Finding the largest area rectangle of arbitrary orientation in a closed contour

For many software applications, it is sometimes necessary to find the rectangle of largest area inscribed in a polygon, in any possible direction. Thus, given a closed contour C, we consider approximation algorithms for the problem of finding the largest area rectangle of arbitrary orientation that is fully contained in C. Furthermore, we compute the largest area rectangle of arbitrary orientation in a quasi-lattice polygon, which models the C contour. In this paper, we propose an approximation algorithm that solves this problem with an Oðn 3 Þ computational cost, where n is the number of vertices of the polygon. There is no other algorithm having lower computational complexity regardless of any constraints. In addition, we have developed a web application that uses the proposed algorithm. Many Computer Vision algorithms focus on parts of an image, instead of processing the whole image. These Region of Interest (ROI) are usually sub-images with basic shapes [1], mainly rectangles. However, in many cases the regions are available as irregular polygons with many vertices and it is essential to compute the largest area rectangle contained in them. The algorithm developed and proposed in this paper derives from the need for specific practical applications developed in the field of food technology. The most representative muscle in a ripening meat piece is automatically segmented with active contours by magnetic resonance imaging (MRI), a non-destructive, non-invasive method [2,3]. The shape of this muscle is represented as a closed polygon. Then, computational textures features are obtained from these extracted muscles, whereas texture algorithms work over rectangular ROIs [4]. Therefore, the aim of this paper is to compute the largest of these ROIs, and thus have it be more representative for the study of product quality. The problem of finding the largest area axis-aligned rectangle contained in a convex polygon was considered by Fischer and Höffgen [5]: given a convex polygon of n vertices (S), compute the rectangle R & S with a maximum area whose sides are parallel to the x-axis and y-axis; their approach solved the problem in Oðlog 2 nÞ time. Later, in [6] this problem was solved in Oðlog nÞ time. The restriction of the problem for convex polygons was removed by Daniels et al. [7], computing the largest area axis-parallel rectangle in an n vertex general polygon in Oðnlog 2 nÞ time. Later, the authors Boland and Urrutia [8], showed how to solve the problem …