A combinatorial technique for construction of triangular covers of digital objects

Abstract

The construction of a minimum-area geometric cover of a digital object is important in many fields of image analysis and computer vision. We propose here the first algorithm for constructing a minimum-area polygonal cover of a 2D digital object as perceived on a uniform triangular grid. The polygonal cover is triangular in the sense that its boundary consists of a sequence of edges on the underlying grid. The proposed algorithm is based on certain combinatorial properties of a digital object on a grid, and it computes the tightest cover in time linear in perimeter of the object. We present experimental results to demonstrate the efficacy, robustness, and versatility of the algorithm, and they indicate that the runtime varies inversely with the grid size. © 2014 Springer International Publishing.