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Digital shapes, digital boundaries and rigid transformations: A topological discussion
Actes des rencontres du CIRM, Tome 3 (2013) no. 1, pp. 195-201.

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 ℝ n to ℤ n , can also be stated in ℤ n itself, when applying geometric transformations on digital shapes. This paper proposes a preliminary discussion on this topic.

Publié le :
DOI : https://doi.org/10.5802/acirm.68
Classification : 00X99
Mots clés : 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},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.68/}
}
Kenmochi, Yukiko; Ngo, Phuc; Passat, Nicolas; Talbot, Hugues. Digital shapes, digital boundaries and rigid transformations: A topological discussion. Actes des rencontres du CIRM, Tome 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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