Image Classification Based on Bayes Discriminant Functions

Abstract

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.