Topological Approaches for Theoretical Mathematical Morphology

Marzouk, Eman; Maghrabi, Ahmed; ElGhawalby, Hewayda

doi:10.21608/ajbas.2023.178049.1134

Topological Approaches for Theoretical Mathematical Morphology

Document Type : Original Article

Authors

¹ Department of Physics and Engineering Mathematics, Faculty of Engineering, Port Said University, Egypt.

² Department of Mathematics, Faculty of Science, Kafrelsheikh University, Egypt.

³ Port Said University, Faculty of Engineering, Physics and Engineering Mathematics Department, Egypt

10.21608/ajbas.2023.178049.1134

Abstract

the mathematical morphology was originally developed to analyze and process binary image using the concepts and operations. Sets in mathematical morphology represented the shapes which were manifested on binary or gray images. The set of all the black pixels in a black and white image, constitutes a complete description of the binary image. In this paper, a novel point of view for mathematical morphology via topological concepts is proposed. And, the concepts of set theory and topological spaces will be imported to mathematical morphology. Furthermore, several topological spaces using morphological point of view are presented; by giving definitions for the families of sets that generates each space. we will first discuss the concept of morphological topological spaces, more topological structures and based on examples. Also, we will introduce new concepts based on these principles and definitions. Further, their topological properties are studied. we presented several topological spaces using morphological point of view; namely, morphological topological spaces, morphological co-topological spaces, morphological semi-topological spaces, morphological α-topological spaces and morphological pre-topological spaces.

Keywords