Computable Proximity of $\ell_1$-Discs on the Digital Plane

James F. Peters; K. Kordzaya; İ. Dochviri

doi:10.33434/cams.541413

Araştırma Makalesi

Yıl 2019, Cilt: 2 Sayı: 3, 213 - 218, 30.09.2019

James F. Peters K. Kordzaya İ. Dochviri

https://doi.org/10.33434/cams.541413

Cited By: 1

Öz

Kaynakça

[1] I. Dochviri, J.F. Peters, Topological sorting of finitely near sets, Math. Comput. Sci., 10(2) (2016), 273–277. 1
[2] E. Andres, T. Roussillon, Analytical description of digital circles, Lecture Notes Comput. Sci., 6607 (2011), 901–917. 1
[3] M.D. McIlroy, Best approximate circles on integer grids, ACM Transactions Graph., 2(4) (1983), 237–263. 1
[4] J.-L. Toutant, E. Andres, T. Roussillon, Digital circles, spheres and hyperspheres: from morphological models to analytical characterizations and topological properties, Discrete Appl. Math., 161(16-17) (2011), 2662–2677. 1
[5] O. Fujita, Metrics based on average distance between sets, Jpn. J. Ind. Appl. Math., 30(1) (2013), 1–19. 2
[6] A. Gardner, J. Kanno, C.A. Duncan, R. Selmic, Measuring distance between unordered sets of different sizes, Proceeding 2014 IEEE Conference on Computer Vision and Pattern Recognition, (2014), 137–143. 2
[7] S. Kosub, A note on the triangle inequality for the Jaccard distance, Pattern Recognition Letters, 120 (2019), 36–38. 2
[8] M. Sharir, Intersection and closest-pair problems for a set of planar discs, SIAM J. Comput., 14(2) (1985), 448–468. 2
[9] E. Bishop, R.R. Phelps, The support functionals of a convex set, 1963 Proc. Sympos. Pure Math., Amer. Math. Soc., VII (1985), 27–35. 2, 2.5
[10] J. F. Peters, Proximal planar shape signatures. Homology nerves and descriptive proximity, Adv. Math.: Sci. J., 6(2) (2017), 71–85. 2
[11] P. Alexandroff, Elementary Concepts of Topology, Dover Publications, New York, 1965. 3
[12] P. Alexandroff, Simpliziale approximationen in der allgemeinen topologie, Math. Ann., 101(1) (1926), 452–456. 3
[13] P.S. Alexandrov, Combinatorial Topology, Graylock Press, Baltimore, Md, USA, 1956. 3
[14] P. Alexandroff, H. Hopf, Topologie. Band I, Springer, Berlin, 1935. 3
[15] J.F. Peters, Proximal planar shapes. Correspondence between triangulated shapes and nerve complexes, Bull. Allahabad Math. Soc., 33(1) (2018), 113–137. 3

Computable Proximity of $\ell_1$-Discs on the Digital Plane

Yıl 2019, Cilt: 2 Sayı: 3, 213 - 218, 30.09.2019

James F. Peters K. Kordzaya İ. Dochviri

https://doi.org/10.33434/cams.541413

Cited By: 1

Öz

This paper investigates problems in the characterization of the proximity of digital discs. Based on the $l_1$-metric structure for the 2D digital plane and using a Jaccard-like metric, we determine numerical characters for intersecting digital discs.

Anahtar Kelimeler

Digital discs, $l_1$-metric, Jaccard like metric

Kaynakça

[1] I. Dochviri, J.F. Peters, Topological sorting of finitely near sets, Math. Comput. Sci., 10(2) (2016), 273–277. 1
[2] E. Andres, T. Roussillon, Analytical description of digital circles, Lecture Notes Comput. Sci., 6607 (2011), 901–917. 1
[3] M.D. McIlroy, Best approximate circles on integer grids, ACM Transactions Graph., 2(4) (1983), 237–263. 1
[4] J.-L. Toutant, E. Andres, T. Roussillon, Digital circles, spheres and hyperspheres: from morphological models to analytical characterizations and topological properties, Discrete Appl. Math., 161(16-17) (2011), 2662–2677. 1
[5] O. Fujita, Metrics based on average distance between sets, Jpn. J. Ind. Appl. Math., 30(1) (2013), 1–19. 2
[6] A. Gardner, J. Kanno, C.A. Duncan, R. Selmic, Measuring distance between unordered sets of different sizes, Proceeding 2014 IEEE Conference on Computer Vision and Pattern Recognition, (2014), 137–143. 2
[7] S. Kosub, A note on the triangle inequality for the Jaccard distance, Pattern Recognition Letters, 120 (2019), 36–38. 2
[8] M. Sharir, Intersection and closest-pair problems for a set of planar discs, SIAM J. Comput., 14(2) (1985), 448–468. 2
[9] E. Bishop, R.R. Phelps, The support functionals of a convex set, 1963 Proc. Sympos. Pure Math., Amer. Math. Soc., VII (1985), 27–35. 2, 2.5
[10] J. F. Peters, Proximal planar shape signatures. Homology nerves and descriptive proximity, Adv. Math.: Sci. J., 6(2) (2017), 71–85. 2
[11] P. Alexandroff, Elementary Concepts of Topology, Dover Publications, New York, 1965. 3
[12] P. Alexandroff, Simpliziale approximationen in der allgemeinen topologie, Math. Ann., 101(1) (1926), 452–456. 3
[13] P.S. Alexandrov, Combinatorial Topology, Graylock Press, Baltimore, Md, USA, 1956. 3
[14] P. Alexandroff, H. Hopf, Topologie. Band I, Springer, Berlin, 1935. 3
[15] J.F. Peters, Proximal planar shapes. Correspondence between triangulated shapes and nerve complexes, Bull. Allahabad Math. Soc., 33(1) (2018), 113–137. 3

Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Articles
Yazarlar	James F. Peters 0000-0002-1026-4638 K. Kordzaya Bu kişi benim İ. Dochviri Bu kişi benim
Yayımlanma Tarihi	30 Eylül 2019
Gönderilme Tarihi	18 Mart 2019
Kabul Tarihi	1 Ağustos 2019
Yayımlandığı Sayı	Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA	Peters, J. F., Kordzaya, K., & Dochviri, İ. (2019). Computable Proximity of $\ell_1$-Discs on the Digital Plane. Communications in Advanced Mathematical Sciences, 2(3), 213-218. https://doi.org/10.33434/cams.541413
AMA	Peters JF, Kordzaya K, Dochviri İ. Computable Proximity of $\ell_1$-Discs on the Digital Plane. Communications in Advanced Mathematical Sciences. Eylül 2019;2(3):213-218. doi:10.33434/cams.541413
Chicago	Peters, James F., K. Kordzaya, ve İ. Dochviri. “Computable Proximity of $\ell_1$-Discs on the Digital Plane”. Communications in Advanced Mathematical Sciences 2, sy. 3 (Eylül 2019): 213-18. https://doi.org/10.33434/cams.541413.
EndNote	Peters JF, Kordzaya K, Dochviri İ (01 Eylül 2019) Computable Proximity of $\ell_1$-Discs on the Digital Plane. Communications in Advanced Mathematical Sciences 2 3 213–218.
IEEE	J. F. Peters, K. Kordzaya, ve İ. Dochviri, “Computable Proximity of $\ell_1$-Discs on the Digital Plane”, Communications in Advanced Mathematical Sciences, c. 2, sy. 3, ss. 213–218, 2019, doi: 10.33434/cams.541413.
ISNAD	Peters, James F. vd. “Computable Proximity of $\ell_1$-Discs on the Digital Plane”. Communications in Advanced Mathematical Sciences 2/3 (Eylül 2019), 213-218. https://doi.org/10.33434/cams.541413.
JAMA	Peters JF, Kordzaya K, Dochviri İ. Computable Proximity of $\ell_1$-Discs on the Digital Plane. Communications in Advanced Mathematical Sciences. 2019;2:213–218.
MLA	Peters, James F. vd. “Computable Proximity of $\ell_1$-Discs on the Digital Plane”. Communications in Advanced Mathematical Sciences, c. 2, sy. 3, 2019, ss. 213-8, doi:10.33434/cams.541413.
Vancouver	Peters JF, Kordzaya K, Dochviri İ. Computable Proximity of $\ell_1$-Discs on the Digital Plane. Communications in Advanced Mathematical Sciences. 2019;2(3):213-8.