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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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Book cover Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam

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

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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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30343-2

  • Online ISBN: 978-3-642-30344-9

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