Obtaining the user-defined polygons inside a closed contour with holes

Abstract

In image processing, computer vision algorithms are applied to regions bounded by closed contours. These contours are often irregular, poorly defined, and contain holes or unavailable areas inside. A common problem in computational geometry includes finding the k-sided polygon (k-gon) of maximum area or maximum perimeter inscribed within a contour. This paper presents a generic method to obtain user-defined polygons within a region. Users can specify the number k of sides of the polygon to obtain. Additionally, users can also decide whether the calculated polygon should be the largest in area or perimeter. This algorithm produces a polygon or set of polygons that can be used to segment an image, allowing only relevant areas to be processed. In a real-world application, the validity and versatility of the proposed method are demonstrated. In addition, the source code developed in Java and Python is available in a GitHub repository so that researchers can use it freely.