  Minkowski functionals quantify the morphology of smooth random fields. They
are widely used to probe statistical properties of cosmological fields.
Analytic formulae for ensemble expectations of Minkowski functionals are well
known for Gaussian and mildly non-Gaussian fields. In this paper we extend the
formulae to composite fields which are sums of two fields and explicitly derive
the expressions for the sum of uncorrelated mildly non-Gaussian and Gaussian
fields. These formulae are applicable to observed data which is usually a sum
of the true signal and one or more secondary fields that can be either noise,
or some residual contaminating signal. Our formulae provide explicit
quantification of the effect of the secondary field on the morphology and
statistical nature of the true signal. As examples, we apply the formulae to
determine how the presence of Gaussian noise can bias the morphological
properties and statistical nature of Gaussian and non-Gaussian CMB temperature
maps.
