Curvature and Flow in Digital Space

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

Actes des rencontres du CIRM (2013)

  • Volume: 3, Issue: 1, page 183-194
  • ISSN: 2105-0597

Abstract

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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.

How to cite

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Imiya, Atsushi. "Curvature and Flow in Digital Space." Actes des rencontres du CIRM 3.1 (2013): 183-194. <http://eudml.org/doc/275328>.

@article{Imiya2013,
abstract = {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.},
affiliation = {Supercomputing Laboratory Institute of Management and Information Technologies Chiba University Yayoi-cho 1-33, Inage-ku, Chiba 263-8522, Chiba Japan},
author = {Imiya, Atsushi},
journal = {Actes des rencontres du CIRM},
keywords = {Digital Space; Surgery; Curvature flow; Topology},
language = {eng},
month = {11},
number = {1},
pages = {183-194},
publisher = {CIRM},
title = {Curvature and Flow in Digital Space},
url = {http://eudml.org/doc/275328},
volume = {3},
year = {2013},
}

TY - JOUR
AU - Imiya, Atsushi
TI - Curvature and Flow in Digital Space
JO - Actes des rencontres du CIRM
DA - 2013/11//
PB - CIRM
VL - 3
IS - 1
SP - 183
EP - 194
AB - 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.
LA - eng
KW - Digital Space; Surgery; Curvature flow; Topology
UR - http://eudml.org/doc/275328
ER -

References

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