Uncertain Curve Simplification

TL;DR

This paper addresses polygonal curve simplification under uncertainty by developing polynomial-time algorithms that find the shortest subsequence ensuring valid simplification under Hausdorff or Fréchet distances, despite uncertain point locations.

Contribution

It introduces the first polynomial-time algorithms for uncertain curve simplification considering various uncertainty regions and distance measures.

Findings

Algorithms work for disks, line segments, convex polygons, and discrete points.

Valid simplifications are guaranteed under all possible true locations.

Efficient solutions for both Hausdorff and Fréchet distances.

Abstract

We study the problem of polygonal curve simplification under uncertainty, where instead of a sequence of exact points, each uncertain point is represented by a region, which contains the (unknown) true location of the vertex. The regions we consider are disks, line segments, convex polygons, and discrete sets of points. We are interested in finding the shortest subsequence of uncertain points such that no matter what the true location of each uncertain point is, the resulting polygonal curve is a valid simplification of the original polygonal curve under the Hausdorff or the Fr\'echet distance. For both these distance measures, we present polynomial-time algorithms for this problem.