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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 Frechet distance. For both these distance measures, we present polynomial-time algorithms for this problem.
Simplification is one of the fundamental operations used in geoinformation science (GIS) to reduce size or representation complexity of geometric objects. Although different simplification methods can be applied depending on ones purpose, a simplific
In the classic polyline simplification problem we want to replace a given polygonal curve $P$, consisting of $n$ vertices, by a subsequence $P$ of $k$ vertices from $P$ such that the polygonal curves $P$ and $P$ are as close as possible. Closeness is
In this paper we study a wide range of variants for computing the (discrete and continuous) Frechet distance between uncertain curves. We define an uncertain curve as a sequence of uncertainty regions, where each region is a disk, a line segment, or
We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a se
We study the complexity of clustering curves under $k$-median and $k$-center objectives in the metric space of the Frechet distance and related distance measures. Building upon recent hardness results for the minimum-enclosing-ball problem under the