Digital Topological Complexity of Digital Maps

2021/02/28 by Melih İs, Is, Melih, İsmet Karaca +1
Computer Science · #46M20 #54C15 #55M30 #55R10 #68U10 #Algebraic Topology (math.AT) #Digital Image Processing Techniques #FOS: Mathematics #I.4.9 #Medical Image Segmentation Techniques #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2103.00585

openalex publication_date 2021/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal differences in topological complexity computations of maps between digital images and topological spaces. Moreover, we emphasize the importance of the adjacency relation on the domain and the range of a digital map in these computations.

Related

• Certain topological methods for computing digital topological complexity
• Discrete version of topological complexity of maps
• The Topological Complexity of Spaces of Digital Jordan Curves
• Essential concepts of digital topology (digital k-connectivity and k-adjacencis for digital products)
• Algorithms for Computing Topological Invariants in 2D and 3D Digital Spaces