Coding cells of digital spaces: a framework to write generic digital topology algorithms

TL;DR

This paper introduces a concise coding framework for cells in n-dimensional grids, enabling efficient, dimension-independent digital topology algorithms applicable to various digital image structures.

Contribution

It presents a novel, generic coding scheme for digital cells that simplifies implementation of topology algorithms across dimensions and image types.

Findings

Framework is efficient and dimension-independent

Algorithms are straightforward to implement and benchmarked

Supports various digital topology structures like surfaces and cubical complexes

Abstract

This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of multidimensional images (e.g. regions, digital surfaces, cubical cell complexes) have then a common and compact representation. Moreover, algorithms have a straightforward and efficient implementation, which is independent from the dimension or sizes of digital images. We illustrate that point with generic hypersurface boundary extraction algorithms by scanning or tracking. This framework has been implemented and basic operations as well as the presented applications have been benchmarked.