Abstract
This paper introduces a perceptual tolerance intersection of sets as an example of near set operations. Such operations are motivated by the need to consider similarities between digital images viewed as disjoint sets of points. The proposed approach is in keeping with work by E.C. Zeeman on tolerance spaces and visual perception and J.H. Poincaré on sets of similar sensations used to define representative (aka tolerance) spaces such as visual, tactile and motile spaces. Perceptual tolerance intersection of sets is a direct consequence of recent work on near sets and a solution to the problem of how one goes about discovering affinities between digital images. The main contribution of this article is a description-based approach to assessing the resemblances between digital images.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Engelking, R.: General Topology, Revised & completed edition. Heldermann Verlag, Berlin (1989)
Gratzer, G., Wenzel, G.: Tolerances, covering systems, and the axiom of choice. Archivum Mathematicum 25(1-2), 27–34 (1989)
Pawlak, Z.: Rough sets. International J. Comp. Inform. Science 11, 341–356 (1981)
Pawlak, Z.: Rough sets. Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)
Peters, J.F.: Near sets. Special theory about nearness of objects. Fundamenta Informaticae 75(1-4), 407–433 (2007)
Peters, J., Ramanna, S.: Affinities between perceptual granules: Foundations and perspectives. In: Bargiela, A., Pedrycz, W. (eds.) Human-Centric Information Processing Through Granular Modelling. SCI, vol. 182, pp. 49–66. Springer, Berlin (2009)
Peters, J., Skowron, A., Stepaniuk, J.: Nearness of objects: Extension of approximation space model. Fundamenta Informaticae 79(3-4), 497–512 (2007)
Peters, J.F., Wasilewski, P.: Foundations of near sets. Information Science 179(18), 3091–3109 (2009)
Pogonowski, J.: Tolerance Spaces with Applications to Linguistics. University of Adam Mickiewicz Press, Poznań (1981)
PoincarĂ©, J.: Sur certaines surfaces algĂ©briques; troisième complĂ©ment ‘a l’analysis situs. Bulletin de la SociĂ©tĂ© de France 30, 49–70 (1902)
Poincaré, J.: Dernières pensées, trans. by J.W. Bolduc as Mathematics and Science: Last Essays. Flammarion & Kessinger Pub., Paris (1913 & 2009), http://docenti.lett.unisi.it/files/4/1/1/36/Dernierespenseespoinc.pdf
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)
Wasilewski, P.: On selected similarity relations and their applications into cognitive science. PhD thesis, Department of Logic, Jagiellonian University, Cracow (2004) (in Polish)
Zeeman, E.: The topology of the brain and visual perception. In: Fort Jr., M.K. (ed.) University of Georgia Institute Conference Proceedings, Topology of 3-Manifolds and Related Topics, vol. 1962, pp. 240–256. Prentice-Hall, Inc., Englewood Cliffs (1962)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wasilewski, P., Peters, J.F., Ramanna, S. (2010). Perceptual Tolerance Intersection. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds) Rough Sets and Current Trends in Computing. RSCTC 2010. Lecture Notes in Computer Science(), vol 6086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13529-3_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-13529-3_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13528-6
Online ISBN: 978-3-642-13529-3
eBook Packages: Computer ScienceComputer Science (R0)