Digital shy maps

Laurence Boxer

doi:10.4995/agt.2017.6663

Authors

Laurence Boxer Niagara University

DOI:

https://doi.org/10.4995/agt.2017.6663

Keywords:

digital image, continuous multivalued function, shy map, isomorphism, Cartesian product, wedge

Abstract

We study properties of shy maps in digital topology.

Downloads

Download data is not yet available.

Author Biography

Laurence Boxer, Niagara University

Professor of Computer and Information Sciences at Niagara University; and Research Professor of Computer Science and Engineering at State University of New York at Buffalo

References

C. Berge, Graphs and Hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.

L. Boxer, Digitally continuous functions, Pattern Recognition Letters 15 (1994), 833-839.

https://doi.org/10.1016/0167-8655(94)90012-4

L. Boxer, A classical construction for the digital fundamental group, Pattern Recognition Letters 10 (1999), 51-62.

L. Boxer, Properties of digital homotopy, Journal of Mathematical Imaging and Vision 22 (2005),19-26.

https://doi.org/10.1007/s10851-005-4780-y

L. Boxer, Digital products, wedges, and covering spaces, Journal of Mathematical Imaging and Vision 25 (2006), 159-171.

https://doi.org/10.1007/s10851-006-9698-5

L. Boxer, Remarks on digitally continuous multivalued functions, Journal of Advances in Mathematics 9, no. 1 (2014), 1755-1762.

L. Boxer, Generalized normal product adjacency in digital topology, submitted (available at https://arxiv.org/abs/1608.03204).

L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences 11, no. 4 (2012), 161-180.

L. Boxer and P. C. Staecker, Connectivity preserving multivalued functions in digital topology, Journal of Mathematical Imaging and Vision 55, no. 3 (2016), 370-377.

https://doi.org/10.1007/s10851-015-0625-5

C. Escribano, A. Giraldo and M. Sastre, Digitally continuous multivalued functions, in: Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 4992, Springer, 2008, 81-92.

https://doi.org/10.1007/978-3-540-79126-3_9

C. Escribano, A. Giraldo and M. Sastre, Digitally continuous multivalued functions, morphological operations and thinning algorithms, Journal of Mathematical Imaging and Vision 42 (2012), 76-91.

https://doi.org/10.1007/s10851-011-0277-z

A. Giraldo and M. Sastre, On the composition of digitally continuous multivalued functions, Journal of Mathematical Imaging and Vision 58 (2015), 196-209.

https://doi.org/10.1007/s10851-015-0570-3

S.-E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (2005), 73-91.

https://doi.org/10.1016/j.ins.2004.03.018

V. A. Kovalevsky, A new concept for digital geometry, shape in picture, Springer, New York (1994).

A. Rosenfeld, "Continuous" functions on digital images, Pattern Recognition Letters 4 (1987), 177-184.

https://doi.org/10.1016/0167-8655(86)90017-6

R. Tsaur and M. Smyth, Continuous multifunctions in discrete spaces with applications to fixed point theory, in: Digital and Image Geometry, Bertrand, G., Imiya, A., Klette, R. (eds.), Lecture Notes in Computer Science, vol. 2243, pp. 151-162, Springer, Berlin (2001).

https://doi.org/10.1007/3-540-45576-0_5