A fundamental group for digital images

Gregory M Lupton; John Oprea; Nicholas A. Scoville

doi:10.1007/s41468-021-00067-1

A fundamental group for digital images

Gregory M Lupton
, John Oprea
, Nicholas A. Scoville

Cleveland State University
Ursinus College

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways from previously established versions of a fundamental group in the digital setting. Our development gives a prominent role to subdivision of digital images. We show that our fundamental group is preserved by subdivision.

Original language	English
Pages (from-to)	249-311
Number of pages	63
Journal	Journal of Applied and Computational Topology
Volume	5
Issue number	2
DOIs	https://doi.org/10.1007/s41468-021-00067-1
State	Published - Jun 1 2021

Keywords

Digital fundamental group
Digital image
Digital simple closed curve
Digital topology
Subdivision
Winding number

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10.1007/s41468-021-00067-1

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AU - Oprea, John

AU - Scoville, Nicholas A.

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AB - We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways from previously established versions of a fundamental group in the digital setting. Our development gives a prominent role to subdivision of digital images. We show that our fundamental group is preserved by subdivision.

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KW - Digital image

KW - Digital simple closed curve

KW - Digital topology

KW - Subdivision

KW - Winding number

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A fundamental group for digital images

Abstract

Keywords

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