Abstract: Starting with an intuitive concept of “nearness” as a binary relation, semi-proximity spaces (sp-spaces) are defined. The restrictions on semi-proximity spaces are weaker than the restrictions on topological proximity spaces. Thus, semi-proximity spaces generalize classical topological spaces. We will use semi-proximity spaces to establish a formal relationship between the topological concepts of digital image processing and their continuous counterparts in ℝ n . This is possible, since ℝ n with the usual topology and digital images with their usual structure are sp-spaces. Examples of different semi-proximity relations on digital images are given which induce the usual connectedness on digital images. This is not possible in classical topology.
Publication Year: 1998
Publication Date: 1998-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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