Journal of Mathematical Imaging and Vision

, Volume 61, Issue 4, pp 432–442 | Cite as

Multi-scale Arithmetization of Linear Transformations

  • Loïc MazoEmail author


A constructive nonstandard interpretation of a multiscale affine transformation scheme is presented. It is based on the \(\Omega \)-numbers of Laugwitz and Schmieden and on the discrete model of the real line of Reeb and Harthong. In this setting, the nonstandard version of the Euclidean affine transformation gives rise to a sequence of quasi-linear transformations over integer spaces, allowing integer-only computations.


Affine transformation Discretization Multigrid convergence Digital geometry Nonstandard analysis Constructive mathematics 



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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ICube, CNRSUniversity of StrasbourgIllkirchFrance

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