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Measuring Linearity of Planar Curves

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Pattern Recognition Applications and Methods

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 318))

Abstract

In this paper we define a new linearity measure which can be applied to open planar curve segments. We have considered the sum of the distances between the curve end points and the curve centroid. We have shown that this sum is bounded from above by the length of the curve segment considered. In addition, we have proven that this sum equals the length of the curve segment only in the case of straight line segments. Exploiting such a nice characterization of straight line segments, we define a new linearity measure for planar curves. The new measure ranges over the interval \((0,1],\) and produces the value \(1\) if and only if the measured line is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations.

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Acknowledgments

This work is partially supported by the Serbian Ministry of Science and Technology/project III44006/OI174008.

Author information

Authors and Affiliations

  1. Computer Science, University of Exeter, Exeter, EX4 4QF, UK

    Joviša Žunić

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Joviša Žunić & Jovanka Pantović

  3. Faculty of Technical Sciences, University of Novi Sad, 21000, Novi Sad, Serbia

    Jovanka Pantović

  4. Cardiff University, School of Computer Science, Cardiff, CF24 3AA, UK

    Paul L. Rosin

Authors
  1. Joviša Žunić
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  2. Jovanka Pantović
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  3. Paul L. Rosin
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Corresponding author

Correspondence to Joviša Žunić .

Editor information

Editors and Affiliations

  1. Instituto de Telecomunicações, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

    Ana Fred

  2. Department of Computer Science, Sapienza University of Rome, Roma, Italy

    Maria De Marsico

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Žunić, J., Pantović, J., Rosin, P.L. (2015). Measuring Linearity of Planar Curves. In: Fred, A., De Marsico, M. (eds) Pattern Recognition Applications and Methods. Advances in Intelligent Systems and Computing, vol 318. Springer, Cham. https://doi.org/10.1007/978-3-319-12610-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-12610-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12609-8

  • Online ISBN: 978-3-319-12610-4

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