Difference between revisions of "Publications/najman.13.ismm"
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| abstract = The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same wayfaces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper. |
| abstract = The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same wayfaces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper. |
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pages = <nowiki>{</nowiki>37--48<nowiki>}</nowiki>, |
pages = <nowiki>{</nowiki>37--48<nowiki>}</nowiki>, |
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abstract = <nowiki>{</nowiki>The main question of this paper is to retrieve some |
abstract = <nowiki>{</nowiki>The main question of this paper is to retrieve some |
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continuity properties on (discrete) T0-Alexandroff spaces. |
continuity properties on (discrete) T0-Alexandroff spaces. |
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Revision as of 12:15, 26 April 2016
- Authors
- Laurent Najman, Thierry Géraud
- Where
- Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 11th International Symposium on Mathematical Morphology (ISMM)
- Place
- Uppsala, Sweden
- Type
- inproceedings
- Publisher
- Springer
- Projects
- Image"Image" is not in the list (Vaucanson, Spot, URBI, Olena, APMC, Tiger, Climb, Speaker ID, Transformers, Bison, ...) of allowed values for the "Related project" property.
- Keywords
- Image
- Date
- 2013-03-14
Abstract
The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same wayfaces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper.
Bibtex (lrde.bib)
@InProceedings{ najman.13.ismm,
author = {Laurent Najman and Thierry G\'eraud},
title = {Discrete set-valued continuity and interpolation},
booktitle = {Mathematical Morphology and Its Application to Signal and
Image Processing -- Proceedings of the 11th International
Symposium on Mathematical Morphology (ISMM)},
year = 2013,
editor = {C.L. Luengo Hendriks and G. Borgefors and R. Strand},
volume = 7883,
series = {Lecture Notes in Computer Science Series},
address = {Uppsala, Sweden},
publisher = {Springer},
pages = {37--48},
abstract = {The main question of this paper is to retrieve some
continuity properties on (discrete) T0-Alexandroff spaces.
One possible application, which will guide us, is the
construction of the so-called "tree of shapes"
(intuitively, the tree of level lines). This tree, which
should allow to process maxima and minima in the same way,
faces quite a number of theoretical difficulties that we
propose to solve using set-valued analysis in a purely
discrete setting. We also propose a way to interpret any
function defined on a grid as a "continuous" function
thanks to an interpolation scheme. The continuity
properties are essential to obtain a quasi-linear algorithm
for computing the tree of shapes in any dimension, which is
exposed in a companion paper.}
}