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Minkowski functionals quantify the morphology of smooth random fields. Theyare widely used to probe statistical properties of cosmological fields.Analytic formulae for ensemble expectations of Minkowski functionals are wellknown for Gaussian and mildly non-Gaussian fields. In this paper we extend theformulae to composite fields which are sums of two fields and explicitly derivethe expressions for the sum of uncorrelated mildly non-Gaussian and Gaussianfields. These formulae are applicable to observed data which is usually a sumof the true signal and one or more secondary fields that can be either noise,or some residual contaminating signal. Our formulae provide explicitquantification of the effect of the secondary field on the morphology andstatistical nature of the true signal. As examples, we apply the formulae todetermine how the presence of Gaussian noise can bias the morphologicalproperties and statistical nature of Gaussian and non-Gaussian CMB temperaturemaps.

Minkowski Functionals for composite smooth random fields