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In this paper supervised classification method is proposed. It is based on Bayes discriminant functions (BDF) and it deals with the problem of optimal classification for images, which are corrupted by natural phenomenon such as cloud, smoke or fog. Solving such a problem is very important when we have remotely sensed information, which very often is corrupted by clouds. For example, the remotely sensed images from the territory of Lithuania are very often corrupted by clouds. The idea of classification, using BDF with incorporated spatial dependency between the observation to be classified and the training sample is presented in earlier works of the author. The novelty of this paper is the method how to use these methods for the real situation, i.e. for the remotely sensed image which is naturally covered by clouds. Visual and numerical results are presented in this paper, which show the advantage of this method against BDF ignoring spatial dependency between training sample and observation to be classified and against the method using grey level cooccurrence matrices.

In this paper, spatial data specified by auto-beta models is analysed by considering a supervised classification problem of classifying feature observation into one of two populations. Two classification rules based on conditional Bayes discriminant function (BDF) and linear discriminant function (LDF) are proposed. These classification rules are critically compared by the values of the actual error rates through the simulation study.

In this paper the problem of classification of an observation into one of two Gaussian populations with different means and common variance is considered in the case when equicorrelated training sample is given. Unknown means and common variance are estimated from training sample and these estimators are pluged in the Bayes discriminant function. The maximum likelihood estimators are used. The approximation of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of that approximation for various values of correlation is presented.

In this paper we use the pluged-in Bayes discriminant function (PBDF) for classification of spatial Gaussian data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. The pluged-in Bayes discriminant function is constructed by using ML estimators of unknown mean and anisotropy ratio parameters. We focus on the asymptotic approximation of expected error rate (AER) and our aim is to investigate the effects of two different spatial sampling designs (based on increasing and fixed domain asymptotics) on AER.

In image classification often occur such situations, when images in some level are corrupted by additive noise. Such noise in image classification can be modeled by Gaussian random fields (GRF). In image classification supervised and unsupervised methods are used. In this paper we compare our proposed supervised classification methods based on plugin Bayes discriminant functions (PBDF) (see [6] and [11]) with unsupervised classification method based on grey level co-occurrence matrix (GLCM) (see e.g. [8] and [1]). The remotely sensed image is used for classification (USGS Earth Explorer). Also GRF with different spatial correlation range are generated and added to the original remotely sensed image. Such situation can naturally occur during forest fire, when smoke covers some territory. These images are used for classification accuracy examination.