Multi-scale arithmetization of linear transformations

Loïc Mazo (1, 2)

1 ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

A constructive non-standard interpretation of a multi-scale affine transformation scheme is exposed. It is based on the Ω-numbers of Laugwitz and Schmieden and on the discrete model of the real line of Reeb and Harthong. In this setting, the non-standard version of the Euclidean affine transformation gives rise to a sequence of so-called quasi-linear transformations over integer spaces, allowing integer-only computations.

Mots clés: constructive mathematics; nonstandard analysis; ✦; Index Terms—affine transformation; affine transformation; digital geometry; discretization; multigrid convergence; Omega-number; Harthong-Reeb line; digital; geometry

Domaines: Traitement des images [eess.IV]

Loïc Mazo. Multi-scale arithmetization of linear transformations. Journal of Mathematical Imaging and Vision, 2018, 61, pp.432-442. ⟨10.1007/s10851-018-0853-6⟩. ⟨hal-01405461v3⟩