We introduce 2D digital Jordan curves as the curves satisfying a digital Jordan curve theorem. The theorem builds on the connectedness in the digital plane ℤ2 provided by a closure operator. An advantage of using the closure operator instead of the Khalimsky topology is that the operator provides a richer variety of Jordan curves.
REFERENCES
1.
T.
Kong
and A.
Rosenfeld
, Comput. Vision Graphics Image Process.
48
(1989
).2.
3.
E.
Khalimsky
, R.
Kopperman
, and P.
Meyer
, Topology Appl.
36
, 1
–17
(1990
).4.
U.
Eckhardt
and L.
Latecki
, Comput Vision Image Understanding
90
, 295
–312
(2003
).5.
C.
Kiselman
, “Digital jordan curve theorems,” in Discrete Geometry for Computer Imagery
, Lect. Notes Comput. Sci. 1953
, edited by G.
Borgefors
, I.
Nystrom
, and G.
Baja
(Springer
, Heidelberg
, 2000
), pp. 46
–56
.6.
J.
Slapal
, “Jordan curve theorems with respect to certain pretopologies on z2,” in Discrete Geometry for Computer Imagery, Lect. Notes Comput. Sci
. 5810
, edited by C. R. S.
Brlek
and X.
Provencal
(Springer
, Heidelberg
, 2009
), pp. 252
–262
.7.
J.
Slapal
, “Convenient closure operators on z2,” in Combinatorial Image Analysis, Lect. Notes Comput. Sci
. 5852
, edited by P.
Wiederhold
and R.
Barneva
(Springer
, Heidelberg
, 2009
), pp. 425
–436
.8.
J.
Slapal
, "A Jordan curve theorem in the digital plane", in Combinatorial Image Analysis, Lect. Notes Comput. Sci
. 6636
, edited by J.K.
Agarwal
, et al (Springer
, Heidelberg
, 2011
), pp 120
–131
This content is only available via PDF.
© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.