Measuring Linearity of Planar Curves

  • Joviša Žunić
  • Jovanka Pantović
  • Paul L. Rosin
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 318)


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.


Shape Shape descriptors Curves Linearity measure Image processing. 



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


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Joviša Žunić
    • 1
    • 2
  • Jovanka Pantović
    • 2
    • 3
  • Paul L. Rosin
    • 4
  1. 1.Computer ScienceUniversity of ExeterExeterUK
  2. 2.Mathematical Institute of the Serbian Academy of Sciences and ArtsBelgradeSerbia
  3. 3.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia
  4. 4.Cardiff UniversitySchool of Computer ScienceCardiffUK

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