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Spatial Classification Rule with Distance (SCRD) method is used in two dimensional coordinate system, which limits the usage of existing spatial information in MRI, CT and other three dimensional (layered) images. The SCRD method is extended to be applied in three dimensional coordinate space. Artificial experiment is performed in order to show ability to use SCRD method with three dimensional medical or other similar images where training sample is available.

When using Spatial Correlation Rule with Distance (SCRD) the selection of the neighborhood scheme influences classification accuracy. Spatial dependency in different situations remains at various distances, so, according to this, in applications it is important to choose a suitable neighborhood scheme. In the earlier papers of the authors, the nearest neighbor scheme was used. In this paper, several different neighborhood schemes are examined by large experiment.

In this paper the remote sensed image classification example using spacial classification rule with distance (SCRD) is examined. This supervised classification method was first presented in paper [11]. This method is improved version of earlier method PBDF [4, 10, 9], during the classification it incorporates more spatial information. The advantage of this method is its ability to classify data which is corrupted by Gaussian random field and it is typical to remotely sensed images classified in this letter which are corrupted by clouds. Classification accuracy is compared with earlier method and with other commonly used supervised classification methods.

In this paper spatial classification rules based on Bayes discriminant functions are considered. The novelty of this work is that the statistical supervised classification method is improved by extending the influence of spatial correlation between observation to be classified and training sample. Such methods are used for data containing spatially correlated noise. Method accuracy is tested experimentally on artificially corrupted images. This classification rule with distance based conditional distribution for class label shows advantage against other classification rule ignoring such influence and against other commonly used supervised classification methods.

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.

In statistical image classification it is usually assumed that feature observations given labels are independently distributed. We have retracted this assumption by proposing stationary Gaussian random field (GRF) model for features observations. Conditional distribution of label of observation to be classified is assumed to be dependent on its spatial adjacency with training sample spatial framework. Perfomance of the Bayes discriminant function (BDF) and performance of plug-in BDF are tested and are compared with ones ignoring spatial correlation among feature observations.For illustration image of figure corrupted by additive GRF is analyzed. Advantage of proposed BDF against competing ones is shown visually and numerically.