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How Near Are Zdzisław Pawlak’s Paintings?

Study of Merotopic Distances between Digital Picture Regions-of-Interest

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Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 42))

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Abstract

This chapter commemorates the work of Zdzisław Pawlak as a painter with the focus on the subtleties that come to light in considering the symmetries in his paintings. Specifically, this chapter considers how merotopic distance functions can be used as an aid to visual perception in determining the nearness of Zdzisław Pawlak’s paintings. Eventually, the study of the resemblance of perceptual fragments found in nature (e.g., collections of falling snow flakes) in the poem How Near? by Z. Pawlak and J.F. Peters in 2002 led to the discovery of descriptively near sets by J.F. Peters in 2007 and a merotopological approach to measuring the nearness of collections of subsets recently introduced by J.F. Peters, S.A. Naimpally and S. Tiwari. The main contribution of this chapter is the introduction of an approach to measuring the nearness or apartness of Z. Pawlak’s paintings in terms of the merotopic distances between collections of neighbourhoods in digital picture regions-of-interest. This study includes a consideration of ε-approach nearness spaces as frameworks in the search for patterns in digital pictures. An application of the proposed approach to measuring visual image nearness is reported relative to resemblances between Z. Pawlak’s paintings of waterscapes that span more than a half century, starting in 1954. This study offers a partial answer to the question How near are Zdzisław Pawlak’s paintings?

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References

  1. Beer, G., Lechnicki, A., Levi, S., Naimpally, S.: Distance functionals and suprema of hyperspace topologies. In: Annali di Matematica Pura Ed Applicata CLXII(IV), pp. 367–381 (1992)

    Google Scholar 

  2. Bourbaki, N.: Elements of Mathematics. General Topology, Pt. 1. Hermann, Addison-Wesley, Paris, Reading (1966, 1974)

    Google Scholar 

  3. Engelking, R.: General Topology, Revised & completed edition. Heldermann Verlag, Berlin (1989)

    Google Scholar 

  4. Hausdorff, F.: Grundzüge der Mengenlehre, pp. Viii+ 476. Veit and Company, Leipzig (1914)

    MATH  Google Scholar 

  5. Hausdorff, F.: Set Theory, p. 352. AMS Chelsea Publishing, Providence (1914)

    Google Scholar 

  6. Henry, C.: Near sets: Theory and applications, Ph.D. dissertation, supervisor: J.f. Peters. Ph.D. thesis, Department of Electrical & Computer Engineering (2010)

    Google Scholar 

  7. Henry, C., Ramanna, S.: Parallel Computation in Finding Near Neighbourhoods. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 523–532. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Hocking, J., Young, G.: Topology, Dover, NY (1988)

    Google Scholar 

  9. Katětov, M.: On continuity structures and spaces of mappings. Comment. Math. Univ. Carolinae 6, 257–278 (1965)

    MathSciNet  MATH  Google Scholar 

  10. Khare, M., Tiwari, S.: Grill determined L-approach merotopological spaces. Fund. Inform. 48, 1–12 (2010)

    MathSciNet  Google Scholar 

  11. Khare, M., Tiwari, S.: L-approach merotopies and their categorical perspective. International Journal of Mathematics and Mathematical Sciences 2010, 1–16 (2010), doi:10.1155/2010

    Article  Google Scholar 

  12. Leader, S.: On clusters in proximity spaces. Fundamenta Mathematicae 47, 205–213 (1959)

    MathSciNet  MATH  Google Scholar 

  13. Liu, G.: Closures and topological closures in quasi-discrete closure spaces. Appl. Math. Let. 23, 772–776 (2010)

    Article  MATH  Google Scholar 

  14. Lowen, R.: Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, pp. Viii + 253. Oxford University Press, Oxford (1997)

    Google Scholar 

  15. Lowen, R., Vaughan, D., Sioen, M.: Completing quasi metric spaces: an alternative approach. Houstan J. Math. 29(1), 113–136 (2003)

    MathSciNet  MATH  Google Scholar 

  16. Naimpally, S.: Proximity Spaces, pp. X + 128. Cambridge University Press, Cambridge (1970)

    MATH  Google Scholar 

  17. Naimpally, S.: Reflective functors via nearness. Fund. Math. 85, 245–255 (1974)

    MathSciNet  MATH  Google Scholar 

  18. Naimpally, S.: Generalized metric spaces via annihilators. Questions and Answers in General Topology 9, 203–226 (1991)

    MathSciNet  MATH  Google Scholar 

  19. Naimpally, S.: Plasticity in metric spaces. J. of Math. Analyis and Applications 313(1), 38–48 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pawlak, Z.: Classification of objects by means of attributes. Institute of Computer Science, Polish Academy of Sciences, ICS PAS Reports, vol. 429, pp. 1-20. Warsaw (1981)

    Google Scholar 

  21. Pawlak, Z.: Rough sets. International J. Comp. Inform. Science 11, 341–356 (1981)

    Article  MathSciNet  Google Scholar 

  22. Pawlak, Z., Peters, J.: Jak blisko (how near). In: Systemy Wspomagania Decyzji, vol. I, pp. 57–109. University of Silesia, Katowice (2007) ISBN 83-920730-4-5

    Google Scholar 

  23. Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Information Sciences 177, 41–73 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Peters, J.: Near sets. General theory about nearness of objects. Ap. Math. Sci. 1(53), 2609–2629 (2007)

    MATH  Google Scholar 

  27. Peters, J.: Near sets. Special theory about nearness of objects. Fund. Inf. 75(1-4), 407–433 (2007)

    MATH  Google Scholar 

  28. Peters, J.: Sufficiently near sets of neighbourhoods. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 17–24. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  29. Peters, J.F., Borkowski, M.: ε-near collections. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 533–542. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  30. Peters, J., Naimpally, S.: Approach spaces for near families. Gen. Math. Notes 2(1), 159–164 (2011)

    MATH  Google Scholar 

  31. Peters, J.F., Skowron, A.: Zdzisław Pawlak: Life and Work. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 1–24. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  32. Peters, J., Skowron, A., Stepaniuk, J.: Nearness in approximation spaces. In: Proc. Concurrency, Specification and Programming (CS&P 2006), pp. 435–445. Humboldt Universität (2006)

    Google Scholar 

  33. Peters, J., Skowron, A., Stepaniuk, J.: Nearness of objects: Extension of approximation space model. Fundamenta Informaticae 79(3-4), 497–512 (2007)

    MathSciNet  MATH  Google Scholar 

  34. Peters, J., Tiwari, S.: Approach merotopies and near filters. Theory and application. Gen. Math. Notes 3(1), 1–15 (2011)

    Google Scholar 

  35. Peters, J., Tiwari, S.: Completing extended metric spaces. An alternative approach. Applied Mathematics Letters (2012), doi:10.1016/j.aml.2012.01.012

    Google Scholar 

  36. Peters, J.F., Wasilewski, P.: Foundations of near sets. Inf. Sci. 179(18), 3091–3109 (2009), http://dx.doi.org/10.1016/j.ins.2009.04.018

    Article  MathSciNet  MATH  Google Scholar 

  37. Puzio, L., Peters, J.: Nearness of Subtly Different Digital Images. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 543–552. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  38. Skowron, A., Peters, J.: Rough-granular computing. In: Handbook on Granular Computing. ch. 13, pp. 285–328. John Wiley & Sons Inc., USA (2008)

    Chapter  Google Scholar 

  39. Thron, W.: Topological Spaces. Holt, Rinehart and Winston Inc., NY (1966)

    Google Scholar 

  40. Tiwari, S.: Some aspects of general topology and applications. Approach merotopic structures and applications, supervisor: M. khare. Ph.D. thesis, Department of Mathematics, Allahabad (U.P.), India (2010)

    Google Scholar 

  41. Čech, E.: Topological Spaces. John Wiley & Sons, NY (1966) revised Ed. by Z. Frolik and M. Katătov

    MATH  Google Scholar 

  42. Wang, L., Liu, X., Tian, X.: A Generalization of Near Set Model. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 553–558. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  43. Wolski, M.: Gauges, Pregauges and Completions: Some Theoretical Aspects of Near and Rough Set Approaches to Data. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 559–568. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, EITC Room E1-526, Winnipeg, Manitoba, R3T 3E2, Canada

    James F. Peters

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  1. James F. Peters
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Correspondence to James F. Peters .

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Editors and Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, Warsaw, 02097, Poland

    Andrzej Skowron

  2. Institute of Computer Science, University of Rzeszów, ul. Dekerta 2, Rzeszów, 35-030, Poland

    Zbigniew Suraj

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Peters, J.F. (2013). How Near Are Zdzisław Pawlak’s Paintings?. In: Skowron, A., Suraj, Z. (eds) Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam. Intelligent Systems Reference Library, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30344-9_20

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  • DOI: https://doi.org/10.1007/978-3-642-30344-9_20

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