Measuring linearity of curves in 2D and 3D

Rosin, Paul L. ORCID: https://orcid.org/0000-0002-4965-3884, Pantovic, Jovanka and Zunic, Jovisa 2016. Measuring linearity of curves in 2D and 3D. Pattern Recognition 49 , pp. 65-78. 10.1016/j.patcog.2015.07.011

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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.

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
Publisher:	Elsevier
ISSN:	0031-3203
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	22 July 2015
Last Modified:	07 Nov 2023 04:56
URI:	https://orca.cardiff.ac.uk/id/eprint/78356

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