Vergili, Tane2024-07-122024-07-122019Vergili, T. (2019). The shortest length distance and the digital r-thickening on digital images. International Conference of Mathematical Sciences (ICMS 2019). s. 28.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2092A digital image X is a subset of the Cartesian product of the set of integers Z n. To study the features of X without constructing a topology on it, we impose a relation, ?, called an adjacency relation [1] on the points of it to adapt the fundamental concepts of topology such as connectedness, path connectedness, and continuity [2, 3]. Suppose X is a connected digital image, ? is an adjacency relation defined on it, and A is a subset of X. For a point x ? X, Boxer defined the shortest length distance from x to A [4]. Then the shortest length distance turns into a metric function on X by assuming A as a singleton subset of X. The main goal of this study is to measure the distance of two subsets of a connected digital image which is compatible with continuous functions. To do this, we consider this metric function on a connected digital image X and define the concept of r-thickening of a nonempty subset of X for a nonnegative integer r to define the distance between the subsets of X. This talk is about the recent progress of this studyenCC0 1.0 Universalinfo:eu-repo/semantics/openAccessDigital topologyHausdorff distanceMetric spaceArticle2828