Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets, mainly based on the context of image retrieval and the basic image correspondence problem. Mathematical morphological procedures and set approximations in rough set theory have some clear parallels. Numerous initiatives have been made to connect rough sets with mathematical morphology. Numerous significant publications have been written in this field. Others attempt to show a direct connection between mathematical morphology and rough sets through relations, a pair of dual operations, and neighborhood systems. Rough sets are used to suggest a strategy to approximate mathematical morphology within the general paradigm of soft computing. A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology. This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of the morphological structures of dilation, erosion, opening, and closing. These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject. The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays. The foundations of mathematical morphology are covered in this article. After that, rough set theory ideas are taken into account, and their connections are examined. Finally, a suggested image retrieval application of the concepts from these two fields is provided.