Measuring Linearity of Closed Curves and Connected Compound Curves

  • Paul L. Rosin
  • Jovanka Pantović
  • Joviša Žunić
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7726)


In this paper we define a new linearity measure for closed curves. We start with simple closed curves which represent the boundaries of bounded planar regions. It turns out that the method can be extended to closed curves which self-intersect and also to certain configurations consisting of several curves, including open curve segments. In all cases, the measured linearities range over the interval (0,1], and do not change under translation, rotation and scaling transformations of the considered curve. In addition, the highest possible linearity (which is 1) is reached if and only if the measured curve consists of two overlapping (i.e. coincident) straight line segments. The new linearity measure is theoretically well founded and all related statements are supported with rigorous mathematical proofs.


Closed Curve Linearity Measure Shape Descriptor Straight Line Segment Closed Curf 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Paul L. Rosin
    • 1
  • Jovanka Pantović
    • 2
  • Joviša Žunić
    • 3
  1. 1.School of Computer ScienceCardiff UniversityCardiffUK
  2. 2.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia
  3. 3.Computer ScienceUniversity of ExeterExeterUK

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