Fast guaranteed polygonal approximations of closed digital curves

Abstract

We present in this paper a new non-parametric method for polygonal approximations of digital curves. In classical polygonal approximation algorithms, a starting point is randomly chosen on the curve and heuristics are used to ensure its effectiveness. We propose to use a new canonical representation of digital curves where no point is privileged. We restrict the class of approximation polygons to the class of digital polygonalizations of the curve. We describe the first algorithm which computes the polygon with minimal Integral Summed Squared Error in the class in both linear time and space, which is optimal, independently of any starting point. © Springer-Verlag Berlin Heidelberg 2005.