Discrete set-valued continuity and interpolation

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.
Complete list of metadatas

Cited literature [23 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00798574
Contributor : Laurent Najman <>
Submitted on : Saturday, March 9, 2013 - 6:03:57 PM
Last modification on : Thursday, July 5, 2018 - 2:29:14 PM
Long-term archiving on: Sunday, April 2, 2017 - 10:44:34 AM

File

discreteContinuityISMM2013.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00798574, version 1

Citation

Laurent Najman, Thierry Géraud. Discrete set-valued continuity and interpolation. International Symposium on Mathematical Morphology, May 2013, Uppsala, Sweden. pp.37-48. ⟨hal-00798574⟩

Share

Metrics

Record views

476

Files downloads

567