Summary: Let \(Y^*(s)\) represent a Gaussian random field with location index \(s\in D\subset R^2\), and let \(Y(s)\) represent a binary random field on the same locations. We suppose that \(Y(s)\) is the indicator variable of the event \(Y^*(s)>c\) for some cutoff value \(c\). Moreover, we assume that \(Y(s)\), but not \(Y^*(s)\), is observable. This could model, for example, trees in a plantation that are observed to be alive or dead as a result of the latent build-up of a toxin. The purpose of this article is to evaluate the relationship between the correlation structure of the latent \(Y^*(s)\) and the observable \(Y(s)\). The results that we derive are relevant to the computer simulation of binary random fields.