields.

Hadwiger Integration of Random Fields