# Omega-Arithmetization: A Discrete Multi-resolution Representation of Real Functions

@inproceedings{Chollet2009OmegaArithmetizationAD, title={Omega-Arithmetization: A Discrete Multi-resolution Representation of Real Functions}, author={Agathe Chollet and Guy Wallet and Laurent Fuchs and Eric Andres and Ga{\"e}lle Largeteau-Skapin}, booktitle={IWCIA}, year={2009} }

Multi-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of previous works of the authors, we expose in this article a new method called the $\it \Omega$-arithmetization. It is a process to obtain a multi-scale discretization of a continuous function that is a solution of a differential equation. The constructive properties of the underlying theory leads to algorithms which can be exactly…

## 6 Citations

Omega-Arithmetization of Ellipses

- Mathematics, Computer ScienceCompIMAGE
- 2010

A discrete multi-resolution representation of arcs of ellipses is obtained and the corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs.

Ω-Arithmetization of Ellipses

- Mathematics, Computer Science
- 2012

A discrete multi-resolution representation of arcs of ellipses is obtained and the corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs.

Multi-scale Arithmetization of Linear Transformations

- MathematicsJournal of Mathematical Imaging and Vision
- 2018

A constructive nonstandard interpretation of a multiscale affine transformation scheme is presented. It is based on the $$\Omega $$Ω-numbers of Laugwitz and Schmieden and on the discrete model of the…

Formalizing a discrete model of the continuum in Coq from a discrete geometry perspective

- Computer ScienceAnnals of Mathematics and Artificial Intelligence
- 2014

It is shown that Laugwitz-Schmieden numbers can be used to actually compute continuous functions and could improve techniques for both implementing numeric computations and reasoning about them in geometric systems.

Décomposition des rotations nD et arithmétisation des cercles

- Physics
- 2011

Cette these est basee sur deux axes principaux : la decomposition des rotations nD et le processus d'arithmetisation des cercles. D'une part, estimer les parametres des rotations est utile dans de…

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Article history: Received 21 July 2008 Received in revised form 20 November 2008 Accepted 9 December 2008