Fundamental improvements of the piecewise semi-smooth Laplace-Beltrami operator numerical stability
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F17%3A10237705" target="_blank" >RIV/61989100:27240/17:10237705 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27740/17:10237705
Result on the web
<a href="http://dx.doi.org/10.1063/1.4992519" target="_blank" >http://dx.doi.org/10.1063/1.4992519</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4992519" target="_blank" >10.1063/1.4992519</a>
Alternative languages
Result language
angličtina
Original language name
Fundamental improvements of the piecewise semi-smooth Laplace-Beltrami operator numerical stability
Original language description
The Laplace-Beltrami operator plays an important role as C2 function smoother and its eigenfunction applications are studied extensively in last five decades, not only, in image processing field but we can meet with these functions ranging from molecular physics scientific field to mechanical engineering. However, in many non-trivial cases, e.g. computations on non-uniform meshes, the discrete Laplace operator could be ill-conditioned and inappropriate for numerical computations. Especially, in the spectral clustering tool, a condition number of the graph Laplacian goes to infinity, when pairwise similarities among most graph nodes go to zero. Therefore, in this paper, we reformulate the image graph Laplacian as the semi-smooth Laplace-Beltrami operator on a non-uniform mesh and study its numerical properties, then we introduce our fundamental approach for improving a numerical stability of this operator. © 2017 Author(s).
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
AIP Conference Proceedings. Volume 1863
ISBN
978-0-7354-1538-6
ISSN
0094-243X
e-ISSN
neuvedeno
Number of pages
4
Pages from-to
"Article number 340012"
Publisher name
American Institute of Physics
Place of publication
Melville
Event location
Rhodos
Event date
Sep 19, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000410159800346