核心概念
Investigating the Fréchet edit distance problem for polygonal curves, exploring various edit operations and their implications.
摘要
The content delves into the Fréchet edit distance problem, focusing on shape matching between polygonal curves. It defines the problem, explores variants, presents algorithms for discrete and continuous cases, discusses hardness results, and reviews related work. The article emphasizes the sensitivity of Fréchet distance to outliers in real-world data.
Introduction
Motivation behind shape matching.
Use of continuous and discrete Fréchet distances.
The Fréchet Edit Distance
Modifications and alternatives to address sensitivity issues.
Results
Polynomial time algorithms for various variants.
DAG Complexes
Definition and application in solving the problem efficiently.
Continuous Fréchet Distance
Algorithms for deletion-only case with insights on minimum vertex curves.
Insertion Only
Minimum vertex curves concept explained.
Minimum Vertex Curves
Definition and theorem regarding computation efficiency.
Canonical Inserted Subcurves
Set definition for inserted subcurves in curve matching.
統計資料
Given two polygonal curves π and σ...
We provide polynomial time algorithms...
For this basic problem we consider a number...
引述
"We define and investigate the Fréchet edit distance problem."
"Adding even a single point to one of the input curves can increase their distance by an arbitrarily high amount."