Novel method to obtain the optimal polygonal approximation of digital planar curves based on Mixed Integer Programming

Abstract

Polygonal approximations of digital planar curves are very useful for a considerable number of applications in computer vision. A great interest in this area has generated a huge number of methods for obtaining polygonal approximations. A good measure to compare these methods is known as Rosin’s merit. This measure uses the optimal polygonal approximation, but the state-of-the-art methods require a tremendous computation time for obtaining this optimal solution.We focus on the problem of obtaining the optimal polygonal approximation of a digital planar curve. Given N ordered points on a Euclidean plane, an efficient method to obtain M points that defines a polygonal approximation with the minimum distortion is proposed.The new solution relies on Mixed Integer Programming techniques in order to obtain the minimum value of distortion. Results, show that computation time for the new method dramatically decreases in comparison with state-of-the-art methods for obtaining the optimal polygonal approximation.