Advertisement

Mathematics in Computer Science

, Volume 7, Issue 1, pp 51–69 | Cite as

Metric Free Nearness Measure using Description-based Neighbourhoods

  • Christopher J. HenryEmail author
Article

Abstract

The focus of this paper is on a metric free nearness measure for quantifying the descriptive nearness of digital images. Regions of Interest (ROI) play an important role in discerning perceptual similarity within a single image, or between a pair of images. In terms of pixels, closeness between ROIs can be assessed in light of the traditional closeness between points and sets and closeness between sets using topology or proximity theory. A metric free nearness measure is introduced in this paper by finding common patterns among disjoint description based neighbourhoods obtained from these spatially defined sets. The contribution of this article is a metric free nearness measure implemented within the Proximity System, an application used to demonstrate near set concepts using digital images.

Keywords

Nearness measure Digital image Near sets Region of interest Description based neighbourhood 

Mathematics Subject Classification (2000)

Primary 54E05 (Proximity structures and generalizations) 62H35 (image analysis) Secondary 68U10 (imageprocessing) 68N01(software) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Peters J.F., Naimpally S.A.: Applications of near sets. Not. Am. Math. Soc. 59(4), 536–542 (2012)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Naimpally S.A.: Near and far. A centennial tribute to Frigyes Riesz. Sib. Electro. Math. Rep. 6, A.1–A.10 (2009)Google Scholar
  3. 3.
    Naimpally, S.A., Peters, J.F.: Topology with Applications.Topological Spaces via Near and Far. World Scientific, Singapore (2013, in press)Google Scholar
  4. 4.
    Di Concilio, A.: Proximity: A powerful tool in extension theory, function spaces, hyperspaces, boolean algebras and point-free geometry. In: Mynard, F., Pearl, E. (eds.): Beyond Topology. American Mathematical Society, Providence (2009)Google Scholar
  5. 5.
    Sossinsky A.B.: Tolerance space theory and some applications. Acta Appl. Math. 5(2), 137–167 (1986)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Poincaré, H.: Science and Hypothesis. The Mead Project, Brock University, L. G. Ward’s translation (1905)Google Scholar
  7. 7.
    Benjamin Jr., L.T.: A Brief History of Modern Psychology. Blackwell Publishing, Malden (2007)Google Scholar
  8. 8.
    Hergenhahn B.R.: An Introduction to the History of Psychology. Wadsworth Publishing, Belmont (2009)Google Scholar
  9. 9.
    Zeeman, E.C.: The topology of the brain and the visual perception. In: Fort, K.M. (ed.) Topoloy of 3-manifolds and selected topices, pp. 240–256. Prentice Hall, New Jersey (1965)Google Scholar
  10. 10.
    Naimpally, S.A., Warrack, B.D.: Proximity spaces. In: Cambridge Tract in Mathematics No. 59. Cambridge University Press, Cambridge (1970)Google Scholar
  11. 11.
    Pawlak Z., Peters J.F.: Jak blisko (how near). Systemy Wspomagania Decyzji I(57), 109 (2002)Google Scholar
  12. 12.
    Peters J.F.: Near sets. General theory about nearness of objects. Appl. Math. Sci. 1(53), 2609–2629 (2007)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Peters J.F.: Near sets. Special theory about nearness of objects. Fundam. Inf. 75(1–4), 407–433 (2007)zbMATHGoogle Scholar
  14. 14.
    Peters J.F.: Tolerance near sets and image correspondence. Int. J. Bio-Inspired Comput. 1(4), 239–245 (2009)CrossRefGoogle Scholar
  15. 15.
    Peters J.F.: Corrigenda and addenda: Tolerance near sets and image correspondence. Int. J. Bio-Inspired Comput. 2(5), 310–318 (2010)CrossRefGoogle Scholar
  16. 16.
    Henry, C.J.: Near Sets: Theory and Applications. PhD thesis (2010) Available at: https://mspace.lib.umanitoba.ca/handle/1993/4267
  17. 17.
    Henry C.J.: Perceptually indiscernibility, rough sets, descriptively near sets, and image analysis. Trans. Rough Sets LNCS 7255, 41–121 (2012)Google Scholar
  18. 18.
    Henry, C.: Near set Evaluation And Recognition (NEAR) system. In: Pal, S.K., Peters, J.F. (eds.) Rough Fuzzy Analysis Foundations and Applications. CRC Press, Taylor & Francis Group (2010) 7-1–7-22 exe. availabe at: http://wren.ee.umanitoba.ca
  19. 19.
    Pavel M.: Fundamentals of Pattern Recognition. Marcel Dekker, Inc., New York (1993)zbMATHGoogle Scholar
  20. 20.
    Peters, J.F.: Classification of objects by means of features. In: Proceedings of the IEEE Symposium Series on Foundations of Computational Intelligence (IEEE SCCI 2007), pp. 1–8 (2007)Google Scholar
  21. 21.
    Peters J.F.: Classification of perceptual objects by means of features. Int. J. Inf. Technol. Intel. Comput. 3(2), 1–35 (2008)Google Scholar
  22. 22.
    Peters J.F., Wasilewski P.: Foundations of near sets. Info. Sci. 179(18), 3091–3109 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Duda, R., Hart, P., Stork, D.: Pattern Classification. 2nd edn. Wiley, Hoboken (2001)Google Scholar
  24. 24.
    Bourbaki, N.: Elements of Mathematics: Theory of Sets. Hermann, Publishers in Arts and Science, Paris (1968)Google Scholar
  25. 25.
    Pal S.K., Mitra P.: Multispectral image segmentation using rough set initialized em algorithm. IEEE Trans. Geosci. Remote Sens. 11, 2495–2501 (2002)CrossRefGoogle Scholar
  26. 26.
    Peters, J.F., Borkowski, M.: k-means indiscernibility over pixels (2004)Google Scholar
  27. 27.
    Pal S.K., Shankar B.U., Mitra P.: Granular computing, rough entropy and object extraction. Pattern Recognit. Lett. 26(16), 401–416 (2005)CrossRefGoogle Scholar
  28. 28.
    Borkowski, M., Peters, J.F.: Matching 2d image segments with genetic algorithms and approximations spaces. Trans. Rough Sets LNCS 4100 (2006)Google Scholar
  29. 29.
    Borkowski, M.: 2D to 3D Conversion with Direct Geometrical Search and Approximation Spaces. PhD thesis (2007)Google Scholar
  30. 30.
    Maji P., Pal S.K.: Maximum class separability for rough-fuzzy c-means based brain mr image segmentation. Trans. Rough Sets IX, LNCS 5390, 114–134 (2008)CrossRefGoogle Scholar
  31. 31.
    Mushrif M., Ray A.K.: Color image segmentation: Rough-set theoretic approach. Pattern Recognit. Lett. 29(4), 483–493 (2008)CrossRefGoogle Scholar
  32. 32.
    Hassanien A.E., Abraham A., Peters J.F., Schaefer G., Henry C.: Rough sets and near sets in medical imaging: A review. IEEE Trans. Inf. Technol. Biomed. 13(6), 955–968 (2009)CrossRefGoogle Scholar
  33. 33.
    Smeulders A.W.M., Worring M., Santini S., Gupta A., Jain R.: Content-based image retrieval at the end of the early years. IEEE Trans. Pattern Anal. Mach. Intel. 22(12), 1349–1380 (2000)CrossRefGoogle Scholar
  34. 34.
    Henry, C.J., Ramanna, S., Levy, D.: Quantifying nearness in visual spaces. Cybern. Syst. J. (2012) (under review)Google Scholar
  35. 35.
    Henry, C.J., Ramanna, S.: Maximal clique enumeration in finding near neighbourhoods. Trans. Rough Sets (2012) (under review)Google Scholar
  36. 36.
    Henry, C.J., Ramanna, S.: Signature-based perceptual nearness. application of near sets to image retrieval. Math. Comput. Sci. (2012) (under review)Google Scholar
  37. 37.
    Peters J.F., Wasilewski P.: Tolerance spaces: Origins, theoretical aspects and applications. Inf. Sci. 195(0), 211–225 (2012)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Applied Computer ScienceUniversity of WinnipegWinnipegCanada

Personalised recommendations