Some results of Morse functions in digital images
Authors :
Ismet Karaca 1 , Tane Vergili 2 *, Gokhan Temizel 3 and Hatice Sevde Denizalti 4
Author Address :
1,3,4 Department of Mathematics, Ege University, 35040-Izmir, Turkey.
2 Department of Mathematics, Karadeniz Technical University, 61080-Trabzon, Turkey.
*Corresponding author.
Abstract :
In many years authors have adapted some notions of topology and combinatorial topology to the digital topology. In this paper we apply some definition of discrete Morse theory to the digital topology. We define a new definition of adjacency relation to show that digital subcomplexes are digitally homotopy equivalent. We conclude that if there is no digitally critical simplex in the digital interval $[m,n]_{\mathbb{Z}}$, then the digital subcomplexes $K(m)$ and $K(n)$ are digitally homotopy equivalent.
Keywords :
Digital morse theory, digital topology, digital simplicial complex.
DOI :
Article Info :
Received : December 05, 2019; Accepted : March 24, 2020.
