Subdivision of Maps of Digital Images

Authors

Gregory Lupton, Cleveland State UniversityFollow
John F. Oprea, Cleveland State UniversityFollow
Nicholas A. Scoville, Ursinus College

Document Type

Article

Publication Date

4-2022

Publication Title

Discrete and Computational Geometry

Abstract

A digital image is a finite set of integer lattice points in an ambient Euclidean space together with a suitable adjacency relation between points. Subdivision, which is a process of enlarging a digital image in the photographic sense, provides a basic tool for operating with digital images. But given a map of digital images, there is as yet no general way to define a map of their subdivisions that might reasonably be called a subdivision of the map. In this paper, we construct such maps of subdivisions when the map of digital images has a 1- or 2-dimensional domain. From our constructions we deduce path covering and homotopy covering results that play a role in our development of the digital fundamental group.

Comments

This work was partially supported by grants from the Simons Foundation: (#209575 to Gregory Lupton and #244393 to John Oprea).

Repository Citation

Lupton, Gregory; Oprea, John F.; and Scoville, Nicholas A., "Subdivision of Maps of Digital Images" (2022). Mathematics and Statistics Faculty Publications. 345.
https://engagedscholarship.csuohio.edu/scimath_facpub/345

DOI

10.1007/s00454-021-00350-z

Volume

67

Issue

3