@Article{RibeiroCampLope:2016:HeDeAn,
author = "Ribeiro, Paula Ceccon and Campos Velho, Haroldo Fraga de and
Lopes, H{\'e}lio",
affiliation = "{Pontif{\'{\i}}cia Universidade Cat{\'o}lica Do Rio de Janeiro
(PUC-Rio)} and {Instituto Nacional de Pesquisas Espaciais (INPE)}
and {Pontif{\'{\i}}cia Universidade Cat{\'o}lica Do Rio de
Janeiro (PUC-Rio)}",
title = "Helmholtz-Hodge decomposition and the analysis of 2D vector field
ensembles",
journal = "Computers and Graphics",
year = "2016",
volume = "55",
pages = "80--96",
month = "Apr.",
keywords = "Ensemble visualization, Helmholtz-Hodge decomposition, Uncertainty
quantification, Vector fields.",
abstract = "The Helmholtz-Hodge decomposition is a very useful instrument for
vector field interpretation because it traditionally distinguishes
conservative (curl-free) components from mass-preserving
(divergence-free) components. In this work, we propose to use the
Helmholtz-Hodge decomposition as a basic tool for the analysis of
an ensemble of 2D vector fields. Given a vector field ensemble
\ε, our approach firstly generates the corresponding
curl-free, divergence-free, and harmonic component ensembles by
using the Natural Helmholtz-Hodge decomposition to each vector
field in \ε. With these ensembles in hand, our proposal not
only quantifies, via a statistical analysis, how much each
component ensemble is point-wisely correlated to the original
vector field ensemble, but also allows to investigate the
uncertainty of curl-free, divergence-free, and harmonic components
separately. We test the proposed method with a synthetic vector
field ensemble and with a simulated vector field ensemble.",
doi = "10.1016/j.cag.2016.01.001",
url = "http://dx.doi.org/10.1016/j.cag.2016.01.001",
issn = "0097-8493",
language = "en",
targetfile = "ribeiro_helmholtz.pdf",
urlaccessdate = "10 maio 2024"
}