Application of Bayes linear discriminant functions in image classification

摘要

In statistical image classification it is usually assumed that feature observations given class labels are independently distributed. Even in the case when training sample is formed by dependent feature observations, the feature observations to be classified are usually assumed to be independent from training sample. In this paper we propose the original method of the incorporation of spatial information into the per-pixel classifiers. Our approach is based on the retraction of the independence assumption by proposing stationary Gaussian random field (GRF) model for features. The conditional distribution of class label of observation to be classified is assumed to be dependent on its spatial adjacency within the spatial framework of the training sample. For a given training sample, plug-in version of the Bayes discriminant function (PBDF) is proposed for classification. Performance of the proposed PBDF is tested and compared with ones ignoring dependence among feature observations to be classified and training sample. For illustration the image of figure corrupted by the additive GRF is analyzed. The advantage of the proposed classifier against the competing one is shown visually and numerically in the first example. In the second example, three spatial sampling designs for training data are compared on the basis of the actual error rate values of the proposed PBDF. For the remotely sensed image, the advantage of the proposed classification method against popular unsupervised classification method is shown in terms of visual evaluation and empirical errors of misclassification.