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Perceptually Near Pawlak Partitions

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Transactions on Rough Sets XII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6190))

Abstract

The problem considered in this paper is how to compare perceptually indiscernible partitions of disjoint, non-empty sets such as pairs of digital images viewed as sets of points. Such partitions are called perceptual Pawlak partitions, named after Z. Pawlak, who introduced a attribute-based equivalence relation in 1981 (the well-known indiscernibility relation from rough set theory). The solution to the problem stems from an approach to pairwise comparison reminiscent of the G. Fechner’s 1860 approach to comparing perceptions in psychophysics experiments. For Fechner, one perception of an object is indistinguishable from the perception of a different object, if there is no perceptible difference in the particular sensed feature value of the objects, e.g., perceptions resulting from lifting small objects where the object feature is weight. In comparing visual perceptions, partitions of images determined by a particular form of indiscernibility relation \(\sim{}_{\mathcal B}\) are used. The L1 (Manhattan distance) norm form of what is known as a perceptual indiscernibility relation defined within the context of a perceptual system is used in this article to define what are known as perceptually indiscernible Pawlak partitions (PIPs). An application of PIPs and near sets is given in this article in terms of a new form of content-based image retrieval (CBIR). This article investigates the efficacy of perceptual CBIR using Hausdorff and Mahalanobis distance measures to determine the degree of correspondence between pairs of perceptual Pawlak partitions of digital images. The contribution of this article is the introduction of an approach to comparing perceptually indiscernible image partitions.

Many thanks to James F. Peters, Amir H. Meghdadi, Som Naimpally, Christopher Henry and Piotr Wasilewski for the suggestions and insights concerning topics in this paper. We especially want to thank Amir H. Meghdadi for the use of his implementation of near set theory in a comprehensive image comparison toolset. This research has been supported by the Natural Science & Engineering Research Council of Canada (NSERC) grant 185986.

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Authors and Affiliations

  1. Dept. Applied Computer Science, University of Winnipeg, 515 Portage Ave., Winnipeg, Manitoba, R3B 2E9, Canada

    Sheela Ramanna

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  1. Sheela Ramanna
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, R3T 5V6, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Insitute of Computing Science, Laboratory of Intelligent Decision Support Systems, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  4. Department of Mathematics and Computing Science, Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  5. School of Electronics and Information Engineering, Tongji University, 201804, Shanghai, P.R. China

    Duoqian Miao

  6. Faculty of Medicine, Department of Medical Informatics, 89-1 Enya-cho, Shimane University, 693-8501, Izumo, Japan

    Shusaku Tsumoto

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Ramanna, S. (2010). Perceptually Near Pawlak Partitions. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds) Transactions on Rough Sets XII. Lecture Notes in Computer Science, vol 6190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14467-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-14467-7_9

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