Araştırma Makalesi
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On Generalized Digital Topology and Root Images of Median Filters

Yıl 2018, Sayı: 20, 13 - 26, 03.01.2018

Öz

In this paper, we extend the concepts of semi-open sets and λ-open sets in the digital topology. In addition, we introduce the concepts of regular semi-open and regular λ-open sets. A relationship between digital topology and image processing is established.

Kaynakça

  • [1] M. E. Abd El Monsef, A. M. Kozae, M. J. Iqelan, Near approximations in topological spaces, Int. Journal of Math. Analysis, Vol. 4, no. 6, p.p. 279-290, 2010.
  • [2] P. Alexandroff, Diskrete Räume, Mathematicheskii Sbornik (Rwceul Mathématique), Vol.2, no.3, p.p 502-519, 1937.
  • [3] A. Alpers, Digital topology: Regular sets and root image of cross-median filter, Journal of Mathematical imaging vision, Vol. 17, p.p. 7-14, 2002.
  • [4] Arenas, F. G. Dontchev, J. and Ganster. M, on λ–sets and dual of generalized continuity. Questions Answers. Gen. Topology. No 15, p.p 3-13, 1997.
  • [5] M. Caidas, S. Jafri, G. Navalagi, More on λ-closed sets in topological spaces, Revesita Colombinnade Mathemάtices, Vol. 41. No. 2, p.p. 355-369, 2007.
  • [6] H. U. Döhler, Generation of root signals of two-dimensional median filters, Signal Processing, Vol. 18, p.p. 269-276, 1989. In: Ulrich Eckhardt, Root images of median filters, Journal of Mathematical Imaging and Vision, No. 19, p.p 63-70, 2003.
  • [7] U. Eckhardt, L. J. Latecki, Topologies for the digital spaces and, Computer vision and image understanding, Vol. 90, p.p. 295-312,2003.
  • [8] U. Eckhardt, Root image of median filters: Semi-Topological Approach, T. Asano et al. (Eds): Geometry, Morphology, LNCS 2616, p.p. 176-195, Springer Verlag Berlin Heidelberg, 2003.
  • [9] U. Eckhardt, Root Images of Median Filters, Journal of Mathematical Imaging and Vision, Vol. 19, p.p. 63-70, 2003.
  • [10] E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl. Vol. 36, p.p. 1-17, 1990.
  • [11] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, Vol. 70, p.p. 36-41, 1963. In: M. E. Abd El-Monsef, A M. Kozea, M. J. Iqelan, Near approximations in topological spaces, Int. Journal of Math. Analysis, Vol. 4, No 6, p.p 279-290, 2010.
  • [12] Maki, H. Generalized -sets and the associated closure operator. The Special Issue in commemoration of Prof. Kazusada Ikeda's Retirement, Vol. 1, p.p 139-146, 1986. In: Miguel Caladas, Saeid Jafari, Govindappa Navalagi, More on λ-closed sets in topological spaces, Revisita Colombiana de Mathemáticas, Vol. 41, p.p. 355-369, no. 2, 2007.
  • [13] D. Marcus. F. Wyse et al., A special topology for the integers (Problem 5712). Amer. Math. Monthly, Vol. 77, p.p. 85-1119, 1970. In: Ulrich Eckhardt, Longin J. Latecki, Topologies for the digital spaces and, Computer Vision and Image Understanding, Vol. 90, p.p. 295-312, 2003.
  • [14] S. I. Nada, Semi-open and semi-closed sets in digital spaces, Commun. Fac.Sci. Univ. Ank. Series, Vol 53, no.1, p.p.1-6, 2004.
  • [15] A. Rosenfeld, Digital topology, American Mathematical Monthly, vol. 86, p.p. 621-630, 1979.
  • [16] Tuckey, J. W.: Exploratory Data Analysis. Addision-Wesley, Reading. Mass. Vol. 177, 1977. In: Ulrich Eckhardt, Root images of Median filters-Semi-topological approach, Geomtry Morphology, LNCS 2616, P.P. 176-195, 2003, Springer-Verlag. Berlin Heidelberg, 2003.
Yıl 2018, Sayı: 20, 13 - 26, 03.01.2018

Öz

Kaynakça

  • [1] M. E. Abd El Monsef, A. M. Kozae, M. J. Iqelan, Near approximations in topological spaces, Int. Journal of Math. Analysis, Vol. 4, no. 6, p.p. 279-290, 2010.
  • [2] P. Alexandroff, Diskrete Räume, Mathematicheskii Sbornik (Rwceul Mathématique), Vol.2, no.3, p.p 502-519, 1937.
  • [3] A. Alpers, Digital topology: Regular sets and root image of cross-median filter, Journal of Mathematical imaging vision, Vol. 17, p.p. 7-14, 2002.
  • [4] Arenas, F. G. Dontchev, J. and Ganster. M, on λ–sets and dual of generalized continuity. Questions Answers. Gen. Topology. No 15, p.p 3-13, 1997.
  • [5] M. Caidas, S. Jafri, G. Navalagi, More on λ-closed sets in topological spaces, Revesita Colombinnade Mathemάtices, Vol. 41. No. 2, p.p. 355-369, 2007.
  • [6] H. U. Döhler, Generation of root signals of two-dimensional median filters, Signal Processing, Vol. 18, p.p. 269-276, 1989. In: Ulrich Eckhardt, Root images of median filters, Journal of Mathematical Imaging and Vision, No. 19, p.p 63-70, 2003.
  • [7] U. Eckhardt, L. J. Latecki, Topologies for the digital spaces and, Computer vision and image understanding, Vol. 90, p.p. 295-312,2003.
  • [8] U. Eckhardt, Root image of median filters: Semi-Topological Approach, T. Asano et al. (Eds): Geometry, Morphology, LNCS 2616, p.p. 176-195, Springer Verlag Berlin Heidelberg, 2003.
  • [9] U. Eckhardt, Root Images of Median Filters, Journal of Mathematical Imaging and Vision, Vol. 19, p.p. 63-70, 2003.
  • [10] E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl. Vol. 36, p.p. 1-17, 1990.
  • [11] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, Vol. 70, p.p. 36-41, 1963. In: M. E. Abd El-Monsef, A M. Kozea, M. J. Iqelan, Near approximations in topological spaces, Int. Journal of Math. Analysis, Vol. 4, No 6, p.p 279-290, 2010.
  • [12] Maki, H. Generalized -sets and the associated closure operator. The Special Issue in commemoration of Prof. Kazusada Ikeda's Retirement, Vol. 1, p.p 139-146, 1986. In: Miguel Caladas, Saeid Jafari, Govindappa Navalagi, More on λ-closed sets in topological spaces, Revisita Colombiana de Mathemáticas, Vol. 41, p.p. 355-369, no. 2, 2007.
  • [13] D. Marcus. F. Wyse et al., A special topology for the integers (Problem 5712). Amer. Math. Monthly, Vol. 77, p.p. 85-1119, 1970. In: Ulrich Eckhardt, Longin J. Latecki, Topologies for the digital spaces and, Computer Vision and Image Understanding, Vol. 90, p.p. 295-312, 2003.
  • [14] S. I. Nada, Semi-open and semi-closed sets in digital spaces, Commun. Fac.Sci. Univ. Ank. Series, Vol 53, no.1, p.p.1-6, 2004.
  • [15] A. Rosenfeld, Digital topology, American Mathematical Monthly, vol. 86, p.p. 621-630, 1979.
  • [16] Tuckey, J. W.: Exploratory Data Analysis. Addision-Wesley, Reading. Mass. Vol. 177, 1977. In: Ulrich Eckhardt, Root images of Median filters-Semi-topological approach, Geomtry Morphology, LNCS 2616, P.P. 176-195, 2003, Springer-Verlag. Berlin Heidelberg, 2003.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Bölüm Araştırma Makalesi
Yazarlar

Osama Tantawy

Sobhy El Shiekh Bu kişi benim

Mohamed Yakout Bu kişi benim

Sawsan El Sayed Bu kişi benim

Yayımlanma Tarihi 3 Ocak 2018
Gönderilme Tarihi 30 Kasım 2017
Yayımlandığı Sayı Yıl 2018 Sayı: 20

Kaynak Göster

APA Tantawy, O., El Shiekh, S., Yakout, M., El Sayed, S. (2018). On Generalized Digital Topology and Root Images of Median Filters. Journal of New Theory(20), 13-26.
AMA Tantawy O, El Shiekh S, Yakout M, El Sayed S. On Generalized Digital Topology and Root Images of Median Filters. JNT. Ocak 2018;(20):13-26.
Chicago Tantawy, Osama, Sobhy El Shiekh, Mohamed Yakout, ve Sawsan El Sayed. “On Generalized Digital Topology and Root Images of Median Filters”. Journal of New Theory, sy. 20 (Ocak 2018): 13-26.
EndNote Tantawy O, El Shiekh S, Yakout M, El Sayed S (01 Ocak 2018) On Generalized Digital Topology and Root Images of Median Filters. Journal of New Theory 20 13–26.
IEEE O. Tantawy, S. El Shiekh, M. Yakout, ve S. El Sayed, “On Generalized Digital Topology and Root Images of Median Filters”, JNT, sy. 20, ss. 13–26, Ocak 2018.
ISNAD Tantawy, Osama vd. “On Generalized Digital Topology and Root Images of Median Filters”. Journal of New Theory 20 (Ocak 2018), 13-26.
JAMA Tantawy O, El Shiekh S, Yakout M, El Sayed S. On Generalized Digital Topology and Root Images of Median Filters. JNT. 2018;:13–26.
MLA Tantawy, Osama vd. “On Generalized Digital Topology and Root Images of Median Filters”. Journal of New Theory, sy. 20, 2018, ss. 13-26.
Vancouver Tantawy O, El Shiekh S, Yakout M, El Sayed S. On Generalized Digital Topology and Root Images of Median Filters. JNT. 2018(20):13-26.


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