An algorithm to compute any simple k-gon of a maximum area or perimeter inscribed in a region of interest

Abstract

Computational and mathematical models are research subjects for solving engineering, computer science, and computer vision problems. Image preprocessing usually needs to efficiently compute polygons related to some previously delimited region of interest. Most of the solved problems are limited to the search for some type of polygon with k sides (triangles, rectangles, squares, etc.) with maximum area, maximum perimeter, or similar. This paper presents a generic algorithm that computes in O(n5k) computational time the polygon of any number of sides (any simple k-gon) inscribed in a region of interest (in any closed contour without restrictions). The polygon obtained fulfills the requirements specified by the user: maximum area or perimeter or minimum area or perimeter. No previous work has been proposed to obtain any k-gon inscribed in any unconstrained contour. The algorithms and mathematical models are presented and explained, and the source code is available in a GitHub repository for research purposes.