Authors: Žunić, Joviša 
Pantović, Jovanka
Rosin, Paul
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Measuring linearity of planar curves
Journal: Pattern Recognition Applications and Methods
Series/Report no.: Advances in Intelligent Systems and Computing
Issue Date: 1-Jan-2015
Rank: M10
ISBN: 978-3-319-12609-8
ISSN: 2194-5357
DOI: 10.1007/978-3-319-12610-4_16
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.
Keywords: Curves | Image processing | Linearity measure | Shape | Shape descriptors
Publisher: Springer Link
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 

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