Measuring linearity of open planar curve segments

Žunić, J. and Rosin, Paul L. ORCID: https://orcid.org/0000-0002-4965-3884 2011. Measuring linearity of open planar curve segments. Image and Vision Computing 29 (12) , pp. 873-879. 10.1016/j.imavis.2011.10.002

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Abstract

In this paper we define a new linearity measure for open planar curve segments. We start with the integral of the squared distances between all the pairs of points belonging to the measured curve segment, and show that, for curves of a fixed length, such an integral reaches its maximum for straight line segments. We exploit this nice property to define a new linearity measure for open curve segments. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured open line is a straight line segment. The new linearity measure is invariant with respect to translations, rotations and scaling transformations. Furthermore, it can be efficiently and simply computed using line moments. Several experimental results are provided in order to illustrate the behaviour of the new measure.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	Shape; Curves; Linearity measure; Image processing
Additional Information:	Pdf uploaded in accordance with the publisher’s policy at http://www.sherpa.ac.uk/romeo/issn/0262-8856/ (accessed 30/07/2014)
Publisher:	Elsevier
ISSN:	0262-8856
Date of First Compliant Deposit:	30 March 2016
Last Modified:	07 Nov 2023 02:52
URI:	https://orca.cardiff.ac.uk/id/eprint/27588

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