Subdivision of Maps of Digital Images
| Autor: | Gregory Lupton, John Oprea, Nicholas A. Scoville |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Computational Theory and Mathematics
FOS: Mathematics Algebraic Topology (math.AT) Discrete Mathematics and Combinatorics Mathematics - Combinatorics (Primary) 54A99 55M30 55P05 55P99 (Secondary) 54A40 68R99 68T45 68U10 Combinatorics (math.CO) Geometry and Topology Mathematics - Algebraic Topology Theoretical Computer Science |
| Popis: | With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as the fundamental group are invariants of homotopy type. In the digital setting, however, the usual notion of homotopy leads to a very rigid invariance that does not correspond well with the topological notion of homotopy invariance. In this paper, we establish fundamental results about subdivision of maps of digital images with $1$- or $2$-dimensional domains. Our results lay the groundwork for showing that the digital fundamental group is an invariant of a much less rigid equivalence relation on digital images, that is more akin to the topological notion of homotopy invariance. Our results also lay the groundwork for defining other invariants of digital images in a way that makes them invariants of this less rigid equivalence. 40 pages, 14 figures |
| Databáze: | OpenAIRE |
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