Following a curve with the discrete Fréchet distance

Following a curve with the discrete Fréchet distance

A Middle Curve Based on Discrete Fréchet Distance

Given a set of polygonal curves we seek to find a “middle curve” that represents the set of curves. We ask that the middle curve consists of points of the input curves and that it minimizes the discrete Fréchet distance to the input curves. We develop algorithms for three different variants of this problem.

Approximability of the Discrete Fréchet Distance

The Fréchet distance is a popular and widespread distance measure for point sequences and for curves. About two years ago, Agarwal et al [SIAM J. Comput. 2014] presented a new (mildly) subquadratic algorithm for the discrete version of the problem. This spawned a flurry of activity that has led to several new algorithms and lower bounds. In this paper, we study the approximability of the discre...

Computing the Discrete Fréchet Distance with Imprecise Input

We consider the problem of computing the discrete Fréchet distance between two polygonal curves when their vertices are imprecise. An imprecise point is given by a region and this point could lie anywhere within this region. By modelling imprecise points as balls in arbitrary fixed dimension, we present an algorithm for this problem that returns in time O(mn log(mn)) the Fréchet distance lower ...

Intermittent Map Matching with the Discrete Fréchet Distance

In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with the Fréchet distance matching the edges of the path as well. Here, we formally define the discrete map matching problem based on the discrete Fréchet distanc...