The Prefix Fréchet Similarity

Abstract

We present the prefix Frechet similarity as a new measure for similarity of curves which is e.g. motivated by evacuation analysis and defined as follows. Given two (polygonal) curves T and \(T'\), we ask for two prefix curves of T and \(T'\) which have a Frechet distance no larger than a given distance threshold \(\delta \ge 0\) w.r.t. \(L_1\) metric such that the sum of the prefix curves is maximal. As parameterized Frechet measures as, e.g., the prefix Frechet similarity are highly unstable w.r.t. to the value of the distance threshold \(\delta \), we give an algorithm that computes exactly the profile of the prefix Frechet similarity, i.e., the complete functional relation between \(\delta \) and the prefix Frechet similarity of T and \(T'\). This is the first efficient algorithm for computing exactly the whole profile of a parametrized Frechet distance.