An output-sensitive algorithm for the minimization of 2-dimensional String Covers

TL;DR

This paper introduces an output-sensitive algorithm for minimizing 2D string covers, extending the concept from linear strings to images, with applications in image processing, texture analysis, and crystallography.

Contribution

It generalizes string covers to two-dimensional data and presents an efficient algorithm for their minimization, enabling new applications in image and lattice data analysis.

Findings

Efficient algorithm for 2D string cover minimization

Applications in texture extraction and image compression

Enhanced analysis of lattice structures

Abstract

String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a string $C$ for which every letter of $T$ lies within some occurrence of $C$. String covers have been generalized in many ways, leading to \emph{k-covers}, \emph{$\lambda$-covers}, \emph{approximate covers} and were studied in different contexts such as \emph{indeterminate strings}. In this paper we generalize string covers to the context of 2-dimensional data, such as images. We show how they can be used for the extraction of textures from images and identification of primitive cells in lattice data. This has interesting applications in image compression, procedural terrain generation and crystallography.