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Rough Geometry and Its Applications in Character Recognition

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Transactions on Rough Sets X

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5656))

Abstract

The absolutely abstract and accurate geometric elements defined in Euclidean geometry always have lengths or sizes in reality. While the figures in the real world should be viewed as the approximate descriptions of traditional geometric elements at the rougher granular level. How can we generate and recognize the geometric features of the configurations in the novel space? Motivated by this question, rough geometry is proposed as the result of applying the rough set theory to the traditional geometry. In the new theory, the geometric configuration can be constructed by its upper approximation at different levels of granularity and the properties of the rough geometric elements should offer us a new perspective to observe the figures. In this paper, we focus on the foundation of the theory and try to observe the topologic features of the approximate configuration at multiple granular levels in rough space. Then we also attempt to apply the research results to the problems in different areas for novel solutions, such as the applications of rough geometry in the traditional geometric problem (the question whether there exists a convex shape with two distinct equichordal points) and the recognition work with principal curves. Finally, we will describe the questions induced from our exploratory research and discuss the future work.

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Author information

Authors and Affiliations

  1. Department of Computer Science & Technology, Tongji University, Shanghai, 201804, PR China

    Xiaodong Yue & Duoqian Miao

Authors
  1. Xiaodong Yue
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  2. Duoqian Miao
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Editor information

Editors and Affiliations

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

    James F. Peters

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

    Andrzej Skowron

  3. Department of Logic and Philosophy of Science, Maria Curie-Skłodowska University, Marii Curie-Skłodowskiej 4, 20-031, Lublin, Poland

    Marcin Wolski

  4. University of Calcutta, Kolkata, India

    Mihir K. Chakraborty

  5. Zhejiang Ocean University, Zhejiang, P.R. China

    Wei-Zhi Wu

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© 2009 Springer-Verlag Berlin Heidelberg

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Yue, X., Miao, D. (2009). Rough Geometry and Its Applications in Character Recognition. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, WZ. (eds) Transactions on Rough Sets X. Lecture Notes in Computer Science, vol 5656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03281-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-03281-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03280-6

  • Online ISBN: 978-3-642-03281-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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