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Measuring linearity of connected configurations of a finite number of 2D and 3D curves

Rosin, Paul L., Pantovic, Jovanka and Zunic, Jovisa 2015. Measuring linearity of connected configurations of a finite number of 2D and 3D curves. Journal of Mathematical Imaging and Vision 53 (1) , pp. 1-11. 10.1007/s10851-014-0542-z

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Abstract

We define a new linearity measure for a wide class of objects consisting of a set of of curves, in both 2D and 3D . After initially observing closed curves, which can be represented in a parametric form, we extended the method to connected compound curves—i.e. to connected configurations of a number of curves representable in a parametric form. 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. We prove that the linearity is equal to 1 if and only if the measured curve consists of two straight line overlapping segments. The new linearity measure is theoretically well founded and all related statements are supported with rigorous mathematical proofs. The behavior and applicability of the new linearity measure are explained and illustrated by a number of experiments.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > Q Science (General)
Additional Information: Published online 21 October 2014
Publisher: Springer
ISSN: 0924-9907
Date of First Compliant Deposit: 30 March 2016
Last Modified: 12 Mar 2019 15:10
URI: http://orca.cf.ac.uk/id/eprint/69210

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