Authors: Rosin, Paul
Pantović, Jovanka
Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Measuring Linearity of Connected Configurations of a Finite Number of 2D and 3D Curves
Journal: Journal of Mathematical Imaging and Vision
Volume: 53
Issue: 1
First page: 1
Last page: 11
Issue Date: 3-Sep-2015
Rank: M21a
ISSN: 0924-9907
DOI: 10.1007/s10851-014-0542-z
We define a new linearity measure for a wide class of objects consisting of a set of of curves, in both $$2D$$2D and $$3D$$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 $$(0,1],$$(0,1], and do not change under translation, rotation and scaling transformations of the considered curve. We prove that the linearity is equal to $$1$$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.
Keywords: 2D Curves | 3D Curves | Compound curves | Image processing | Linearity measure | Shape | Shape descriptors
Publisher: Springer Link
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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