CNCUR : A simple 2D Curve Reconstruction Algorithm based on constrained neighbours
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
Given a planar point set S ∈ R2 (where S = {v1, . . . , vn}) sampled from an unknown curve Σ, the goal is to obtain a piece-wise linear reconstruction the curve from S that best approximates Σ. In this work, we propose a simple and intuitive Delaunay triangulation(DT)-based algorithm for curve reconstruction. We start by constructing a Delaunay Triangulation (DT) of the input point set. Next, we identify the set of edges, ENp in the natural neighborhood of each point p in the DT. From the set of edges in ENp, we retain the first two shorter edges connected to each point. To take care of open curves, one of the retained edges has to be removed based on a parameter δ. Here, δ is a parameter used to eliminate the longer edge based on the allowable ratio between the maximum and minimum edge lengths. Our algorithm inherently handles self-intersections, multiple components, sharp corners, and different levels of Gaussian noise, all without requiring any parameters, pre-processing, or post-processing.
Description
CCS Concepts: Computing methodologies → Shape modeling
@inproceedings{10.2312:pg.20241329,
booktitle = {Pacific Graphics Conference Papers and Posters},
editor = {Chen, Renjie and Ritschel, Tobias and Whiting, Emily},
title = {{CNCUR : A simple 2D Curve Reconstruction Algorithm based on constrained neighbours}},
author = {Antony, Joms and Reghunath, Minu and Muthuganapathy, Ramanathan},
year = {2024},
publisher = {The Eurographics Association},
ISBN = {978-3-03868-250-9},
DOI = {10.2312/pg.20241329}
}