[1] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging
Vision 10, 51-62, 1999.
[2] L. Boxer, Fixed point sets in digital topology, 2, Appl. Gen. Topol. 21 (1), 111-133,
2020.
[3] L. Boxer, Convexity and Freezing Sets in Digital Topology, Appl. Gen. Topol. 22 (1),
121-137, 2021.
[4] L. Boxer and P.C. Staecker, Fixed point sets in digital topology, 1, Appl. Gen. Topol.
21 (1), 87-110, 2020.
[5] L. Chen, Gradually varied surface and its optimal uniform approximation, SPIE Proceedings
2182, 300-307, 1994.
[6] L. Chen, Discrete Surfaces and Manifolds, Scientific Practical Computing, Rockville,
MD, 2004.
[7] J. Haarmann, M.P. Murphy, C.S. Peters, and P.C. Staecker, Homotopy equivalence
in finite digital images, J. Math. Imaging Vision 53, 288-302, 2015.
[8] A. Rosenfeld, Digital topology, Amer. Math. Monthly 86 (8), 621-630, 1979.
[9] A. Rosenfeld, ‘Continuous’ functions on digital pictures, Pattern Recognit. Lett. 4,
177-184, 1986.
We continue the study of freezing sets for digital images introduced in [L. Boxer and P.C. Staecker, Fixed point sets in digital topology, 1, Applied General Topology 2020; L. Boxer, Fixed point sets in digital topology, 2, Applied General Topology 2020; L. Boxer, Convexity and Freezing Sets in Digital Topology, Applied General Topology, 2021]. We prove methods for obtaining freezing sets for digital images $(X,c_i)$ for $X \subset \mathbb{Z}^2$ and $i \in \{1,2\}$. We give examples to show how these methods can lead to the determination of minimal freezing sets.
[1] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging
Vision 10, 51-62, 1999.
[2] L. Boxer, Fixed point sets in digital topology, 2, Appl. Gen. Topol. 21 (1), 111-133,
2020.
[3] L. Boxer, Convexity and Freezing Sets in Digital Topology, Appl. Gen. Topol. 22 (1),
121-137, 2021.
[4] L. Boxer and P.C. Staecker, Fixed point sets in digital topology, 1, Appl. Gen. Topol.
21 (1), 87-110, 2020.
[5] L. Chen, Gradually varied surface and its optimal uniform approximation, SPIE Proceedings
2182, 300-307, 1994.
[6] L. Chen, Discrete Surfaces and Manifolds, Scientific Practical Computing, Rockville,
MD, 2004.
[7] J. Haarmann, M.P. Murphy, C.S. Peters, and P.C. Staecker, Homotopy equivalence
in finite digital images, J. Math. Imaging Vision 53, 288-302, 2015.
[8] A. Rosenfeld, Digital topology, Amer. Math. Monthly 86 (8), 621-630, 1979.
[9] A. Rosenfeld, ‘Continuous’ functions on digital pictures, Pattern Recognit. Lett. 4,
177-184, 1986.
Boxer, L. (2021). Subsets and freezing sets in the digital plane. Hacettepe Journal of Mathematics and Statistics, 50(4), 991-1001. https://doi.org/10.15672/hujms.827556
AMA
Boxer L. Subsets and freezing sets in the digital plane. Hacettepe Journal of Mathematics and Statistics. August 2021;50(4):991-1001. doi:10.15672/hujms.827556
Chicago
Boxer, Laurence. “Subsets and Freezing Sets in the Digital Plane”. Hacettepe Journal of Mathematics and Statistics 50, no. 4 (August 2021): 991-1001. https://doi.org/10.15672/hujms.827556.
EndNote
Boxer L (August 1, 2021) Subsets and freezing sets in the digital plane. Hacettepe Journal of Mathematics and Statistics 50 4 991–1001.
IEEE
L. Boxer, “Subsets and freezing sets in the digital plane”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 4, pp. 991–1001, 2021, doi: 10.15672/hujms.827556.
ISNAD
Boxer, Laurence. “Subsets and Freezing Sets in the Digital Plane”. Hacettepe Journal of Mathematics and Statistics 50/4 (August 2021), 991-1001. https://doi.org/10.15672/hujms.827556.
JAMA
Boxer L. Subsets and freezing sets in the digital plane. Hacettepe Journal of Mathematics and Statistics. 2021;50:991–1001.
MLA
Boxer, Laurence. “Subsets and Freezing Sets in the Digital Plane”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 4, 2021, pp. 991-1001, doi:10.15672/hujms.827556.
Vancouver
Boxer L. Subsets and freezing sets in the digital plane. Hacettepe Journal of Mathematics and Statistics. 2021;50(4):991-1001.