A Fundamental Group for Digital Images

Gregory Lupton; John Oprea; Nicholas Scoville

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arXiv · 1906.05976

A Fundamental Group for Digital Images

Gregory Lupton·John Oprea·Nicholas Scoville

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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.

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Gregory Lupton, John Oprea, Nicholas Scoville. 2019-06-14. A Fundamental Group for Digital Images. https://arxiv.org/abs/1906.05976

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