On contour representation of two dimensional patterns

TL;DR

This paper introduces a new formal contour-based representation for 2D patterns, along with algorithms for verification, aiming to improve software tools handling two-dimensional words across various computer science domains.

Contribution

It presents a novel contour-based formalism for 2D patterns and efficient algorithms for correctness verification, with potential applications in software tool development.

Findings

Developed a new formal representation based on contours

Created algorithms to verify correctness of the contour representation

Discussed applications in software tools for 2D words

Abstract

Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we present the basis of a new formal representation of two-dimensional patterns based on contours and their compositions. Then, we present efficient algorithms to verify correctness of the contour-representation. Finally, we briefly discuss possible applications, in particular using them as a basic instrument in developing software tools for handling two dimensional words.