The problem of supervised classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and factorised covariance matrices is considered. Unknown means and the common covariance matrix of the feature vector components are estimated from spatially correlated training samples assuming spatial correlation to be known. For the estimation of unknown parameters two methods, namely, maximum likelihood and ordinary least squares are used. The performance of the plug-in discriminant functions is evaluated by the asymptotic expansion of the misclassification error. A set of numerical calculations is done for the spherical spatial correlation function.