Neighborhood Morphological Operators and Accuracy Measures for Information Systems

In the context of information systems, mathematical morphology can be applied to diverse tasks like as image analysis and pattern recognition. It provides a set of powerful tools for processing and analyzing data, particularly in fields like computer vision, medical imaging, remote sensing, and document processing. By applying morphological operations to data sets, information systems can extract useful features, detect patterns, and enhance the quality of information for further analysis and decision-making. This paper is devoted to introducing and studying a topological perspective for the two main operators of mathematical morphology. Based on the concept of a neighborhood, a system of neighborhood structure elements is constructed. The new system is used to define the two main operators of mathematical morphology, namely neighborhood-dilation and neighborhood-erosion. Moreover, the properties of the proposed mathematical morphological operators are deduced and proven. Furthermore, an empirical information system is used to experiment with the proposed operators and the results are compared with those derived from rough set theory. Finally, two novel accuracy measurements are introduced using the concept of the proposed neighborhood morphological operators; namely the morphological accuracy and weighted morphological accuracy. Compared with the concepts derived from rough set theory, the experimental results are relatively similar.