Parametric Estimation of a Boolean Random Field

We develop generalized method of moments estimators to estimate the parameters of a two-dimensional Boolean random field from measurements made on the coverage process induced on a straight line in the field. This is distinct from earlier studies e.g. P. Hall (1988), I. Molchanov and D. Stoyan (2004), where the parameters of a two-dimensional Boolean field are obtained from the coverage properties of a two-dimensional set. This problem has applications in radio-active field monitoring.