A heuristic homotopic path simplification algorithm

Abstract

We study the well-known problem of approximating a polygonal path P by a coarse one, whose vertices are a subset of the vertices of P. In this problem, for a given error, the goal is to find a path with the minimum number of vertices while preserving the homotopy in presence of a given set of extra points in the plane. We present a heuristic method for homotopy-preserving simplification under any desired measure for general paths. Our algorithm for finding homotopic shortcuts runs in O( mlog(n + m) + nlogn log(nm) + k) time, where k is the number of homotopic shortcuts. Using this method, we obtain an O(n 2 + mlog(n + m) + nlogn log(nm)) time algorithm for simplification under the Hausdorff measure. © 2011 Springer-Verlag.