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Finding a Curve in a Point Set (1405.0762v1)
Published 5 May 2014 in cs.CG and cs.DS
Abstract: Let $P$ be a polygonal curve in $\mathbb{R}D$ of length $n$, and $S$ be a point set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that its Fr\'echet distance from $P$ is less than a given $\varepsilon$. In this paper, we consider this problem with the added freedom to transform the input curve $P$ by translating it, rotating it, or applying an arbitrary affine transform. We present exact and approximation algorithms for several variations of this problem.