Pattern Matching for sets of segments
Alon Efrat, Piotr Indyk, Suresh Venkatasubramanian

TL;DR
This paper introduces new algorithms for geometric pattern matching of segments and chains, improving efficiency and extending existing methods to handle translations and specific measures like coverage and Fréchet distance.
Contribution
It presents novel algorithms for segment similarity, coverage measures, and Fréchet distance under translations, with significant improvements in computational complexity.
Findings
Algorithms run in $O(n^3 ext{polylog} n)$ for general cases
Efficient $O(n^2 ext{polylog} n)$ algorithms for horizontal segments
First algorithm for Fréchet distance under general translations
Abstract
In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and measures that relate to collections of orthogonal line segments in the plane. Such collections arise naturally from problems in mapping buildings and robot exploration. We propose a new measure of segment similarity called a \emph{coverage measure}, and present efficient algorithms for maximising this measure between sets of axis-parallel segments under translations. Our algorithms run in time in the general case, and run in time for the case when all segments are horizontal. In addition, we show that when restricted to translations that are only vertical, the Hausdorff distance between two sets of horizontal segments…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Robotics and Sensor-Based Localization · Advanced Image and Video Retrieval Techniques
