Authors: Rosin, Paul
Pantović, Jovanka
Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Measuring linearity of curves in 2D and 3D
Journal: Pattern Recognition
Volume: 49
First page: 65
Last page: 78
Issue Date: 1-Jan-2016
Rank: M21a
ISSN: 0031-3203
DOI: 10.1016/j.patcog.2015.07.011
Abstract: 
In this paper we define a new linearity measure for open curve segments in 2D and 3D. The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0,1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application. Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure.
Keywords: Curves | Image processing | Linearity measure | Shape
Publisher: Elsevier
Project: Representations of logical structures and formal languages and their application in computing 
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 

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