# Parametric Curve Reconstruction from Point Clouds using Minimization Techniques

## Fecha

2013

## Título de la revista

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## Título del volumen

## Editor

SCITEPRESS

## Resumen

Smooth (C1-, C2-,...) curve reconstruction from noisy point samples is central to reverse engineering, medical imaging, etc -- Unresolved issues in this problem are (1) high computational expenses, (2) presence of artifacts and outlier curls, (3) erratic behavior at self-intersections and sharp corners -- Some of these issues are related to non-Nyquist (i.e. sparse) samples -- Our work reconstructs curves by minimizing the accumulative distance curve cs. point sample -- We address the open issues above by using (a) Principal Component Analysis (PCA) pre-processing to obtain a topologically correct approximation of the sampled curve -- (b) Numerical, instead of algebraic, calculation of roots in point-to-curve distances -- (c) Penalties for curve excursions by using point cloud to - curve and curve to point cloud -- (d) Objective functions which are economic to minimize -- The implemented algorithms successfully deal with self - intersecting and / or non-Nyquist samples -- Ongoing research includes self-tuning of the algorithms and decimation of the point cloud and the control polygon

## Descripción

## Palabras clave

## Citación

@inproceedings{oruiz2013parametric,
author ={Oscar E. Ruiz and C. Cortes and M. Aristizabal and Diego A. Acosta and Carlos A. Vanegas},
title ={Parametric Curve Reconstruction from Point Clouds using Minimization Techniques},
booktitle ={Proceedings of the International Conference on Computer Graphics Theory (GRAPP2013) and Applications and International Conference on Information Visualization Theory and Applications (IVAPP2013)},
year ={2013},
editor ={Sabine Coquillart and Carlos Andujar and Robert S. Laramee and Andreas Kerren and Jose Braz},
month ={February 21-24},
address ={Barcelona, Spain},
keys ={Parametric Curve Reconstruction, Noisy Point Cloud, Principal Component Analysis, Minimization},
organization ={INSTICC},
pages ={35--48},
publisher ={SCITEPRESS},
abstract ={Curve reconstruction from noisy point samples is central to surface reconstruction and therefore to reverse
engineering, medical imaging, etc. Although Piecewise Linear (PL) curve reconstruction plays an important
role, smooth (C^1-, C^2-,...) curves are needed for many applications. In reconstruction of parametric curves
from noisy point samples there remain unsolved issues such as (1) high computational expenses, (2) presence
of artifacts and outlier curls, (3) erratic behavior of self-intersecting curves, and (4) erratic excursions at
sharp corners. Some of these issues are related to non-Nyquist (i.e. sparse) samples. In response to these
shortcomings, this article reports the minimization-based ï¿½tting of parametric curves for noisy point clouds.
Our approach features: (a) Principal Component Analysis (PCA) pre-processing to obtain a topologically
correct approximation of the sampled curve. (b) Numerical, instead of algebraic, calculation of roots in point-
to-curve distances. (c) Penalties for curve excursions by using point cloud to - curve and curve to point cloud.
(d) Objective functions which are economic to minimize. The implemented algorithms successfully deal with
self - intersecting and / or non-Nyquist samples. Ongoing research includes self-tuning of the algorithms and
decimation of the point cloud and the control polygon},
isbn ={978-989-8565-46-4},
}