Curvature is a continuous and infinitesimal notion. These properties induce geometrical difficulties in digital frameworks, and the following question is naturally asked: “How to define and compute curvatures of digital shapes?” In fact, not only geometrical but also topological difficulties are also induced in digital frameworks. The – deeper – question thus arises: “Can we still define and compute curvatures?” This latter question, that is relevant in the context of digitization, i.e., when passing from to , can also be stated in itself, when applying geometric transformations on digital shapes. This paper proposes a preliminary discussion on this topic.
Keywords: topology, digitization, geometric transformations
@article{ACIRM_2013__3_1_195_0,
author = {Yukiko Kenmochi and Phuc Ngo and Nicolas Passat and Hugues Talbot},
title = {Digital shapes, digital boundaries and rigid transformations: {A} topological discussion},
journal = {Actes des rencontres du CIRM},
pages = {195--201},
publisher = {CIRM},
volume = {3},
number = {1},
year = {2013},
doi = {10.5802/acirm.68},
zbl = {06938616},
language = {en},
url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.68/}
}
TY - JOUR AU - Yukiko Kenmochi AU - Phuc Ngo AU - Nicolas Passat AU - Hugues Talbot TI - Digital shapes, digital boundaries and rigid transformations: A topological discussion JO - Actes des rencontres du CIRM PY - 2013 SP - 195 EP - 201 VL - 3 IS - 1 PB - CIRM UR - https://acirm.centre-mersenne.org/articles/10.5802/acirm.68/ DO - 10.5802/acirm.68 LA - en ID - ACIRM_2013__3_1_195_0 ER -
%0 Journal Article %A Yukiko Kenmochi %A Phuc Ngo %A Nicolas Passat %A Hugues Talbot %T Digital shapes, digital boundaries and rigid transformations: A topological discussion %J Actes des rencontres du CIRM %D 2013 %P 195-201 %V 3 %N 1 %I CIRM %U https://acirm.centre-mersenne.org/articles/10.5802/acirm.68/ %R 10.5802/acirm.68 %G en %F ACIRM_2013__3_1_195_0
Yukiko Kenmochi; Phuc Ngo; Nicolas Passat; Hugues Talbot. Digital shapes, digital boundaries and rigid transformations: A topological discussion. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 195-201. doi : 10.5802/acirm.68. https://acirm.centre-mersenne.org/articles/10.5802/acirm.68/
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