Multi-scale Arithmetization of Linear Transformations

被引：2
|
作者：
Mazo, Loic [1 ]
机构：
[1] Univ Strasbourg, CNRS, ICube, 300 Bd Sebastien Brant CS 10413, F-67412 Illkirch Graffenstaden, France
来源：
JOURNAL OF MATHEMATICAL IMAGING AND VISION | 2019年 / 61卷 / 04期
关键词：
Affine transformation; Discretization; Multigrid convergence; Digital geometry; Nonstandard analysis; Constructive mathematics; QUASI-AFFINE TRANSFORMATION;
D O I：
10.1007/s10851-018-0853-6
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
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.
引用
收藏
页码：432 / 442
页数：11
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