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Eye fundus imaging is a useful, non-invasive tool in disease progress tracking, in early detection of disease and other cases. Often, the disease diagnosis is made by an ophthalmologist and automatic analysis systems are used only for support. There are several commonly used features for disease detection, one of them is the artery and vein ratio measured according to the width of the main vessels. Arteries must be separated from veins automatically in order to calculate the ratio, therefore, vessel classification is a vital step. For most analysis methods high quality images are required for correct classification. This paper presents an adaptive algorithm for vessel measurements without the necessity to tune the algorithm for concrete imaging equipment or a specific situation. The main novelty of the proposed method is the extraction of blood vessel features based on vessel width measurement algorithm and vessel spatial dependency. Vessel classification accuracy rates of 0.855 and 0.859 are obtained on publicly available eye fundus image databases used for comparison with another state of the art algorithms for vessel classification in order to evaluate artery-vein ratio (AV R). The method is also evaluated with images that represent artery and vein size changes before and after physical load. Optomed OY digital mobile eye fundus camera SmartscopeM5 PRO is used for image gathering.

Many diseases can be early detected from eye fundus images by several different features. One of the features is the artery and vein ratio. Width measurement is made on the main vessels. The aim of this automatization process is to create a fully automated method for eye fundus analysis. The fully automated system consists of blood vessel tree extraction and optic nerve disc detection in order to perform measurements at the standard place. Vessel tree extraction is complicated in some situations, so the vessel measurement algorithm is developed independently of the extracted blood vessel tree, and the tree is used only for direction enhancement and only when it is available. Vessel measurements are compared with manual measurements, performed by an expert. Automated measurements are not different from the expert’s measurements with the confidence level of 95%. For this investigation, the Optomed OY digital mobile eye fundus camera Smartscope M5 PRO was used, but the algorithm can be used on any type of eye fundus images.

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.

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.

In statistical image classification, it is usually assumed that feature observations given class labels are independently distributed [1] . Even in the case when training sample is formed by dependent feature observations, the feature observations to be classified are often assumed to be independent from training sample [2] , [3] . Proposed approach is based on the retraction of this assumption by considering the stationary Gaussian random field (GRF) model for features [4] . The conditional distribution of class label at unclassified location (pixel) is assumed to be dependent on its location spatial adjacency with spatial framework of training sample. For given training sample, the Bayes discriminant function (BDF) and plug-in BDF (PBDF) are proposed for classification. Performance of the proposed BDF and PBDF are tested and compared with ones ignoring spatial correlation among feature observations to be classified and training sample. In the first example, the restoration of the image of figure corrupted by the GRF is performed by pixels classification. In the numerous parametric structure cases, the advantage of proposed BDF against competing one is shown visually and is confirmed numerically. In the second example, three spatial sampling designs for training data are compared on the basis of actual error rate values of proposed PBDF.

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 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 BDFare 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.