Global Curve Simplification

Kerkhof, Mees van de; Kostitsyna, Irina; Löffler, Maarten; Mirzanezhad, Majid; Wenk, Carola

doi:10.4230/lipics.esa.2019.67

Cited by 4 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a large volume of foundational previous work in the area of curve simplification [4], including work on vertex-constrained simplification, such as the well-known algorithms by Ramer and by Douglas and Peucker [16,33] using the Hausdorff distance, by Imai and Iri [22] using either the Hausdorff or the Fréchet distance, by Agarwal et al [3] using the Fréchet distance, and various improvements and related approaches [7,8,10,15,20,21,30,35]. In particular, the basic approach of the Imai-Iri algorithm involves computing the shortcut graph, which captures all the possible simplifications of a curve, and then finding a shortest path through the graph in terms of the number of edges from the start node to the end node, thus finding the simplification with fewest edges.…”

Section: Introductionmentioning

confidence: 99%

Uncertain Curve Simplification

Buchin¹,

Löffler²,

Попов³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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 Fréchet distance. For both these distance measures, we present polynomial-time algorithms for this problem.

show abstract