# A Fundamental Group for Digital Images

## TL;DR

This paper introduces a new fundamental group for digital images, constructed as a functor to groups, emphasizing subdivision preservation and differing from prior digital fundamental groups.

## Contribution

It presents a novel digital fundamental group that closely parallels the classical one, with a focus on subdivision invariance and fundamental differences from existing models.

## Key findings

- Fundamental group is preserved under subdivision.
- Constructs a functor from digital images to groups.
- Highlights key differences from previous digital fundamental groups.

## 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.