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Curvature and Flow in Digital Space
Atsushi Imiya1
1 Supercomputing Laboratory Institute of Management and Information Technologies Chiba University Yayoi-cho 1-33, Inage-ku, Chiba 263-8522, Chiba Japan
Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 183-194.

We first define the curvature indices of vertices of digital objects. Second, using these indices, we define the principal normal vectors of digital curves and surfaces. These definitions allow us to derive the Gauss-Bonnet theorem for digital objects. Third, we introduce curvature flow for isothetic polytopes defined in a digital space.

Published online:
DOI: 10.5802/acirm.67
Classification: 52C07, 65Q10, 68R10
Keywords: Digital Space, Surgery, Curvature flow, Topology
Atsushi Imiya 1

1 Supercomputing Laboratory Institute of Management and Information Technologies Chiba University Yayoi-cho 1-33, Inage-ku, Chiba 263-8522, Chiba Japan 
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Atsushi Imiya. Curvature and Flow in Digital Space. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 183-194. doi : 10.5802/acirm.67. https://acirm.centre-mersenne.org/articles/10.5802/acirm.67/

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