Digitalna topologija na grafih

Drusany, Jakob (author), Pavešić, Petar (mentor)

V delu obravnavajte vprašanje, ali je mogoče grafe, ki opisujejo digitalizirane slike, opremiti s kompatibilno topologijo v smislu, da se za poljuben del slike povezanost induciranega podgrafa ujema s topološko povezanostjo. Za osnovo vzemite članek "D. Nogly, M. Schladt. Digital Topology on graphs. Computer vision and image understanding, Vol. 63 (No. 2): 394 - 396}".

• Language: Slovenian
• Keywords: procesiranje slik, simplicialni kompleksi, topologija aleksandrova, teorija grafov
• Work type: Bachelor thesis/paper
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2024
• PID: 20.500.12556/RUL-162181
• Publication date in RUL: 19.09.2024

Secondary language

• Language: English
• Title: Digital topology on graphs

Abstract

In your thesis consider the question of whether it is possible to equip graphs describing digital images with a compatible topology in the sense that for any part of the image the connectivity of the induced subgraph matches the topological connectivity. Base your thesis on the article "D. Nogly, M. Schladt. Digital Topology on graphs. Computer vision and image understanding, Vol. 63 (No. 2): 394 - 396}''.

• Keywords: image processing, simplicial complexes, Alexandrov topology, graph theory