Bulletin of the Belgian Mathematical Society - Simon Stevin

Applications of the Lefschetz Number to Digital Images

Ozgur Ege and Ismet Karaca

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Abstract

The goal of this paper is to develop some applications of the Lefschetz fixed point theorem to digital images. We also deal with relative and reduced Lefschetz fixed point theorem for digital complexes. We give some examples related to the topic. We calculate the degree of the antipodal map for sphere-like digital images using fixed point properties.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 5 (2014), 823-839.

Dates
First available in Project Euclid: 1 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1420071856

Digital Object Identifier
doi:10.36045/bbms/1420071856

Mathematical Reviews number (MathSciNet)
MR3298480

Zentralblatt MATH identifier
1318.55006

Subjects
Primary: 55N35: Other homology theories 55M20: Fixed points and coincidences [See also 54H25] 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35] 68U05: Computer graphics; computational geometry [See also 65D18] 68U10: Image processing

Keywords
Digital image the Lefschetz Fixed Point Theorem the Euler Characteristic Lefschetz number

Citation

Ege, Ozgur; Karaca, Ismet. Applications of the Lefschetz Number to Digital Images. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 5, 823--839. doi:10.36045/bbms/1420071856. https://projecteuclid.org/euclid.bbms/1420071856


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